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.007 825 2.014 102 3.016 049 3.016 029 4.002 603 12 (by definition) 16.006 102 15.994 915 19.992 440 21.991 385 21.994 436 22.989 769 23.985 042 27.976 927 29.973 770 29.978 314 38.963 707 39.963 998 39.962 591 55.934 938 57.933 276 59.933 817 59.930 786 86.920 711 91.926 156 93.906 315 tellurium-112 tellurium-139 cerium-140 cesium-140 barium-141 neodymium-144 lanthanum-146 lead-204 lead-208 polonium-208 lead-210 polonium-212 polonium-214 radon-222 radium-226 thorium-230 thorium-234 protactinium-234 uranium-235 uranium-238 Te Te Ce Cs Ba Nd La Pb Pb Po Pb Po Po Rn Ra Th Th Pa U U 111.917 010 138.934 700 139.905 439 139.917 282 140.914 412 143.910 087 145.925 791 203.973 044 207.976 652 207.981 246 209.984 189 211.988 868 213.995 201 222.017 578 226.025 410 230.033 134 234.043 601 234.043 308 235.043 930 238.050 788 Note: Measurements of the atomic mass of most stable isotopes are accurate to at least a millionth of an atomic mass unit. However, the masses of highly unstable isotopes are more difficult to measure. For such isotopes, measurement errors can be large enough that the last one or two digits listed for their masses are not known for certain. Appendix Student References 881 20-PearsonPhys-Glossary 7/25/08 7:39 AM Page 882 GLOSSARY Note: The number in parentheses at the end of each definition indicates the page number in this book where the term first appears. A acceleration vector quantity representing the change in velocity (magnitude or direction) per unit time; non-uniform motion (23) acceleration due to gravity constant acceleration of an object falling near Earth’s surface (54
) activity (decay rate) number of nuclei in a sample that decay within a given time (812) alpha radiation emission of a helium nucleus; symbol is (797) altitude elevation of the ground above sea level (221) flow of 1 C of charge past ampere a point in a conductor in 1 s (602) amplitude of oscillation maximum displacement of a body from its equilibrium position during oscillatory motion (355) angle of diffraction angle formed between the perpendicular bisector and the straight line to a nodal or antinodal point on the interference pattern (689) angle of incidence angle formed between the incident ray and the normal line (654) angle of reflection angle formed between the reflected ray and the normal line (654) angle of refraction angle formed between the normal line and the refracted ray (666) annihilate energy (836) convert entirely into form of matter that antimatter has a key property, such as charge, opposite to that of ordinary matter (804) antinode point of interaction between waves on a spring or other medium at which only constructive interference occurs; in a standing wave, antinodes occur at intervals ; in an interference pattern, of 1 2 antinodes occur at path difference intervals of whole wavelengths (417) 882 Glossary fundamental armature (rotor) component of a simple DC electric motor consisting of a rotating loop of conducting wire on a shaft (608) artificial satellite artificially created object intended to orbit Earth or other celestial body to perform a variety of tasks; includes weather, communication, observation, science, broadcast, navigation, and military satellites (284) at rest not moving; stationary (13) atomic mass number number of nucleons in the nucleus, Z N; symbol is A (790) 1 of exactly atomic mass unit 1 2 the mass of the carbon-12 atom; symbol is u, where 1 u 1.660 539 1027 kg (791) atomic number number of protons in a nucleus; symbol is Z (790) axis of rotation imaginary line that passes through the centre of rotation perpendicular to circular motion (242) shaft on which a wheel axle rotates (242) B ballistic pendulum type of pendulum used to determine the speed of bullets before electronic timing devices were invented (483) baryon hadron with half-integer spin (842) becquerel unit of activity equal to 1 decay per second; unit is Bq (812) beta-negative decay nuclear decay involving emission of
an electron; symbol is (802) beta-positive decay nuclear decay involving emission of a positron; symbol is (805) beta radiation emission of a highenergy electron; symbol is (797) binding energy net energy required to liberate all of the protons and neutrons in a nucleus (793) blackbody object that completely absorbs any light energy that falls on it (705) blackbody radiation curve of the intensity of light emitted versus wavelength for an object of a given temperature (705) graph Bohr radius orbit in a hydrogen atom (774) radius of the smallest boson particle with integer spin (842) bright fringe (antinodal line) of constructive interference (686) region bubble chamber device that uses trails of bubbles in a superheated liquid to show the paths of charged particles (831) C capacitor two conductors, holding equal amounts of opposite charges, placed near one another without touching (642) cathode ray free electrons emitted by a negative electrode (754) central maximum line of antinodes along the perpendicular bisector of the line joining the point sources (426) centre of curvature (C) point in space representing the centre of the sphere from which a curved mirror was cut (657) centre of mass point where the total mass of an object can be assumed to be concentrated (492) centripetal acceleration acceleration acting toward the centre of a circle (244) force acting centripetal force toward the centre of a circle causing an object to move in a circular path; centre-seeking acceleration (244) charge migration movement of electrons in a neutral object where one side of the object becomes positive and the other side becomes negative (520) charge shift movement of electrons in an atom where one side of an atom becomes positive and the other side becomes negative (521) charging by induction process of polarizing an object by induction while grounding it (521) closed pipe (closed tube) pipe closed at one end; the longest wavelength that can resonate in a closed pipe is four times the length of the pipe (419) closed-pipe (closed-tube) resonance if an antinode occurs at 20-PearsonPhys-Glossary 7/25/08 7:39 AM Page 883 the open end of a pipe, a point of resonance (resulting from constructive interference) occurs at the open end of the pipe, and the sound appears to be amplified (419) cloud chamber device that uses trails of droplets of condensed vapour to show the paths of
charged particles (830) along the same straight collinear line, either in the same or in opposite directions (71) non-collinear not along the same straight line (80) collision interaction between two objects where each receives an impulse (469) elastic collision collision in which the total kinetic energy of Ekf ) a system is conserved (Eki (481) inelastic collision collision in which the total kinetic energy of a system is not conserved (Eki Ekf ) (483) colour quantum property related to the strong nuclear force (848) commutator fundamental component of a simple DC electric motor consisting of a mechanism for maintaining a properly polarized connection to the moving coil in a motor or generator (608) components perpendicular parts (Rx and Ry) into which a vector can be separated (77) Compton effect length of the scattered X-ray photon (721) change in wave- Compton scattering an X ray by an electron (721) scattering of conduction process of charging an object through the direct transfer of electrons when a charged object touches a neutral object (519) conductor material in which electrons in the outermost regions of the atom are free to move (513) forces that act conservative forces within systems but do not change their mechanical energy; includes gravity and elastic forces (314) non-conservative forces such as friction, and forces applied from outside a system, that cause the energy of the forces, system to change so that energy is not conserved (319) converging lens lens that refracts rays travelling parallel to the principal axis inward to intersect at the principal focus (677) converging mirror concave reflecting surface that causes parallel light rays to converge after being reflected (657) coulomb (C) SI unit for electric charge, equivalent to the charge on 6.25 1018 electrons or protons (517) Coulomb’s law magnitude of the force of electrostatic attraction or repulsion (⏐F e⏐) is directly proportional to the product of the two e⏐ q1q2) and charges q1 and q2 (⏐F inversely proportional to the square of the distance between their centres r (529) crest region where the medium rises above the equilibrium position (394) for any two media, critical angle the size of the incident angle for which the angle of refraction is 90° (672) current quantity of charge that flows through a wire in a given unit of time (602) cycle one
complete back-and-forth motion or oscillation (249) cyclotron particle accelerator Particle accelerator in which the magnetic field perpendicular to the paths of the charged particles makes them follow circular paths within two hollow semicircular electrodes. An alternating voltage accelerates the charged particles each time they cross the gap between the two electrodes. The radius of each particle’s path increases with its speed, so the accelerated particles spiral toward the outer wall of the cyclotron. (841) D dark fringe (nodal line) destructive interference (686) region of daughter element duced by a decay process (799) element pro- decay constant probability of a nucleus decaying in a given time; symbol is (811) diffraction change in shape and direction of a wave front as a result of encountering a small opening or aperture in a barrier, or a corner (685) sheet of glass diffraction grating or plastic etched with a large number of parallel lines; when light is incident on the grating, each line or slit acts as one individual light source (692) diffuse (irregular) reflection behaviour describing parallel incident rays scattered in different directions when reflected from an irregular surface (653) dispersion separation of white light into its components (675) displacement straight line between initial and final positions; includes magnitude and direction (7) length of the path taken distance to move from one position to another (7) lens that refracts diverging lens rays travelling parallel to the principal axis outward to appear as though they have originated at a virtual principal focus (677) convex reflecting diverging mirror surface that causes parallel light rays to spread out after being reflected (657) diverging ray ray that spreads out as it moves away from the origin (397) domain region of a material in which the magnetic fields of most of the atoms are aligned (589) Doppler effect apparent change in frequency and wavelength of a wave that is perceived by an observer moving relative to the source of the wave (429) drift tube particle accelerator particle accelerator in which alternating voltage accelerates charged particles through a series of electrodes shaped like open tubes; particles are always attracted to the next tube in the line (841) Glossary 883 20-PearsonPhys-Glossary 7/25/08 7:39 AM Page 884 dynamics branch of mechanics dealing with the cause of motion (126) E eccentricity degree to which an ellipse is elongated; number between 0 and 1, with 0 being a perfect circle and 1 being
a parabola (269) efficiency ratio of the energy output to the energy input of any system (324) elastic potential energy energy resulting from an object being altered from its standard shape, without permanent deformation (300) electric field lines lines drawn to represent the electric field; density of the lines represents the magnitude of the electric field (554) electric poten- electric potential tial energy stored per unit charge at a given point in an electric field; symbol is V (564) electric potential difference change in electric potential experienced by a charge moving between two points in an electric field (565) electric potential energy energy stored in a system of two charges a certain distance apart; change in electric potential energy equals work done to move a small charge (Ep electromagnet magnet having its magnetic field produced by electric current flowing through a coil of wire (588) W) (561) electromagnetic radiation (EMR) radiant energy in the form of a wave produced by the acceleration of electrons or other charged particles; does not require a material medium; can travel through a vacuum (636) electron volt change in energy of an electron when it moves through a potential difference of 1 V; unit is eV (564) electrostatics charges at rest (513) study of electric fundamental electroweak force force that combines the electromagnetic force and the weak nuclear force (848) 884 Glossary elementary unit of charge on a proton; symbol is e (762) charge elongated circle; consists ellipse of two foci, a major, and a minor axis (269) energy ability to do work (292) energy level discrete and quantized amount of energy (773) equilibrium position rest position or position of a medium from which the amplitude of a wave can be measured (394) excited state higher than the ground state (775) any energy level F femto metric prefix meaning 1015 (790) fermion particle with half-integer spin (842) ferromagnetic having magnetic properties, like those of iron (589) field three-dimensional region of influence surrounding an object (200) electric field three-dimensional region of electrostatic influence surrounding a charged object (641) gravitational field region of influence surrounding any object that has mass (200) magnetic field three-dimensional region of magnetic influence surrounding a magnet, in which other magnets are affected by magnetic forces (584) first order maximum line of antinodes resulting from a onewavelength phase shift (427) fission reaction in which a nucleus with A
120 splits into smaller nuclei that have greater binding energy per nucleon (818) focal length (f) distance from the vertex to the focal point, measured along the principal axis; related to the radius of curvature by f r/2 (657) force quantity measuring a push or a pull on an object; measured in newtons (127) action force object A on object B (160) force initiated by action-at-a-distance force force that acts even if the objects involved are not touching (200) force exerted applied force directly on an object by a app (130) person; symbol is F gravitational force attractive force between any two objects due to their masses; symbol is F g (196) net force vector sum of all the forces acting simultaneously on net (131) an object; symbol is F force on an object normal force that is perpendicular to a common contact surface; N (130) symbol is F reaction force object B on object A (160) force exerted by force acting restoring force opposite to the displacement to move an object back to its equilibrium position (353) strong nuclear force binds together the protons and neutrons in a nucleus (793) force that weak nuclear force tal force that acts on electrons and neutrinos (804) fundamen- forced frequency frequency at which an external force is applied to an oscillating object (382) Fraunhofer line dark line in the spectrum of the Sun (773) free-body diagram vector diagram of an object in isolation showing all the forces acting on it (129) situation in which the only free fall force acting on an object that has mass is the gravitational force (226) frequency number of cycles per second measured in hertz (Hz) (249) friction force that opposes either the motion of an object or the direction the object would be moving in if there were no friction; symbol is f (169) F fundamental forces basic forces of nature that physicists think underlie all interactions in the universe (194) fundamental frequency lowest frequency produced by a particular instrument; corresponds to the standing wave having a single antinode, with a node at each end of the string (422) fusion reaction in which two lowmass nuclei combine to form a single nucleus with A 60; the resulting nucleus is more tightly bound (818) 20-PearsonPhys-Glossary 7/25/08 7:39 AM Page 885 G gamma decay emission of a highenergy photon by a nucleus; symbol is (806) gamma radiation emission
of a high-energy photon; symbol is (797) generator effect (electromagnetic induction) production of electricity by magnetism (611) gluon mediating particle for the strong nuclear force (838) grand unified theory quantum theory unifying the electromagnetic, strong nuclear, and weak nuclear forces (849) sensitive instrument gravimeter used to detect small variations in the magnitude of the gravitational field strength on Earth’s surface (222) gravitational field strength gravitational force per unit mass at a specific location (201) gravitational mass mass measurement based on comparing the known weight of one object to the unknown weight of another object (199) gravitational potential energy energy of an object due to its position relative to the surface of Earth (295) graviton hypothetical mediating particle for the gravitational force (838) gravity assist use of the gravitational force exerted by celestial bodies to reduce interplanetary travel times (214) gray dose of ionizing radiation that delivers 1 J of energy to each kilogram of material absorbing the radiation; unit is Gy (809) ground state energy level (774) lowest possible grounding process of transferring charge to and from Earth (521) H hadron subatomic particle that interacts via the strong nuclear force (842) half-life time it takes for half of the radioactive nuclei in a sample to decay (812) Heisenberg’s uncertainty principle it is impossible to know both the position and momentum of a particle with unlimited precision at the same time (735) high tide highest level of ocean water that occurs near Earth’s coastlines (211) Hooke’s Law relationship where the stretch produced by a force applied to a spring is proportional to the magnitude of the force (299) horsepower (hp) unit used to identify the power output of motors, mainly in the automotive industry (324) Huygens’ Principle model of wave theory, which predicted the motion of a wave front as being many small point sources propagating outward in a concentric circle at the same speed as the wave itself (684) I image attitude orientation characteristic of an image, whether erect or inverted (656) image position where the image forms relative to the surface of the mirror (656) image type distinction between real and virtual images (656) real image image from which light rays come; can be formed on a diffusely reflecting surface or screen (654) virtual image image from which light rays appear to come; cannot be formed on a non-reflective surface or
screen (654) impulse product of the net force on an object and the time interval during an interaction. Impulse causes a change in the momentum of the object. (457) incandescent (704) glowing with heat induction movement of charge caused by an external charged object (520) inertia property of an object that resists acceleration (138) inertial mass mass measurement based on the ratio of a known net force on an object to the acceleration of the object (148) insulator material in which the electrons are tightly bound to the nucleus and are not free to move within the substance (513) interference (or two waves) crossing within a effect of two pulses medium; the medium takes on a shape that is different from the shape of either pulse alone (411) constructive interference overlap of pulses to create a pulse of greater amplitude (412) destructive interference overlap of pulses to create a pulse of lesser amplitude (412) interference fringes ence pattern of light and dark bands (686) fixed interfer- interference pattern pattern of maxima and minima resulting from the interaction of waves, as crests and troughs overlap while the waves move through each other (425) ionization energy energy required to remove an electron from an atom (775) atoms that have the same isotopes number of protons, but different numbers of neutrons (791) K kinematics branch of physics that describes motion (6) kinetic energy energy due to the motion of an object; symbol is Ek (302) kinetic friction force exerted on an object in motion that opposes the motion of the object as it slides on another object; symbol is F fkinetic (176) coefficient of kinetic friction proportionality constant relating F fkinetic and FN (183) L latitude south of the equator (221) angular distance north or law of conservation of charge net charge of an isolated system is conserved (517) law of conservation of energy within an isolated system, energy may be transferred from one object to another or transformed from one form to another, but it cannot be increased nor decreased (312) law of conservation of momentum momentum of an isolated system is constant (473) law of magnetism like magnetic ends repel and unlike ends attract each other Glossary 885 20-PearsonPhys-Glossary 7/25/08 7:39 AM Page 886 law of reflection angle of reflection is equal to the angle of incidence and is in the same plane (654) Lenz’s law direction of a magnetically induced current is such
as to oppose the cause of the current (618) lepton subatomic particle that does not interact via the strong nuclear force (842) lowest level of ocean low tide water that occurs near Earth’s coastlines (211) M magnification relationship of the size of the image to the size of the object (656) mass defect difference between the sum of the masses of the separate nucleons and the mass of the nucleus; symbol is m (794) maximum (line of antinodes) of points linking antinodes that occur as the result of constructive interference between waves (426) line Maxwell’s Equations series of equations that summarized the relationships between electricity and magnetism, and predicted the existence of electromagnetic waves and their propagation through space (642) mechanical energy sum of potential and kinetic energies; symbol is Em (306) increase in mechanical resonance amplitude of oscillation of a system as a result of a periodic force whose frequency is equal or very close to the resonant frequency of the system (382) mechanics statics, and dynamics (306) study of kinematics, medium material, for example, air or water through which waves travel; the medium does not travel with the wave (394) meson hadron with integer spin (842) minimum (nodal line) points linking nodes that occur as the result of destructive interference between waves (426) line of mirror equation equation relating the focal length of a curved mirror to the image and object distances (662) 886 Glossary momentum product of the mass of an object and its velocity (449) sum of momentum (of a system) the momenta of all the objects in the system (470) motor effect force deflecting force acting on a charged particle moving in a magnetic field (593) muon unstable subatomic particle having many of the properties of an electron but a mass 207 times greater (842) N natural satellite naturally formed body that revolves around a planet (moon) (273) navigator method method commonly used to show direction for vector quantities in two dimensions; uses compass bearings north [N], south [S], east [E], and west [W] to identify vector directions (78) net charge charges in the system (517) sum of all electric neutrino extremely small neutral subatomic particle; symbol is v (804) neutron neutral particle found in nuclei (790) neutron number number of neutrons in the nucleus; symbol is N (790) Newton’s first law of motion an object will continue
either being at rest or moving at constant velocity unless acted upon by an external non-zero net force (139) Newton’s law of universal gravitation Any two objects, A and B, in the universe exert gravitational forces of equal magnitude but opposite direction on each other. The forces are directed along the line joining the centres of both objects. (204) Newton’s second law of motion when an external non-zero net force acts on an object, the object accelerates in the direction of the net force; the magnitude of the acceleration is directly proportional to the magnitude of the net force and inversely proportional to the mass of the object (148) Newton’s third law of motion if object A exerts a force on object B, then B exerts a force on A that is equal in magnitude and opposite in direction (161) node (nodal point) point on a spring or other medium at which only destructive interference occurs; in a standing wave, a point that never vibrates between maximum positive amplitude and maximum negative amplitude; in a standing wave, nodes occur at intervals of ; in an interference pattern, 1 2 nodes occur at path difference (417) intervals of 1 2 normal line perpendicular to the reflecting surface (654) nucleon proton or neutron (790) nucleosynthesis elements by the fusion of lighter elements (823) imaginary line drawn formation of O open pipe (open tube) pipe opened at both ends; the longest wavelength that can resonate in an open pipe is twice the length of the pipe (424) optical fibre central core of glass with a refractive index of approximately 1.5, surrounded by a cladding material of a slightly lower refractive index (671) orbital probability distribution of an electron in an atom (783) orbital period time required for a planet to make one full orbit; may be measured in Earth days (271) orbital perturbation irregularity or disturbance in the predicted orbit of a planet (282) orbital radius distance between the centre of the ellipse and the planet; average orbital radius corresponds to the semi-major axis (269) origin reference point (6) oscillation repetitive back-andforth motion (344) oscillatory motion motion in which the period of each cycle is constant (344) overtone any frequency of vibration of a string that may exist simultaneously with the fundamental frequency (423) P parent element original element in a decay process (799) 20-PearsonPhys-Glossary 7/25/08 7:39 AM
Page 887 particle discrete unit of matter having mass, momentum, and the ability to carry an electric charge (639) alpha particle two neutrons bound together to form a stable particle (497) two protons and electron emitted beta particle by a nucleus; symbol is (802) fundamental particle particle that cannot be divided into smaller particles; an elementary particle (836) mediating particle virtual particle that carries one of the fundamental forces (837) strange particle particle that interacts primarily via the strong nuclear force yet decays only via the weak nuclear force (845) virtual particle particle that exists for such a short time that it is not detectable (837) particle model describes EMR as a stream of tiny particles radiating outward from a source (639) path length distance between a point source and a chosen point in space (688) difference in path length difference between two path lengths, each measured from a different origin and extending to a common point in space (688) period time required for an object to make one complete oscillation (cycle); measured in s/cycle (249) phase shift result of waves from one source having to travel farther to reach a particular point in the interference pattern than waves from another source (426) emission of photoelectric effect electrons when a metal is illuminated by short wavelengths of light (712) photoelectron electron emitted from a metal because of the photoelectric effect (712) photon (from the Greek word meaning “light”) quantum of light; discrete packet of energy associated with an electromagnetic field (640) pion unstable subatomic particle with a mass roughly 270 times that of an electron (842) Planck’s formula light comes in quanta of energy that can be calculated using the equation E nhf (705) plane mirror ing surface (654) smooth, flat, reflect- light resultplane polarized light ing from polarization, in which only one plane of the electric field is allowed to pass through a filter (696) close to the principal axis converge, or appear to diverge from, after being reflected (657) principal quantum number quantum number that determines the size and energy of an orbit (774) planetary model that has electrons orbiting a nucleus (768) atomic model plasma highly ionized gas containing nearly equal numbers of free electrons and positive ions (522) point of incidence point at which the incident ray contacts a polished, reflecting surface and is reflected from the surface as the reflected ray (652) point source single point of disturbance that generates a circular
wave (395) polar coordinates method method commonly used to show direction for vector quantities in two dimensions; the positive x-axis is at 0° and angles are measured by moving counterclockwise about the origin, or pole (78) polarization production of a state in which the plane of the electric field for each electromagnetic wave occurs only in one direction (696) polarizing filter filter that allows only one plane of the electric field to pass through it; plane polarized EMR emerges (696) position straight-line distance between the origin and an object’s location; includes magnitude and direction (6) positron antielectron; positively charged particle with its other properties the same as those of an (804) electron; symbol is e or 0 1 potential energy energy that is stored and held in readiness; includes gravitational and elastic potential energies; symbol is Ep rate of doing work (324) power primary cosmic rays high-energy particles that flow from space into Earth’s atmosphere (841) imaginary line principal axis (PA) drawn through the vertex, perpendicular to the surface of the curved mirror at this point (657) principal focal point (F) point where light rays parallel to and principle of superposition displacement of the combined pulse at each point of interference is the sum of the displacements of the individual pulses (412) projectile object released or thrown into the air (54) projectile motion motion in a vertical plane (54) proton positively charged particle found in all nuclei (790) proton–proton chain fusion process in which four hydrogen nuclei combine to form a helium nucleus (821) pulse disturbance of short duration in a medium; usually seen as the crest or trough of a wave (401) compression pulse where the coils of a spring are more tightly compressed (404) region rarefaction pulse the coils of a spring are more widely spaced (404) region where transverse pulse pulse in which the coils of the spring move at right angles to the direction of the pulse’s motion (401) Q quanta discrete units of energy (638) quantized limited to whole multiples of a basic amount (quantum) (705) quantum smallest amount or “bundle” of energy that a wavelength of light can possess (pl. quanta) (705) quantum chromodynamics quantum field theory that describes the strong nuclear force in terms of quantum colour (848) quantum electrodynamics quantum field theory dealing with the interactions of electromagnetic fields, charged particles, and photons (
838) quantum field theory field theory developed using both quantum mechanics and relativity theory (837) Glossary 887 20-PearsonPhys-Glossary 7/25/08 7:39 AM Page 888 quantum indeterminacy probability of finding a particle at a particular location in a double-slit interference pattern (740) quantum model light and all other EMR are discrete bundles of energy, each of which has both particle and wave characteristics (640) quark any of the group of fundamental particles in hadrons (845) R radioactive decay series process of successive decays in which a radioactive nucleus decays into a daughter nucleus that is itself radioactive, and the daughter nucleus decays into another unstable nucleus until a stable nucleus is created (807) radioisotope radioactive (808) isotope that is radius of curvature (r) distance from the centre of curvature to the mirror surface (657) range distance a projectile travels horizontally over level ground (105) ray line that indicates only the direction of motion of the wave front at any point where the ray and the wave front intersect (397) ray diagram diagram showing the result of a light ray interacting with a surface (653) recomposition (of the spectrum) production of white light by a combination of light of all colours of the spectrum (674) rectilinear propagation movement of light in straight lines through a uniform medium (653) reference point point from which distances are measured (297) refracted ray path of a light ray after it has changed direction at an interface, due to a change in its speed (664) refraction change in the direction of a light wave due to a change in its speed as it passes from one medium to another (666) refractive index ratio comparing the speed of light in a vacuum to the measured speed of light in the medium (666) relative biological effectiveness (RBE) factor indicating how much arbitrarily chosen 888 Glossary a particular type of radiation affects the human body (809) any light ray passing through the boundary between two media. (667) relative motion motion measured with respect to an observer (91) solenoid electromagnet that operates a mechanical device (589) resonance increase in the amplitude of a wave due to a transfer of energy in phase with the natural frequency of the wave (418) resonant frequencies natural frequencies of vibration of an object that will produce a standing wave pattern; at a resonant frequency, energy added is in phase with existing oscillations (418) sum
of a series of resultant vector vectors; drawn from the tail of the first vector to the tip of the last vector (71) revolution one complete cycle for an object moving in a circular path (249) rpm revolutions per minute; imperial unit used to measure frequency (249) S scalar quantity measurement that has magnitude only (6) secondary cosmic rays particles created by collisions between primary cosmic rays and atoms in the atmosphere (841) shower of semiconductor material that lies in the middle, between a good conductor and a good insulator; because of its nature, a semiconductor is a good conductor in certain situations, and a good insulator in other situations (514) absorbed dose of ionizing sievert radiation that has the same effect on a person as 1 Gy of photon radiation, such as X rays or gamma rays; absorbed dose in sieverts is equal to the dose in grays multiplied by the relative biological effectiveness (RBE); unit is Sv (809) simple harmonic motion (SHM) oscillatory motion where the restoring force is proportional to the displacement of the mass (355) simple harmonic oscillator object that moves with simple harmonic motion (355) Snell’s Law For any angle of incidence greater than zero, the ratio sin r is a constant for i/sin sound barrier term applied to the increase in aerodynamic resistance as an aircraft approaches the speed of sound (433) source charge duces an electric field (546) charge that pro- spectrometer device for measuring the wavelengths of light in a spectrum (773) spectroscopy study of the light emitted and absorbed by different materials (771) spectrum bands of colours making up white light; in order: red, orange, yellow, green, blue, and violet (675) absorption line spectrum pattern of dark lines produced when light passes through a gas at low pressure (772) electromagnetic spectrum all types of EMR considered in terms of frequency, wavelength, or energy (637) emission line spectrum pattern of bright lines produced by a hot gas at low pressure (772) specular (regular) reflection behaviour describing parallel incident rays reflected from a flat, smooth, reflecting surface as parallel reflected rays (653) spin quantum property resembling rotational angular momentum (842) constant of pro- spring constant portionality k which appears in Hooke’s Law for springs; represents the slope of the line and is measured in units of force per unit length; amount of stiffness of a spring (299) standard model describing the nature of matter and the
maximum angle of 90° (672) trajectory parabolic path or motion of a projectile (103) transmute element (806) trough region where the medium is lower than the equilibrium position (394) tuning (a musical instrument) changing the tension in the string of a musical instrument (424) change into a different U uniform circular motion motion in a circular path at a constant speed (242) uniform motion constant velocity (motion or rest) (13) non-uniform motion acceleration (23) uniformly accelerated motion constant change in velocity per unit time (25) universal gravitational constant constant in Newton’s law of universal gravitation that is equal to 6.67 1011 N•m2/kg2; symbol is G (204) universal wave equation relationship between the speed, frequency, and wavelength of a wave: v f (408) V Van de Graaff particle accelerator particle accelerator in which a moving belt transfers charge to a hollow, conductive sphere, building up a large potential difference that propels ions through an accelerator chamber (841) vector quantity measurement that has both magnitude and direction (6) ground velocity velocity relative to an observer on the ground (92) instantaneous velocity moment-to-moment measure of an object’s velocity (24) wind velocity velocity of the wind relative to the ground (92) vertex (V) curved mirror surface (657) geometric centre of the W wave disturbance that moves outward from its point of origin, transferring energy through a medium by means of vibrations (394) bow wave V-shaped wave produced as a boat moves through water or an airplane moves through the atmosphere (433) electromagnetic wave periodic variation in perpendicular electric and magnetic fields, propagating at right angles to both fields (643) incident wave wave front moving out from the point of origin toward a barrier (395) longitudinal wave wave with the motion of the medium being parallel to the motion of the wave (401) reflected wave wave front moving away from a barrier (395) strong compression shock wave wave produced as an aircraft exceeds the speed of sound (433) condition in a standing wave spring or other medium in which a wave seems to oscillate around stationary points called nodes; wavelength of a standing wave is the distance between alternate nodes or alternate antinodes (417) transverse wave wave with the motion of the medium being perpendicular to the motion of the wave (401) wave amplitude distance from the equilibrium position to the top of a crest or the bottom of a trough (395) velocity rate of change in position;
includes magnitude (speed) and direction (12) imaginary line that wave front joins all points reached by the wave at the same instant (395) Glossary 889 20-PearsonPhys-Glossary 7/25/08 7:39 AM Page 890 waves out of phase occurs when a crest from one wave occupies the same point in the medium as a trough from a second wave; produces destructive interference (416) gravitational force exerted weight on an object by a celestial body; symbol is F g (198) apparent weight negative of the normal force acting on an object; symbol is w (224) true weight acting on an object that has mass (222) gravitational force true weightlessness which w 0 for an object and F g 0 on the object (228) situation in work measure of the amount of energy transferred when a force acts over a given displacement; calculated as the product of the magnitude of applied force and the displacement of the object in the direction of the force (293) work–energy theorem work done on a system is equal to the sum of the changes in the potential and kinetic energies of the system (307) work function minimum energy that a photon can have to cause photoemission from a metal; specific for every metal; symbol is W (713) wave model describes EMR as a stream of transverse waves radiating outward from a source (639) wave–particle duality light has both wave-like and particle-like properties (726) wave train series of waves forming a continuous series of crests and troughs (395) wavelength distance between two points on a wave that have identical status; usually measured from crest to crest or from trough to trough (395) waves in phase occurs when crests or troughs from two waves occupy the same point in the medium; produces constructive interference (395) 890 Glossary 21-PearsonPhys-AnswerKey 7/29/08 1:40 PM Page 891 NUMERICAL ANSWERS For some questions, answers may vary slightly depending on the method or data chosen for the solution. page 10, 1.1 Check and Reflect page 63, 1.6 Check and Reflect 4. (e) 13.0 m [right] 5. 45.0 km [W] 6. Distance 11.0 m; Displacement 5.0 m [right] 0.50 m [right] 0.75 m [left] groom best man maid of honour 1.25 m [right] flower girl 1.50
m [left] 7. d d d d page 20, 1.2 Check and Reflect 3. 72.3 m 4. 1.5 m 5. 1.61 m/s2 [down] 6. 2.8 m 7. (1) 26 m/s [down] (2) 33 m 8. 0.376 s 9. 47.9 m 10. 1.6 s 11. 6.22 s 12. 10.6 m 3. (i) D (ii) C (iii) A (iv) B 13. 1.4 s 4. 10 m; A is ahead 5. 7 km [W] 8. 2.5 m right 9. Insect B is ahead by 1.2 m. 11. Distance 26 m; Time 13 s 12. Time 20 s; Displacement 45 m [N] (2) 31 s 13. (1) 22 s (3) 14 s page 30, 1.3 Check and Reflect 1. (a) 5.6 m/s2 [forward] (b) 2.8 m/s2 [forward] (c) 0.30 m/s2 [forward] (iii) C (ii) B 3. (i) A 4. Time (s) Velocity (m/s [forward]) (iv) D 2.0 4.0 6.0 8.0 3.8 7.0 0.0 7.5 page 44, 1.4 Check and Reflect 7. 75 m [E] 8. 36 km [up] 13. 15 m/s2 [E] 15. Acceleration 1.25 m/s2 [W]; Time 8.00 s 16. (a) 81 km/h [N] 17. 0.33 m/s2 [right] page 53, 1.5 Check and Reflect 1. 20 cm [forward] 2. 75 m [right] 3. 59.9 m 4. 1.67 105 m/s2 [forward] 5. 11 s 6. 39.2 m 7. 0.41 m/s2 8. 0.24 m/s2 [forward] 9. 75.0 m/s2 [W] 10. 23.3 m/s2 11. 3.52 m/s2 [S] 12. 9.31 m/s2 13. 9.5 m 14. 0.064 m/s2 [N] 14
. 2.4 m 15. (a) 4.0 m/s2 [up] (b) 5.0 103 m (d) 7.0 103 m 16. 9.68 m/s [down] page 65, Chapter 1 Review 3. (a) 1.0 m/s [backward] (b) 2.0 m/min [right] (c) 1.7 m/s [forward] 4. 27.0 km [W] 5. 42 min 6. (1) 3.75 m/s (2) 1.25 m/s [right] (3) 25.0 m [right] 8. 2.8 s 9. 7.0 s 10. 0 m/s 11. 1.9 102 s 12. 1.5 m/s [W] 14. 60 m 15. 7.2 107 m/s2 16. 18 km 17. 34.5 km 18. 72 times faster 19. 1.1 102 km/h, 31 m/s 20. (1) 2.81 m/s2 [downhill] (2) 22.5 m/s [downhill] 21. (1) 1.3 m/s2 [N] (2) 10 m/s [N] 22. (1) 16.0 m/s [S] (2) 22.0 m/s [S] (3) 0.267 m/s2 [S] 23. 35 m/s 24. (1) 12 s 26. (1) 20 km [right] (2) 39 m/s (2) 0 m/s2 27. 9.03 s 28. 0.467 s 29. 0.298 m/s2 30. 24 km/h [E] 32. 11.2 m/s2 [W] 33. 6.8 s 34. 1.17 s 35. 12 m 36. 9.29 m 37. 1.32 s 38. (1) 15.2 m (2) 17.3 m/s 39. (1) 20 m/s (2) 2.0 s page 75, 2.1 Check and Reflect 3. 24 cm 4. 1.0 cm : 20 km 5. 2.1 103 km 6. (b) 100 yards [down field] (c) 1000 yards 7. 100 km [S], 150 km [S], and 200
km [S] 9. (1) 36.0 m (2) 8.0 m [down] page 90, 2.2 Check and Reflect 28 cm 48 cm; dx 4. dy 5. (a) Distance 11.5 km; Displacement 3.4 km [27° N of W] (b) Distance 522 m; Displacement 522 m [17° E of N] (c) Distance 2.95 km; Displacement 1.45 m [270°] 6. 2.0 km [45° S of E] 7. 178 m/s 8. 2.65 km [48° S of E] 9. Total displacement 2.8 km [49° N of W]; Average velocity 3.0 km/h [49° N of W] 10. (a) 27 m in both the x and y directions (b) 54 m 11. 10.6 m [293°] page 101, 2.3 Check and Reflect 5. (a) 88 s (b) 79 s; 47 m 6. (a) 233 km/h [N] (b) 297 km/h [N] (c) 267 km/h [83.1° N of W] 7. 7.2 102 s 8. 8.4 102 km/h [3° N of E] 9. Ground velocity 2.8 m/s [35° S of E]; Time 19 min 10. 6.3 102 km/h [3° S of W] 11. (a) 4.7 m/s [32° W of N] (b) 2.0 102 s page 112, 2.4 Check and Reflect 5. 2.0 m 6. Initial horizontal velocity component 22.1 m/s; Initial vertical velocity component 15.5 m/s; Up 12.2 m; Out 69.8 m 7. 7.21 m/s 8. 10.8 m/s Numerical Answers 891 21-PearsonPhys-AnswerKey 7/29/08 1:40 PM Page 892 9. (a) 10.0 s (c) 20.5 s (e) Horizontal component 68.8 m/s; Vertical component 103 m/s (b) 542 m (d) 1.41 km page 114, Chapter 2 Review 2. x component 41 m; y component 37 m 5.0 m [N] 140.
0 cm [E] 2.5 km [backward] 80.0 km [right] 3. 0 m/s 7. (a) d (b) d (c) d (d) d 8. 0 m/s 9. 3.9 102 km 10. Range 86.2 m; Maximum height 30.8 m 11. 2.23 102 m horizontally; 2.83 s 12. (a) 6.4 m/s [51° E of N] 28. 99 km/h [W] 29. 1.5 102 m 30. 1.2 m/s [210°]; 4.4 m/s [210°]; 6.7 m/s [210°] 31. 1.1 102 km/h [7° N of E] 32. 13.2 m/s2 33. 375 m [N] 35. 1.93 m 36. (a) 7 squares (b) 8.6 units [54°] 37. 1.6 m/s [N] 38. 320 m [51° S of E] 40. 5.98 m/s2 41. (a) 14.4 m/s [down] 42. (a) 347 m (b) 376 m (c) 82.6 m/s [down] 43. 13 m/s [30°] (b) 10.6 m 9. 1.2 m/s2 [uphill] 10. 16 m 11. 1.9 s page 192, Chapter 3 Review 1. 5.00 102 m/s2 [E] 3. 1850 N [W] 5. (a) 42 N [along rope connecting foot to pulley] 6. 1.2 103 N [forward] 3.7 106 N, R 7. L 8. 7.5 N [backward] 9. (a) 3.4 102 N 3.3 106 N (b) 1.4 103 N [forward] (c) 3.4 102 N [backward] 10. (a) F netA 36 N [W], F netB (b) (curler A) 0.71 m/s2 [W], (curler B) 0.26 m/s2 [E] 21 N [E] (b) 30 s page 136, 3.1 Check and Reflect 11. 0.38 13. (a) 29 m/s [down] (
b) 23 m 3. (b) 300 N [forward] (c) 7.50 m/s [away from cliff] (b) 3.5 m/s [N] 14. 6.5 m/s [76° up] 15. (a) 30° W of N (c) 1.4 102 s 16. 1.82 m 17. 39 s 18. 2.18 s (b) 180° 4. (a) 0° 5. 1.47 102 N [13°] 6. 42 N [153°] 7. F F 1.50 102 N [125°], 1.50 102 N [55°] T1 T2 page 139, 3.2 Concept Check 19. (a) 17° S of W (b) 95 km/h v 17 km/s [toward interstellar space] 20. [42.2°] 21. 5.0 m 22. 60.96 m 23. (a) 1.2 102 km/h 24. 2.92 s; Distance 59.9 m; Maximum height 10.5 m (b) east 25. [39.8°] 26. (a) 36 s (b) 1.5 km page 118, Unit I Review 3. (a) dx (b) vx 0 m; dy 15.0 m/s; vy 5.0 m 5.47 m/s 5. 9.8 km [30° S of E] 6. 2.70 m/s [W] 8. 3.03 s; Distance 78.0 m horizontally; Maximum height 11.3 m 13. 30 m/s 14. 32 km/h 16. (a) 30 m/s [90°] (b) 40 m/s [90°] 17. 12.1 km 18. 1.06 h 19. 5.7 m/s 20. 9.56 m/s2 21. 8.1 102 km/h [4° W of S] 22. 70.4 m/s2 23. 2.2 s 24. 58 m 25. (a) 51 s (b) 0.032 m/s2 26. 13.5 m 27. 63.4 m 892 Numerical Answers page 146, 3.3 Concept Check F app if F f F net 0 page 148, 3.3 Concept Check (a) a (b) a (c)
a 1 6 1 page 158, 3.3 Check and Reflect (b) 15 m/s2 [up] 5. (a) 26 kg 6. 0.11 m/s2 [horizontally] 7. (a) 75 N [97°] 8. 0.75 m/s2 [right] 9. (a) (4.0-kg block) 1.3 m/s2 (b) 37 m/s2 [97°] [toward pulley], (2.0-kg block) 1.3 m/s2 [down] (b) 17 N page 168, 3.4 Check and Reflect 7. 10 N, 10 N [toward spring scale] 8. (a) F X on Y F Y on X (b) F X on Y F Y on X 12 N [right], 12 N [left] 12 N [right], 12 N [left] page 178, 3.5 Concept Check 90° page 190, 3.5 Check and Reflect 4. 2 N [backward] 5. 0.40 6. 2 103 N [backward] 7. 24° 12. 0.423 13. (a) 9.8 102 N (b) (i) (60 kg) 2.0 m/s2 [down], (40 kg) 2.0 m/s2 [up] (ii) 4.7 102 N (c) 9.4 102 N 14. 7.3 102 kg 15. 2 103 kg 18. (a) 6.9 m/s2 [backward] (b) 1.2 s page 201, 4.1 Concept Check (a) 16g (c) g (d) g (b) 1 g 4 (d) 0 page 202, 4.1 Check and Reflect 9. (b) 9.8 N/kg (c) gBanff page 205, 4.2 Concept Check 1 6 1 (c) (b) 4Fg (a) 4Fg Fg page 215, 4.2 Check and Reflect 3. (a) 1 Fg (b) 1 Fg 2 4 (ii) 978 N 4. (a) (i) 162 N 5. (b) (Deimos) 1.9 1014 N, (Phobos) 5.3 1015 N 6. (a) 132 N [toward Earth’s centre] (b)
about 13.4 times greater in magnitude page 229, 4.3 Check and Reflect 5. 2.4 N/kg [toward Earth’s centre] 6. (b) (i) 1.6 N/kg (ii) 0.72 N/kg (iii) 0.40 N/kg (c) 10rMoon 7. 9.8 N/kg 8. 540 N [down] g) 4.9 102 N [down], 9. (b) (F (w) 2.9 103 N [down] 21-PearsonPhys-AnswerKey 7/29/08 1:40 PM Page 893 (c) 0 page 286, 5.3 Check and Reflect 10. (Figure 4.38) 2.45 m/s2 [up], (Figure 4.40) 1.23 m/s2 [down] page 231, Chapter 4 Review 2. (balance) 5.0 kg, (spring scale) 96 N 3. g Msource 4. 3.83 N/kg [toward Earth’s centre] 5. 1.4 s 7. (a) 222 N [toward centre of Mars] (b) 626 N [toward centre of Saturn] 8. 2.0 107 N 9. (a) 2.4 102 N (b) 7.1 102 N (c) 6.8 N 10. (a) 7.3 m/s2 [down] (b) 12 s (c) 4.9 102 N [down] page 234, Unit II Review 2. 86 N [350°] 6. 0.50 kg 7. (a) 4a 8. 40 N (b) 1 a 4 10. 15 N [up] 21. (mass m) Fg, (mass 2m) 2Fg 24. 306 N [357°] 25. 2.097 m/s2 [W] 27. 4.0 s 28. (b) 8.58 N [0°] 29. 0.56 m/s2 [in same direction as train A] 30. 8.0 104 N [up] 31. 2.2 m/s2 [forward] 32. 13 N [up] 33. (a) 5.3 m/s2 [right] (b) 4.8 102 N 34. 0.46 35. (a) 6 101 N [forward] (b)
2 101 N [forward] (c) 6 101 N [backward] 36. 3.2 m/s2 [downhill] 37. 1.5 m/s2 [up] 38. (a) 1.3 m/s2 [toward object A] (b) (string between A and B) 51 N, (string between B and C) 44 N 39. 8.00 N [toward Earth’s centre] 41. 8.57 N/kg [toward Earth’s centre] 42. 24.3 N less on Mars 4 3. (a) (i) and (ii) 5.9 102 N (iii) 8.8 102 N (iv) 3.9 102 N (b) (i) and (ii) (w) 5.9 102 N [down], g) 5.9 102 N [down] (F (iii) (w ) 8.8 102 N [down], g) 5.9 102 N [down] (F (iv) (w ) 3.9 102 N [down], g) 5.9 102 N [down] (F g) 5.9 102 N [down], 44. (F (a) 6.5 m/s2 [down] 45. (a) 9.4 m/s2 [down] (b) 11 N [up] (c) 11 N [down] 46. (Earth) 1.2 s, (Moon) 3.0 s 47. (a) 0.1 N [away from net] (b) 0.8 m/s2 [toward net] (c) 9 s (d) no 51. (a) 3.7 107 N [down] (b) 1.3 107 N [up] (c) 3.3 m/s2 [up] 52. Fg from person on you is 5.8 times greater page 268, 5.2 Check and Reflect 6. 0.2 s 7. 1.88 102 m/s 8. 26 m/s 9. 8.57 m/s2 10. 1.2 102 m/s2; 12 times 11. 1.21 m/s 12. 0.0337 m/s2 13. 1.7 Hz 14. 1.3 Hz or 80 rpm 9. 0.723 AU 10. 1.36 103 m/s 11. 3.5
47 d 12. 1.43 104 m/s 13. 1.98 1030 kg page 288, Chapter 5 Review 14. 4 greater 17. 2.0 101 m/s 18. 7.8 102 N 19. 44.3 m/s 20. 68 N 22. 7.83 102 m/s2 23. 3.0 103 rpm 25. 13.1 m/s 26. (a) 6.00 107 m/s (b) 1.20 1016 m/s2 27. 18.0 AU 28. 1.09 1030 kg 29. (a) 1.16 1018 s or 3.66 1010 a (b) 5.18 1036 kg (c) 6.71 1015 m/s2 30. (a) 7.91 103 m/s (b) 5.07 103 s 31. 2.73 103 m/s2; 2.00 1020 N 32. 0.430 d or 3.71 104 s 33. 5.51 103 m/s 34. (a) 4.01 1033 kg (b) 6.38 1011 m page 305, 6.1 Check and Reflect 5. (a) 3.60 104 J (b) 1.18 104 J 6. 2.76 104 J 7. (a) 6.18 104 J (b) 7.55 104 J (c) 1.37 105 J 8. (a) 3.25 J (b) 0.0732 m 9. (a) A 2.04 105 J; B 3.48 105 J 10. (a) 110 J (b) 33.8 J 11. (a) 160 J (b) 12.6 m/s page 310, 6.2 Check and Reflect 5. 1.79 106 J; Ek 6. 3.54 105 J 7. (a) 5.10 103 J (b) 1.25 103 J (c) 3.85 103 J (d) 31.0 m/s 8. (a) 288 J (c) 126 J (b) 288 J (d) 126 J page 323, 6.3 Check and Reflect 7. 12.4 J 10. (a) 0.482 m (b) 3.08 m/s (c) 2.13 m/s page 330, 6.4 Check and Reflect 4. 164 W 5. 1.50 106 W 6. 4.1
106 J 7. 380 N 8. 1.04 107 W page 332, Chapter 6 Review 5. 3.27 105 J 6. (a) increases by 4 7. (a) 5.12 m/s 8. 1.70 102 N/m 9. 12.7 m 10. 2.30 104 W (b) 5.59 m/s page 336, Unit III Review 16. 1 J 1 kg·m2/s2 29. 0.017 s 30. 62.5 Hz 31. 5.000 Hz, 0.2000 s 32. 1.02 103 m/s 33. 1.6 101 s 34. 3.09 m/s2 35. 1.40 102 m/s 36. 7.10 103 N 37. (a) 28.1 m (b) 4 greater; 113 m (b) 1.41 103 J 38. (a) 2.40 103 J 39. (a) 2.80 103 N [0°] (b) 1.54 105 J (c) 3.79 105 J (d) 19.5 m/s Numerical Answers 893 21-PearsonPhys-AnswerKey 7/29/08 1:40 PM Page 894 40. 1.03 m 41. (a) 1.20 103 J 42. (a) 35.9 J 44. (a) 2.60 J (b) 15.5 m/s (b) 0.814 m (b) 0.0651 m 45. 1.32 m/s 46. (a) 1.31 105 J (b) 917 m (c) 295 m/s 47. (a) 8.91 J 48. 3.68 103 W 49. 1.62 104 W 50. 60.0 m/s (216 km/h) (b) 1.78 N 51. 3.63 m/s 52. (a) 4.01 1030 kg (b) 4.27 1025 kg (c) 2.18 103 m/s 54. (a) 7.75 m/s (b) 4.38 m/s page 347, 7.1 Check and Reflect 7. 20.0 Hz 9. 2.50 102 Hz 10. 0.026 s 11. 0.01250 s 12. (a) 0.400 s (b) 1.50 102 wags page 365, 7.2 Check and
Reflect 4. 6.0 N opposite to the displacement 5. 1.6 m 6. 19 N [away from equilibrium] 7. 1.5 N/m 8. 0.342 N [toward equilibrium] 9. 0.028 N/m page 380, 7.3 Check and Reflect 6. 1.5 m 7. 1.08 103 m/s2 [left] 8. 1.3 103 N/m 9. 11.0° 10. 3.49 s 11. (a) 1.88 s (b) 0.900 kg (c) 16.7 m/s2 12. 3.14 m/s 13. 7.99 cm [east] 14. 0.900 s page 390, Chapter 7 Review 11. (a) 2.5 N [toward equilibrium] (b) 0.85 N [toward equilibrium] 12. 2.5 102 Hz 13. 1.5 s 14. 10.0 Hz 15. 5.1 N [toward equilibrium] 16. 2.0 102 N/m 17. (a) 1.96 N/m (b) 0.392 N (c) 0.300 m 894 Numerical Answers 18. 0.750 m 20. 24.8 cm 21. 3.00 s 22. 0.120 m/s 23. 0.13 m/s2 [down] 24. 1.02 s 25. 0.65 N/kg 26. (a) l/g (b) 0.796 m 27. (a) 1.26 m/s (b) 0.993 s 28. (a) 0.566 Hz (b) 0.800 Hz 46. (a) 10 nodes and 9 antinodes (b) 2.22 Hz 47. (a) 193 m/s (b) 440 Hz 48. (a) 0.552 m (b) 1.66 m 49. 8.62 m/s [away from you] 50. (a) 1.28 103 Hz (b) 9.96 102 Hz page 449, 9.1 Concept Check (b) 1 p 3 (c) p [W] page 410, 8.2 Check and Reflect (a) 2p 5. 1.20 103 Hz 6. 2.07 m 7. 0.135 m 9. (a) 0.911 m (b) 3.91 m page 428, 8.
3 Check and Reflect 7. 0.106 m 9. 0.60 cm page 434, 8.4 Check and Reflect 4. 748 Hz 5. 15.7 m/s (56.6 km/h) page 436, Chapter 8 Review 5. 0.133 s 7. 0.833 cm 8. 8.6 cm 9. 1.59 102 m 10. (b) 5.6 m/s 12. (a) 2.5 Hz (b) 0.50 Hz 13. (a) 435 m/s (b) 777 Hz 14. (a) 19.7 cm (b) 59.0 cm 16. 1.4 cm 17. 308 Hz 18. 86.9 km/h (24.1 m/s) 19. 1.26 103 km/h 20. 694 Hz 21. 175 m/s; f 2 original 3 page 440, Unit IV Review 11. 2.5, 3.5 28. 3.06 N 29. 7.9 g 32. 1.25 m/s2 33. 4.0 mN/cm 34. (a) 0.100 m (b) 2.24 m/s 35. 15 m/s 36. 6.73 s 37. 0.99 m/s 38. 15.9 m 41. 4.00 1014 Hz to 6.98 1014 Hz 42. 240 m 43. 0.294 m 44. 7.76 s 45. 120 m/s page 453, 9.1 Check and Reflect 8. 13 kg•m/s [S] 9. 1.2 102 m/s [N] 11. 0.16 kg 13. 75 m/s [S] 14. (a) 4.28 105 kg•m/s [W] (b) 3.85 105 kg•m/s [W] 15. 1.36 105 kg 16. 32.6 m/s [W] page 456, 9.2 Concept Check pi 0 page 467, 9.2 Check and Reflect 4. (a) 2 (impulse) (b) 1 (impulse) 3 7. (a) 2.3 N•s (b) 47 m/s [S] 8. 6.2 N•s 9. (a) 7.0 103 N•s (b) 11 m/s 10. 12 s 11. 560 N [W] 12.
545 N•s [W] page 486, 9.3 Check and Reflect 6. 0.018 m/s [away from bag] 7. 3.1 103 m/s [down] 8. 1.2 m/s [S] 9. 0.47 m/s [E] 10. (a) 1.11 m/s [right] (b) inelastic 11. (a) 274 kg (b) inelastic page 499, 9.4 Check and Reflect 5. 0.505 m/s [320°] 6. 0.625 m/s [48.1° N of W] 7. inelastic, 0.098 J 9. 0.603 m/s [49.6° S of W] 10. 27.4 m/s [37°] 11. 27.0 m/s [349°] 21-PearsonPhys-AnswerKey 7/29/08 1:40 PM Page 895 page 503, Unit V Review 37. 1.4 104 kg•m/s [N] 39. 1.85 104 kg•m/s [S] 40. 6.2 kg 41. 37 kg•m/s [W] 42. 2.4 kg•m/s [W] 43. (a) 7.5 N•s (b) 0.26 kg 44. (a) 3.02 N•s [210°] (b) 6.9 m/s [210°] 45. 2.7 103 N [toward drop-off] 46. (a) 5.50 103 N•s [W] (b) 7.75 s 47. 11.3 m/s [6.4° S of W] 48. (a) 7.62 103 N•s [forward] (b) 22 m/s [forward] 49. (a) 3.0 N•s (b) 11 m/s 50. 6.5 107 N 51. 8.7 102 N [up] 52. (a) 12 kg•m/s [toward pitcher] (b) 1.6 103 N [toward pitcher] 53. 2.1 m/s [225°] 54. (a) 1.58 m/s (b) 0.948 m/s 55. 0.750 m/s [backward] 56. 1.27 103
m/s [3.5°] 57. 3.5 m/s [65°] 58. 1.26 m/s [8.3° E of N] 59. (a) 1.8 m/s [1.8° E of N] (b) elastic 60. 1.3 m/s [downhill] 61. 15.6 m/s [34.1° S of W] 62. (a) 17 m/s 63. 4.90 m/s [2°] 64. (a) 3.04 m/s [0.0°] (b) elastic 65. 4.21 1025 kg•m/s [W] 66. (a) 3.46 m/s [4.7° W of N] (b) inelastic 67. (a) 40.0 kg (b) 14.0mT kg•m/s [S] 68. 33 m/s [72.5° N of W] 69. (a) 0.36 m/s (b) 18° S of E 70. (a) 5.95 m/s [E] (b) 2.76 s 71. 10 m/s [73.8° N of E] 72. 0.580 kg 73. 1.18 m/s [307.9°] 74. 0.641 m/s [S] 75. (a) S (b) NW (c) 248° 77. 10.5 m/s [46.4° W of S and 52.5° up] 80. (initial velocity of car) 90 km/h [W]; (initial velocity of truck) 88 km/h [N] 82. 6.1 102 m/s page 538, 10.2 Check and Reflect 5. (a) 20 N (b) 40 N 6. (b) 3.1 1010 electrons 7. (a) 6.74 N—repulsive (b) 6.80 N—repulsive 8. (a) 1.20 104 N toward charge B (b) 7.49 103 N toward charge A page 540, Chapter 10 Review 11. 1.69 N—repulsive 12. 6.70 103 m 13. (a) 1.60 102 N [left] (b) 1.24 102 N [left] (b) 6.7 N 22. (a
) 160 N 23. Fe Fg Fe 8.22 108 N 3.63 1047 N 2.27 1039 Fg 24. X—2.43 N [90°]; Y—2.43 N [210°]; Z—2.43 N [330°] 25. (b) Fe varies as 1/r or 1/r2 (e) 0.0360 N•m2 (f ) kq1q2 (g) 2.00 106 C page 553, 11.1 Check and Reflect 7. (a) 4.50 105 N/C [right] (b) 8.99 103 N [right] 8. (a) 2.04 104 N/C [away from larger sphere] (b) 3.63 109 C 9. (a) 2.50 107 N/C [toward the 3.00 C charge] (b) 0.661 m [left of the 3.00 C charge] 10. 0.00 N/C page 569, 11.2 Check and Reflect 4. (a) 2.40 1017 N [downward] (b) 1.64 1026 N [downward] 6. 1.60 103 N/C 7. 7.2 105 N/C [toward the 6.4 C charge] 8. 2.00 103 J 9. 1.8 106 N/C [left] 10. (a) 2.00 104 V/m (b) 3.86 105 J page 575, 11.3 Check and Reflect 4. Speed of electron is 8.79 106 m/s; speed of proton is 2.05 105 m/s 5. 9.4 107 m/s 6. 6.00 1019 C 7. 2.40 104 J 8. (a) 1.38 106 m/s (b) 9.79 105 m/s 9. (a) 1.8 105 J (b) 1.8 105 J (c) 1.1 m/s 10. (b) 2.00 1017 N [down] (c) 2.20 1013 m/s2 [down] (d) 0.130 m page 578, Chapter 11 Review 12. Ep W 17. (a) 5.17 103 N/C [away] (b) 1.03 102 N [toward positive charge] 18. (a) 7.49 1010
N/C [toward the 5.00 C charge] (b) 0.735 m from the 5.00 C charge 19. 1.2 107 N/C [90.0°] (b) 3.0 J 20. (a) 3.0 J 21. 5.62 104 J 22. (a) 545 V/m (b) 20.5 V 23. 0 J 24. 7.0 105 V/m 25. 2.88 1013 J or 1.80 106 eV 26. 6.40 1015 J or 4.00 104 eV page 601, 12.2 Check and Reflect 6. (a) 6.40 1015 N (b) 3.67 1015 N 7. 1.3 106 m/s 8. 6.53 1026 N 9. 1.06 104 m 10. 8.31 109 T page 613, 12.3 Check and Reflect 9. 1.04 102 C 11. 8.4 102 N page 622, Chapter 12 Review 20. 9.86 1014 N 21. (a) 2.31 104 m/s (b) 4.44 1019 J or 2.77 eV 22. 4.08 103 m/s 23. (a) 4.13 1016 N (b) 2.06 1016 N (c) no force 24. 2.7 105 T 26. (b) B varies as 1/r or 1/r 2 28. 25.0 N page 626, Unit VI Review 39. (a) 1.4 108 V/m (b) 1.1 1019 J 41. 2.56 109 m 42. 5.06 107 N—repulsive 45. 15 N/C 46. 3.2 1015 J; maximum speed is 2.0 106 m/s 47. 0.268 m to the right of the first charge 48. 5.0 105 C 49. 0.73 A 50. (a) 2.6 106 N/C [left] (b) 1.6 N—attractive 52. 2.0 103 N 53. 1.67 104 m 54. (a) 3.63 1047 N (b) 8.22 108 N (c) 2.27 1039 times greater 57. 1.53 103 m/s; positive charge Numerical Answers 895 21-PearsonPhys-AnswerKey 7/29/08 1
:40 PM Page 896 58. (a) 3.17 1012 N (b) 1.89 102 m 59. (a) 113 N [right] (b) 28.4 N [left] (c) 30.8 N [69.4°] 60. 6.6 103 V 61. (a) 2.50 104 V (b) 9.37 107 m/s (c) 2.25 1011 N 81. (b) B varies as 1/r (c) Plot B vs 1/r (f ) 0.79 T•m/A (g) 0.789 T•m/A page 647, 13.1 Check and Reflect 8. 2.5 103 Hz page 652, 13.2 Check and Reflect 4. 2.1 108 m/s 5. 6.67 102 s 6. 293 Hz 7. 2.7 103 Hz 8. 3.44 104 m 9. 1.86 103 Hz 10. 2.80 108 m/s 11. 2.85 108 m/s page 665, 13.3 Check and Reflect 8. 50 cm page 683, 13.4 Check and Reflect 9. 2.26 108 m/s 10. 23.0° 11. 32.4° 12. 41.1° 14. angle of refraction 15.9°; wavelength 351 nm 16. 2.25 102 m; inverted 18. (a) 648 cm (b) 140 cm (c) 8.2 cm page 697, 13.5 Check and Reflect 6. 5.7 106 m 7. 6.1° 8. 0.350 m 9. 3.76 103 m 10. wavelength 6.11 107 m; frequency 4.91 1014 Hz 11. wavelength 4.13 107 m; frequency 7.26 1014 Hz page 699, Chapter 13 Review 23. 3.41 104 m 24. 2.88 108 m/s 26. 13 cm 30. 5.00 cm high, 6.67 cm from the mirror 31. 1.82 cm 32. (a) 2.26 108 m/s (b) 2.19 108 m/s (c) 1.97 108 m/s 896 Numerical Answers (d) 2.04 108 m/s (e) 1.24 108 m/s 33. angle of refraction 23°; wavelength 415 nm 34. (a) no (b)
yes (c) yes (d) no 35. 1.12, which is less than that of water 36. (a) 48.8° (c) 33.3° (b) 24.4° (d) 41.1° 37. 2.67 cm high, 3.33 cm from the lens. It is virtual, erect, and diminished. 38. 0.7°, 1.4°, 2.0° 39. 4.4 107 m; violet 40. 4.9 107 m; blue 41. 6.0 105 m page 710, 14.1 Check and Reflect 1. 4.42 1019 J 2. 8.29 108 m 2E600 3. E300 4. (a) 2.41 1019 Hz 5. 2.77 1021 photons 6. 4.93 1021 photons 7. 100 photons/s 15. 0.00388 nm 16. (a) 1.1 1034 m 18. 3.32 1030 photons/s 19. 0.52 eV, 2.1 eV, 4.7 eV 20. 5.33 1023 kg·m/s 22. (c) 9.3 N 23. 1.5 1017 page 746, Unit VII Review 26. 3.62 1019 J 29. 6.00 1014 Hz 33. 3.9 107 m 36. 2.21 1027 N·s 37. 0.243 nm 41. 8.3 1029 photons/s 43. 3.84 105 km 45. 4.84 104 m 46. 3.75 103 Hz 47. 1.39 104 s 49. refractive index 2.42, therefore the material is diamond 51. 2.91 108 m/s; error 2.93% 53. 7.5 cm from mirror. It is erect and page 715, 14.2 Concept Check Ephoton hf W page 720, 14.2 Check and Reflect 1. 3.11 eV 3. 9.82 1014 Hz 4. yes, hf W 5. 1.25 V 9. 4.1 1015 eV•s; this is close to Planck’s constant Page 725, 14.3 Check and Reflect 1. 1.33 1027 N•s 3. wavelength 1.11 1013 m; energy 1.80 1012 J 6. 0.0124 nm 7. 2.0 104 m/s
page 736, 14.4 Check and Reflect 1. 36.4 nm 2. 1.33 1027 kg•m/s 3. 5.3 1026 kg•m/s 4. 2.1 1023 kg•m/s 5. (a) 3.36 1015 J (b) 8.47 1012 m 1.83 103 e/ 6. p page 742, Chapter 14 Review 3. 4.42 1019 J or 2.76 eV 4. Ex/Ev 7. 4.0 1019 J or 2.5 eV 9. It increases by 0.0024 nm. 100 10. 73 nm 11. 6.63 1027 N•s 13. 3.0 1018 photons 14. 3.62 1019 J or 2.26 eV 2.5 cm high. 4 A; pA 4pB 54. B 55. 9° 56. 7.0 1016 J 57. 10 cm from the lens 58. (b) 0.1 m/s 60. 0.0045 nm 62. 0.4 eV 63. for violet light 24.8°; for red light 40.5° 64. 2.63 102 m 67. Energy 0.2 eV; momentum 3 1025 N•s 68. 6.67 102 s 74. 2.5 eV 76. momentum 1.2 1022 kg•m/s; wavelength 5.5 1012 m 78. 6.6 1026 N•s page 760, 15.1 Check and Reflect 1. (a) 8.0 1015 N (b) 0 N 4. (b) 4.00 105 m/s 5. 1.8 107 m/s 6. 1.57 103 T 8. 8.00 104 m/s 9. (a) 8.0 1015 N [downward] 10. (b) 3 109 m/s page 765, 15.2 Check and Reflect 3. 6.40 1019 C 4. 8.00 1017 N [up] 5. (a) 0 N 6. (a) 1.6 1018 C, or 10e (b) gained 10 (c) downward 21-PearsonPhys-AnswerKey 7/29/08 1:40 PM Page 897 page 770, 15.3 Check and Reflect 7. 177.8 MeV 3. (a) 3.6 1016 J (b
) 3.6 1012 J 6. (a) 2 1010 m (b) The gold atom is approximately 7000 times larger than the gold nucleus. 7. (b) 5.0 1015 m page 780, 15.4 Concept Check 634 nm, 654 nm page 780, 15.4 Check and Reflect 5. (b) 486 nm (c) 4.09 1019 J 6. 1.96 eV 7. (b) 1 1.9 eV; 2 2.1 eV; 3 1.5 eV; 4 3.9 eV 654 nm, visible, red; 592 nm, visible, 829 nm; (c) 1 2 yellow; 3 4 319 nm 9. (a) 3.03 1019 J (b) 2.66 1020 J 11. (a) 140 nm (b) 3.27 106 m (c) 15 page 784, 15.5 Check and Reflect 4. (a) 3.32 1010 m (b) 2.00 1024 kg·m/s (c) kinetic energy 2.19 1018 J; speed 2.19 106 m/s 5. (a) 2 2 1; 3 3 1 page 786, Chapter 15 Review 6. 3.68 1018 C 7. 1.76 1011 C 16. 4.76 1010 m 19. 2.4 1016 N 20. (a) 1.09 106 m/s 21. 4.1 104 N/C directed upward 22. (a) 1.06 1019 J; 1.55 1019 J; 1.82 1019 J (b) wavelengths: 1.88 106 m, 1.28 106 m, 1.09 106 m. Frequencies: 1.60 1014 Hz, 2.34 1014 Hz, 2.74 1014 Hz. (c) 1.55 1019 J 23. (b) 634 nm 24. 2.5 103 N/C [up] 25. (a) 2.17 1018 J (b) 9.01 1022 m/s2 (d) 4.72 1011 s page 796, 16.1 Check and Reflect 1. (a) 38 protons, 52 neutrons (b) 6 protons, 7 neutrons (c) 26 protons, 30 neutrons (d) 1 proton, 0 neutrons 2. 1.0 109 eV
1.0 GeV 3. 2.3 108 eV 4. 5.56 108 kg 8. (a) 0.366 642 u (b) 8.538 MeV/nucleon 9. (a) 100 MeV (b) 476 MeV (c) 1737 MeV 13. Nuclear radius 5.38 fm Approximate distance between nucleons 2 fm page 810, 16.2 Check and Reflect 2. 3 : 2 8. 1.819 MeV page 817, 16.3 Check and Reflect 1 1. 6 1 2. 3.7 1012 atoms/s 4. 1.2 million years 5. 1.7 103 of the original quantity 6. 1.1 104 a 7. 1.5 102 Bq 8. (a) 4 h (b) 3600 decays/min Page 824, 16.4 Check and Reflect 6. (b) 4.730 MeV 7. (b) 17.59 MeV 8. (a) 8.1 1019 (b) 1.0 103 kg Page 826, Chapter 16 Review 5. 60 neutrons, 55 protons 6. 8.0 1012 J 7. 9 1013 J 8. 3.4 1010 J 9. 0.322 u 10. 20 MeV 18. 1.8 108 decays/s 19. 2 1019 nuclei 24. (a) 7.074 MeV (b) 8.448 MeV (c) 8.792 MeV (d) 7.591 MeV 26. (b) 8.95 MeV 27. (b) 3.210 MeV 28. about 1.1 104 a 29. (a) 5.1 1015 atoms (b) 1.905 109 kg (c) 1.1 104 Bq 30. (a) 400 Bq (b) 4 h 31. 7.274 MeV 32. (b) 0.23 kg page 844, 17.3 Check and Reflect 7. (a) momentum 5 1021 kg•m/s; kinetic energy 8 1015 J (b) momentum 8.4 1022 kg•m/s; kinetic energy 2.1 1016 J 8. (a) 0.51100 MeV (b) 5.521 1027 kg 9. 931.5 page 851, Chapter 17 Review 19. 3.14 1025 kg 20
. (a) e (b) 83138 MeV/c 2 21. (b) 10 cm (c) 1.9 1020 N•s page 855, Unit VIII Review 1 and 2 5 1 2. 9.6 107 C 3. 1.60 1018 C 4. 1.60 1016 N [N] 8. (a) ni ni (b) ni (c) ni 4 → nf 6 → nf 1 → nf 4 → nf 10. 33 neutrons, 31 protons 12. 2.0 107 eV 13. 1.0 109 J 14. 6.7 MeV 15. 2.3 109 decays/s 17. 1.4 g 22. (a) 1.022 MeV (c) 2.43 1012 m 25. (a) proton (b) kaon (c) pion (d) 27. (b) 7.3 104 m/s 28. 0.48 T 29. (a) electric force 1.6 1017 N [up] magnetic force 2.0 1013 N [up] (b) 2.0 1013 N [up] 30. (a) 1.6 1018 C (b) It has gained 10 electrons. 31. (a) 1005 nm, 1094 nm, 1282 nm, 1875 nm (b) infrared 32. (a) 2.12 1010 m (b) 6.65 1010 m (c) 9.97 1025 kg·m/s (d) speed 1.09 106 m/s; kinetic energy 5.46 1019 J 33. 342.1 MeV 36. 10.42 MeV 37. 7.5% 38. 1.905 MeV; cerium140 39. 1 102 Bq 40. 1.72 104 years old 41. 7.161 MeV 42. 4.033 MeV 44. (a) 2 102 N (b) 2 1013 J 45. 5.10 104 m/s 46. (b) 135 MeV 48. 2.7 1018 N•s 49. 2.33 1050 m 50. (a) 13 Bq Numerical Answers 897 21-PearsonPhys-AnswerKey 7/29/08 1:40 PM Page 898 51. (a) the level of 21.9 Sv is much higher than the background level of 400 Sv (b) 5 102
and mass, 147 and net force, 146 of a mass-spring system, 366–369 units of, 23, 26 Acceleration due to gravity, 54–62 Acceleration-time graph, 26, 42 Accelerometer, 366 Action force, 160–167 Action-at-a-distance force, 200 Activity (also Decay) rate, 812 Adams, Henry, 617 Adams, John, 282 Air velocity, 92–97 Air, refractive index of, 666, 667t, 670, 673 wavelength of light in, 669 Airbag systems, 140, 141 Alpha decay, 799–801 Alpha emission, 797 Alpha particle, 497, 767–769, 799–801 hazards of, 808t Alternating current, 638t Altitude, 221 Ammeter, 604 Ampere (A), 602, 607 Ampere, André-Marie, 602, 607 Ampere’s law, 642 Amplitude, 355f, 371, 378, 382, 386, 395, 408, 412 Amplitude modulation (AM), 646 Analog radio technology, 646 Anderson, Carl, 836, 842, 846 Angle of diffraction, 689–691 Angle of incidence, 654, 666f Angle of reflection, 654, 666f Angle of refraction, 666, 672 Anti-locking brake systems, 187 Antimatter, 804, 836, 837 Antineutrino, 804 Antinodal lines (also Bright fringes), 686–690, 692 Antinodes, 415, 417–419, 422f, 423f, 424f, 426 Apparent weight, 224–226 Applied force, 130, 171–189, 307 Arago, Dominique, 692 Aristotle, 634 Armature (also Rotor), 608 Artificial satellites, 284–286 Astronomical units (AU), 272, 273 At rest, 13 Atom, 513 Bohr model, 773, 774 energy levels, 774–776 nucleus, 766–769, 790–796 orbit size, 774 planetary model, 768 quantum model, 782, 783 raison-bun-model, 758 structure theories of, 752f subatomic particle models, 845–849 subatomic particles, 830–849 Atomic emission spectroscopy, 779 Atomic mass number, 790, 791, 7
98 Atomic mass unit, 791 Atomic number, 790, 791, 794, 795 Attitude of images, 656, 662, 664 Audio frequency signal, 646 Aurora borealis, 580, 597, 598f, 779 Avalanches, 448, 449 Average net force, 450 Average velocity, 12–18, 36–38 Axis of rotation, 242, 244f Axle, 242 B Background radiation, 637 Ballistic pendulum, 483–485 Balmer, Johann Jacob, 773 Balmer’s formula, 773, 774, 778 Balmer series, 776f Baryons, 842, 843t, 847 Bearing method, 78 Becker, Wilhelm, 497 Becquerel, Antoine Henri, 797 Becquerel (Bq), 812 Beta emission, 797 Beta particles, 802–805, 808t Beta-negative decay, 802–805, 847 Beta-positive decay, 805, 848 Bethe, Hans, 821 Binding energy, 793–796, 818 Binoculars, 674 Biomechanics, 29 Blackbody radiation curves, 704f, 705 Blackbody, 705 Blau, Marietta, 842 Bohr, Niels, 513, 771, 773, 774 Bohr model, 773, 774, 783 Bohr radius, 774 Born, Max, 739, 783 Bosons, 842 Bothe, Walther, 497 Bow wave, 433 Brahe, Tycho, 214, 269 Bright-light (also Emission line) spectrum, 772f Bubble chamber, 831, 833 C Capacitor, 642 Carbon dating, 815, 816 Cartesian plane, 127 Cassini, Giovanni, 359 Cathode ray, 593, 754, 755f–757 Cathode ray tube, 568, 593f Cavendish, Henry, 205, 524 Cell phones, 646 Central antinode, 686 Centre of curvature, 657, 658 Centre of mass, 492 Centrifugal force, 247 Centripetal acceleration, 243, 244, 247t, 252–255, 265–267 Centripetal force, 244, 246, 247t, 256, 258–267, 277–280 CERN, 831 CGS system, 642 Chadwick, James
, 497, 790 “Change in” (Δ), 7 Charge, 593–600, 762, 798 determination of, 528, 529 magnitude of, 529–531 transfer of, 517–522 Charge migration, 520 Charge shift, 521 Charge-to-mass ratio, 755–758 Charging by induction, 521 Chemical energy vs nuclear energy, 820 Circular motion, 242–247 and Newton’s laws, 248–267 of satellites and celestial bodies, 269–286 Clocks, 383, 387 Closed-pipe (also Closed-tube) resonance, 419 Cloud chamber, 830, 831, 833, 842 Coaxial cables, 558 Coefficient of friction, 259 Coefficient of kinetic friction, 182, 183 Coefficient of static friction, 182, 183t, 186 Coils, electron flow in, 587f Collinear charges, 532 Collinear collisions (see Collisions in one dimension) Collinear forces, 132, 133 Collinear vectors, 71, 73, 75 Collisions, 469, 470 charge transfer during, 518, 519 impulse in, 458 Collisions in one dimension, 468–485 Collisions in two dimensions, 487–498 Colour of quarks, 848 Commutator, 608, 609 Compression, 404 Compton, Arthur, 721f Compton effect, 721–724 Compton equation, 722–724 Compton scattering, 721 Concave reflecting surface, 657f–659 Conduction, 519 Conductors, 513, 514 and magnetic fields, 602–611 electric field lines of, 555–558 Conservation of momentum, in discovery of subatomic particles, 497, 498 in one-dimensional collisions, 473–479 Index 899 22-PearsonPhys-Index 7/25/08 7:40 AM Page 900 in two-dimensional collisions, 489–495 Conservative forces, 314, 319, 320 Constant acceleration, 450 Constant mass, 450 Constructive interference, 412, 416f, 417, 425–427, 686–689, 782f Continuous spectrum, 772f Converging lens, 677, 678 Converging mirror, 657–659 Convex reflecting surface, 657f–659 Copernicus, Nicholas, 214 Cosmic radiation, 637, 638t Coulomb (C), 529 Coulomb’s constant, 774
Coulomb’s force (see Electrostatic force) Coulomb’s law, 529–531, 768 Coulomb’s proportionality constant (k), 529, 530 Crash test dummies, 29 Crest, 394, 395, 397f, 408, 430 Critical angle, 672, 673 Crookes, William, 754 Curie, Marie and Pierre, 797, 808 Current, 587, 602–609, 642 Curved mirrors, 657–662 Cycle, 249, 344, 355 Cyclotron particle accelerator, 841 D da Vinci, Leonardo, 180 Dalton, John, 754 Damping, 385 Daughter element, 799 Daughter nucleus decay, 807 Davisson, C. J., 729 Davisson-Germer experiment, 729f, 730f de Broglie, Louis, 726f, 782 de Broglie’s wave equation, 726–728, 730–733 de Broglie’s wavelength, 726 de Coulomb, Charles, 524, 528, 529 de Maricourt, Pierre, 582 Decay (also Activity) rate, 812 Decay constant, 811, 812 Defibrillators, 559 Deformation from colliding objects, 481 “Delta” symbol (Δ), 7 Destructive interference, 412, 413f, 416f, 417, 419, 425–427, 687, 689, 782f Diamond, 667t, 670, 672 Difference in path length, 688 Diffraction, 685, 690–694 Diffraction grating, 692, 693, 771 Diffuse (also Irregular) reflection, 653 Digital wireless technology, 646 Dirac, Paul Adrien Maurice, 582, 836 Direct current, 608 Dispersion, 675 Displacement, 7, 9, 56–58, 73–75, 80–89, 293–295 from velocity-time graphs, 33–35, 40, 48–51 Diverging lens, 677, 678 Diverging mirror, 657–659 Diverging rays, 397, 398 Domains, 589 Doping, 515 Doppler, Christian, 429 Doppler effect, 430–432 Doppler frequency, 431, 432 Doppler ultrasound, 434 Doppler wavelength, 431–434 Down quark, 845, 8
46t Drift tube particle accelerator, 841 Dynamics, 126 E Earth, magnetic field of, 591, 597, 598 orbital diameter, 648f, 649 Ebonite rod, 518, 520, 521, 529 Eddington, Arthur Stanley, 821 Efficiency, 324 Effluvium theory, 544 Einstein, Albert, 199, 640, 706, 713 Einstein’s mass-energy equation, 793, 794 Elastic (also Spring) constant, 299 Elastic collisions, 481, 482, 495–497 Elastic force, 128, 129 Elastic limit, 349 Elastic potential energy, 300–302, 307, 370, 402, 406 Electric charge (see Charge) Electric current (see Current) Electric field, 545–553, 554–559, 641–643, 756f between charged plates, 567, 568 in one dimension, 550 in two dimensions, 551, 552 magnitude and direction of, 546–553 Electric field lines, 554–559 Electric force on a charged particle, 755 Electric generators, 617 Electric motor, 602, 608, 609, 614, 617, 619 Electric potential (also Voltage), 564, 565 Electric potential difference, 565, 566 Electric potential energy, 561–564, 571 of an alpha particle, 769 of an electron, 774, 775 Electrical conductivity, 513, 514 Electrical interactions, 512–522, 524–537 and the Law of conservation of energy, 570–575 Electricity, 512–522 Electromagnetic force, 838t Electromagnetic induction (see Generator effect) Electromagnetic radiation (see also Light), 636–646 diffraction and interference, 684–696 models of, 639–643 photoelectric effect, 712–719 production of, 644, 645 speed of, 648–651 Distance, 6, 7, 106–111 Electromagnetic spectrum, 637, 638t, 708, 709f Electromagnets, 588, 589 Electromagnetic theory, 641–643 Electromagnetic wave, 643 Electromotive force, 611 Electron, 498, 513, 842 charge of, 529, 762 charge-to-mass ratio, 755–758 de Broglie’s wave equation for, 726, 727 discovery of,
754 energy level transition of, 776, 778, 779 in charge transfer, 517–522 in Compton scattering, 721, 722 in photoelectric effect, 712–719 kinetic energy of, 730–733 mass of, 792t, 844t wave nature of, 782, 783 wavelength of, 728, 836, 837 Electron microscope, 727 Electron-positron annihilations, 836 Electron volt (eV), 565, 843, 844 Electron-wave interference, 729 Electrostatic discharge, 537 Electrostatic (also Coulomb’s) force, 528–537 Electrostatics, 513–521 Electroweak force, 848 Elementary charge, 774 Elementary unit of charge, 762 Ellipse, 269 Emission line (also Bright-light) spectrum, 772, 776 Energy, 292–304, 306–309, 311–322, 324–329, 639 along a pulse, 402 in quanta, 705–709 Energy conservation, 497, 498 Energy level, 773–776 Energy-mass equation, 843 Equilibrium position, 394, 395 Erect image, 660, 662, 680 Euclid, 634 Excited state, 775 Explosion interaction, 476 Extrasolar planets, 283 F Faraday, Michael, 545, 584, 610, 611, 614 Faraday’s ice pail experiment, 559 Faraday’s law, 642 Femtometres, 790 Fermi, Enrico, 804 Fermilab Tevatron accelerator, 840f Fermions, 842 Ferromagnets, 589 Feynman, Richard, 739 Fibre optics, 674 Field (see also Electric fields), 200, 545 First order maximum, 427 Fission, 818–820 Fizeau, Armand, 649, 666 Fletcher, Harvey, 761 Focal length, 657, 658, 662, 667, 678 Force, 127–135, 293–295 900 Index 22-PearsonPhys-Index 7/25/08 7:40 AM Page 901 and centripetal acceleration, 252–255 effect on momentum and impulse, velocity-displacement, 368f, 369f velocity-time, 21f–28f, 62f 455–466 in collisions
, 474 Forced frequency, 382, 383f, 385 Frame of reference, 13, 14 Franklin, Benjamin, 512, 513 Fraunhofer lines, 773 Free fall, 226, 227 Free-body diagrams, 129–135f, 146f, Gravimeters, 222 Gravitational acceleration, 217–219 Gravitational field, 200, 201, 545 Gravitational field strength, 201, 217, 220–222, 378, 379 Gravitational force, 128, 129, 131, 173–175, 196–201, 203–214, 216–228, 259f–264, 277, 524, 838t 150f, 151f, 161f–167f, 172f–189f, 197f, 198f, 209f, 222f–224f, 226f Frequency, 249, 265–267, 344, 345, 408, Gravitational mass, 199 Gravitational potential energy, 295–298, 307–309, 312–316, 321, 560, 562 409, 429–432, 636, 637 Frequency modulation (FM), 646 Fresnel, Augustin, 691, 692f Fresnel lens, 634f Friction, 130, 165, 169–189, 320 463 and momentum, 449 charging objects by, 518, 519 effects on motion, 184 in circular motion, 258 Friedman, Jerome, 845 Fuel cells, 329 Fundamental forces, 194 Fundamental frequency, 422 Fundamental particles, 836, 837 Fusion, 818, 821, 822 G g force, 216 Galilean telescope, 682f Galileo, 54, 103, 137, 138, 281, 648 Galle, Johann Gottfried, 282 Galvani, Luigi, 602 Galvanometer, 602f, 604f, 611f Gamma decay, 806 Gamma emission, 797, 806, 808t Gamma radiation, 636 Gamma rays, 637f, 638t Gauss (G), 586 Geiger, Hans, 767 Gell-Mann, Murray, 845 Generator effect (also Electromagnetic induction), 609–611 Generator effect, 615, 617–619 Genetic damage, 808 Geostationary satellites, 285, 286 Germer, L. H., 729 Gilbert, William, 512, 583 Glaser, Donald, 831 Glashow, Sheldon, 848 Glass, 666, 667t, 6
68, 673 Gluons, 838 Gramme, Zénoble Théopile, 617 Grand unified theory, 849 Graphs, acceleration-displacement, 367f, 368f, 369f acceleration-time, 26f, 42f force-displacement of a pendulum, 361f force-displacement of a spring, 351f net force-time, 459f–462f position-time, 11f–18f, 61f, 62f Graviton, 838 Gravity, 54–62 Gravity assist, 214 Gray (Gy), 809 Ground state, 774 Ground velocity, 92–99 Grounding, 521, 610 H Hadrons, 842, 843 Half-life, 812–814 Hansen, Hans Marius, 771 Harrison, John, 383 Heisenberg, Werner, 734f Heisenberg’s uncertainty principle, 735 Helium formation, 821, 822 Henry, Joseph, 610, 611 Herschel, William, 282 Hertz (Hz), 249, 250, 344, 345 Hertz, Heinrich, 644, 645, 648, 712 High tide, 210, 211 Hit-and-stick interaction, 477 Hollow conducting objects, 557, 558 Hooke, Robert, 299, 349f, 684 Hooke’s law, 299–301, 349–354, 366, 368 Horsepower (Hp), 324 Huygens, Christiaan, 359, 381, 634, 639, 648, 649, 684f Huygens’ Principle, 684, 685 Hydrogen, 773f Hydrogen fusion, 821–823 I Images, 653–665 formation in a curved mirror, 657–662 formation in a plane mirror, 654–656 Impulse, 457–466, 470 In phase, 395, 416, 425, 426 Incandescent, 704 Incident light, 653, 654f, 666 Incident wave, 395, 398 Inclines, 173, 174, 176–179, 188, 189, 308 Induced current, 611, 617–619 Induction, 520, 521 Induction coils, 615t Inelastic collisions, 483–485, 495–497 Inertia, 138–140, 147–157 Inertial mass, 148–157 Infinity, 5
62 Infrared radiation, 636 Infrared ray, 709f Infrared spectrum, 637, 638t Input energy, 324 Instantaneous momentum, 449 Instantaneous velocity, 24, 25 Insulators, 513, 514 Interference, 411–413, 416, 417, 685–690, 695, 696 Interference fringes, 686 Interference pattern, 425, 426f Interferometer, 649 Inverse square law, 529 Inverted image, 660, 662, 680 Ionization energy, 775 Ionization smoke detectors, 802 Irregular (also Diffuse) reflection, 653 Isolated systems, 311–316, 470, 475 Isotopes, 791, 796f, 806 J Jerk, 26 K Kammerlingh Onnes, Heike, 515 Kendall, Henry, 845 Kepler, Johannes, 214, 269 Kepler’s constant, 271–273 Kepler’s laws of planetary motion, 269–279 Keplerian telescope, 682f Kilogram-metres per second (kg•m/s), 449, 457 Kinematics, 6 Kinematics equations, 47–53, 56, 144 Kinetic energy, 302–304, 306–309, 312–316, 321, 370, 402, 480, 570, 571, 573 in alpha decay, 799, 801 in beta decay, 804 in elastic collisions, 481, 482, 495 in inelastic collisions, 483–485, 495 of alpha particles, 769 of electrons, 774, 775 of photoelectrons, 713–717 Kinetic friction, 176–182, 187, 258 Kirchhoff, Gustav, 705, 771, 772 L “Lambda” symbol (), 408, 409, 417, 419, 424, 427, 429–432 Latitude, 221 Law of charges, 512 Law of conservation of charge, 517 Law of conservation of energy, 312, 497, 498, 721, 722 and electrical interactions, 570–575 for the photoelectric effect, 714, 718 Law of conservation of momentum, 473, 721, 722 in ballistic pendulum system, 484 in two-dimensional collisions, 491, 492, 495 Law of magnetism, 582 Law of reflection, 654, 658 Le Verrier, Urbain, 282 Index 901
22-PearsonPhys-Index 7/25/08 7:40 AM Page 902 Left-hand rule, 834 for deflection of charged particles, 594, 595 for magnetic fields, 588 for magnetic force, 604, 611, 756f Lenses, 677–681 Lenz’s law, 618, 619 Leptons, 842, 843t, 848t Lewis, Gilbert, 706 Light (see also Electromagnetic radiation) from colliding objects, 481 quantum theory of, 705–709, 712–719, 721–724, 726–735 reflection, 653–665 refraction, 666–681 speed of, 636, 648–651, 669, 670 Light waves, 712–719 Lightning, 512, 513, 522, 529 Lightning rod, 554 Lodestone (also leading stone), 582, 583 Longitudinal waves, 401, 404–406, 695f Lord Kelvin (see William Thomson) Loudspeaker, 614t Low tide, 210, 211 Lyman series, 776f M Maglev, 587 Magnesium, 636f Magnetic deflection, 593–597, 603, 604 Magnetic field, 584–591, 593–600, 602–611, 641–643, 756f–758 left-hand rule for, 588 Magnetic field strengths, 586t Magnetic force, between two current carrying conductors, 607 calculation of, 598–600 on a current carrying conductor, 603–606 Magnetic monopoles, 582 Magnetic poles, 582, 585 Magnetism, 512, 587–591 Magnetization, 589, 590 Magnetohydrodynamic propulsion, 614t Magnetron, 599 Magnets, 583, 585, 586, 617, 618 Magnification, 656, 662, 664 Magnitude, 6 Major axis, 269f Marconi, Guglielmo, 646 Marsden, Ernest, 767 Mass, 220 and conservation of momentum, 474 due to gravity, 199 in momentum, 448–452 of celestial bodies, 218t, 280, 281 Mass defect, 794, 795 Mass spectrometer, 759 Mass-energy equation, 793, 794 Mass-spring systems, 354–360, 366–376 Matter waves,
726–735, 729 Maximum, 426 Maxwell, James Clerk, 641, 648, 695, 771 902 Index Maxwell’s equations, 642 Mechanical energy, 306, 309, 311–322 Mechanical resonance, 382 Mechanical waves (see Waves) Mechanics, 306 Mediating particles, 837, 838 Medium, 394, 395, 404, 406, 411 Mesons, 842, 843t, 845, 847 Michell, John, 205 Michelson, Albert, 650, 651 Microwaves, 637f, 638t Millikan, Robert Andrews, 713f–715, 761–763 Minor axis, 269f Mirage, 667 Mirror equation, 662, 664 Mirrors, 654–662 Momentum, 449–452, 470 and impulse, 454–466 and Newton’s Second Law, 450–452, 456 and non-linear net forces, 461, 462 conservation of, 473–479, 489–498 in one-dimensional collisions, 473–479 in two-dimensional collisions, 489–495 of a photon, 728 Motion, in one dimension, 6–62, 70–75 in two dimensions, 76–89 of projectiles, 102–111 sign conventions for, 8–10 Motor effect force, 593 Muons, 842, 843t N Nanotechnology, 619, 674 Navigator method, 77, 78 Neddermeyer, Seth, 842, 846 Negative acceleration, 28, 29, 44 Net charge, 517, 518 Net force, 131–135, 139, 146, 152, 155, 157, 164, 165, 171–189, 306, 307, 356, 366, 456–466, 473, 474, 489 in circular motion, 256 on momentum, 450 Neutrino, 804 Neutron, 497, 498, 790, 792t, 844t, 847 Neutron number, 790, 791, 794, 795 Newton (N), 127 Newton, Isaac, 194, 196, 214, 276–281, 545, 634, 639, 675 Newton’s first law of motion, 139, 140 Newton’s law of gravitation, 524 Newton’s law of universal gravitation, 204–214, 216 Newton’s second law
of motion, 143–157, 366, 367 and horizontal motion, 149–151 and momentum, 450–452, 456 and single pulley system, 154, 155 and two-body systems, 153, 154 and two-pulley system, 156, 157 and vertical motion, 152, 153 on objects in systems, 470, 473 Newton’s third law of motion, 161–167, 459, 474 Newton-second (N•s), 457 Nodal lines (also Minimum; Dark fringes), 426, 686 Nodes (also Nodal points), 415, 417–419, 423f, 424f, 687 Non-collinear forces, 133, 134 Non-collinear vectors, 80–89 Non-conservative forces, 319 Non-isolated systems, 320–322 Non-linear net force, 461, 462 Non-uniform motion, 22–28, 31 Non-zero net force, 307, 450 Normal (also Perpendicular) force, 130, 131 Normal force, 258, 259, 260 Normal line (N), 653, 654f, 666f North pole, 582 Nuclear energy vs chemical energy, 820 Nuclear reactions, 818–823 Nucleon, 790, 795, 796 Nucleosynthesis, 823 Nucleus, 513, 766–769, 790–796 decay rates of, 811–816 reactions in, 818–823 size of, 768, 769 O Oersted, Hans Christian, 587 Oil-drop experiment, 761 Omega particle, 845 Open-pipe (also Open-tube) resonance, 424 Opsin, 636 Optical centre, 678f Optical fibres, 673 Orbital height, 279, 280 Orbital period, 271–289 Orbital perturbations (also Wobbles), 281, 282, 283 Orbital radius, 271–289 Orbital, 783 Origin, 6 Oscillation, 344 Oscillators, 640 Oscillatory motion, 344, 345, 348–364, 366–379, 381–387 Out of phase, 416 Output energy, 324 Overtones, 422, 423, 424 Oxygen, 779f P Parabola, 61, 62 Parabolic mirror, 661 Parallel plates, electric field between, 567 motion of charges between, 572, 573 Parallel-plate capacitors, 558, 559 electric field between, 5
74, 575 electric potential energy between, 563 Parent element, 799 Partially reflected/refracted rays, 666 22-PearsonPhys-Index 7/25/08 7:40 AM Page 903 Particle, 639 Particle accelerator, 840f, 841, 842 Particle model, 639, 640 Particle-in-a-box model, 730–735 Paschen series, 776f Path length, 688, 689 Pauli, Wolfgang, 498, 804 Payne-Gaposchkin, Cecilia, 821 Pendulum, 314–316, 359–362, 377–379, 381, 382, 483 Pendulum-bullet system (also Ballistic pendulum), 483–485 Period, 249, 251, 265–267, 344, 345, 408, 409 of a mass-spring system, 373–376 of a pendulum, 377–379 Perpendicular bisector, 686–691 Perrin, Jean Baptiste, 754 Phase shift, 426 Photoelectric effect, 712–719 Photoelectrons, 712 Photon, 640, 706–709, 722–724, 728, 776 Piezoelectric material, 387 Pions, 842, 843t Pitch, 430 Planck, Max, 640, 641, 705f, 752 Planck’s constant, 705, 706, 713–715, 726, 774 Planck’s formula, 705–708, 713 Plane mirror, 654 Plane polarized light, 696 Planetary (also Solar-system, Nuclear, or Rutherford) model, 768 Planetary motion, 269–289 Plasma, 522 Plates as conductors, 556 Point of incidence, 653, 654f, 666f Point source, 425, 426 Poisson, Simon, 691 Poisson’s Bright Spot, 692 Polar coordinates method, 77, 78 Polarization, 696 Polarizing filters, 696 Porro prism, 674 Position, 6 Position-time graphs, 11–18, 61, 62 Position-time graphs, vs Velocity-time graphs, 25, 26, 28, 41–44 Positron, 804, 836, 837 Positron-emission tomography (PET), 837 Potential energy (see also Elastic potential energy; Gravitational potential energy), 570 Powell
, Cecil Frank, 842 Power, 324–329 Pressure waves, 406, 433 Primary cosmic rays, 841 Principal axis, 657, 677, 678 Principal focal point, 657 Principal focus, 677, 678 Principal quantum number, 774 Principle of superposition, 412, 413 Prisms, 675–677, 771 Projectile, 54, 465 Projectile motion, 54, 102–112, 108–111 Propellar aircraft, 166 Proportionalities, 452 Proton, 497, 498, 513, 529, 790, 792t, 844t, 847 Proton-proton chain, 821 Ptolemy, 214 Pulse, 401–408, 411–413 Pythagorean theorem, 83, 85, 535–537 Q Quadratic equations, 56 Quanta, 640 Quantization of charge, 761–763 Quantized, 705 Quantum, 705 Quantum chromodynamics, 848 Quantum colour, 848 Quantum electrodynamics, 838 Quantum field theory, 837 Quantum indeterminancy, 740 Quantum model (also Quantum theory), 640, 641, 782, 783 Quantum physics, 830–849 Quarks, 845, 846t, 847, 848t Quartz crystals, 387 R Radar vectors, 7 Radial line, 242f–244 Radiation sickness, 808 Radiation, 811–816 Radio frequency signal, 646 Radio waves, 637f, 638t, 645, 646 Radioactive decay, 797–809, 812–814 Radioactive decay series, 807 Radioisotopes, 808, 812–814 Radiotherapy, 815 Radius of celestial bodies, 218t Radius of curvature, 657 Rainbows, 675 Raisin-bun model, 758 Range of a projectile, 105 Rarefaction, 404 Ray diagrams, 653, 654f, 657f–659f, 666f, 678f–681f Rays, 397, 398 Reaction force, 160–167 Real image, 654, 659, 660, 662, 680 Recomposition, 675f, 676 Rectilinear propagation, 653 Reference coordinates, 71 Reference point, 297, 298, 309 Reflected ray, 653, 654f, 666f Reflected wave, 395, 398, 404 Reflection, 653–665 Ref
racted ray, 666 Refraction, 666–681 Refractive index, 666, 667t, 672, 676 Regular (also Specular) reflection, 653 Relative biological effectiveness, 809 Relative motion, 91–100 Resonance, 418–420, 422–424 Resonant frequency, 381–383f, 385, 387, 418, 419 Restoring force, 353, 354, 356, 360, 362, 372, 375 Resultant vector, 71–73 Retinal, 636 Revolution, 249, 251 Revolutions per minute (rpm), 249, 250 Right-hand rule, 833f, 834 Rocket, 167, 459, 460, 475 Rømer, Olaus, 648 Rosette nanotube, 619f Rotational kinetic energy, 302 Rotor (also Armature), 608, 619 Rutherford, Ernest, 513, 767, 790, 797 Rutherford’s scattering experiment, 767 Rydberg, Johannes Robert, 773 Rydberg’s constant, 773, 778 S Safety devices, 463–465 Salaam, Abdus, 848 Satellites, 269–286 Scalar quantity, 6–10, 449 Scanning electron microscope, 727 Schrödinger, Erwin, 783 Secondary cosmic rays, 841 van de Graaf particle accelerator, 841 Semiconductors, 514, 515 Shock wave, 433 Sievert (Sv), 809 Simple harmonic motion, 355–364, 366–379, 381–387, 408 Simple harmonic oscillators, 355, 366–379 Snell, Willebrord, 667 Snell’s law, 667–669, 673 Solenoids, 589 Sonic boom, 433, 434 Sound, 418–420, 422–424, 429–434, 481 Sound barrier, 433 Source charge, 546, 547f, 548f South pole, 582 Spectrometers, 773 Spectroscopy, 771–773 Spectrum, 675, 676, 772 Specular (also Regular) reflection, 653 Speed, 10, 12, 52, 56, 106–111 and power, 327, 328 in circular motion, 242–244, 250, 251, 254, 255, 265–267 of a mass-spring system, 369–372, 374 of a satellite, 277 of a spring pulse, 406, 409 of light
, 636 of sound, 420, 430, 431, 434 Spin, 842 Sports, 466 Spring constant, 350, 351, 357, 374 Spring scale, 128f Spring systems, 349–354 Spring waves, 401, 402 Standard model, 848 Standing wave, 415, 417, 418, 422f, 423f Index 903 22-PearsonPhys-Index 7/25/08 7:40 AM Page 904 Static equilibrium, 555 Static friction, 171–175, 180–183, 258, 259 Statics, 126 Stationary states, 773 Stator, 608 Step leader, 522 Stopping potential, 716, 717 Straight wire, 587 Strange particles, 845 Strange quark, 845, 846t Streamer, 522 String theory, 544, 849 Strong nuclear force, 793, 838t Subatomic models, 845–849 Subatomic particles, 497, 498, 830–849 Sudbury Neutrino Observatory, 498 Sudden infant death syndrome monitors, 615t Sun, 821, 822 Superconductors, 515 Supernova, 823 Superposition, 208–210 Superposition principle, 549 Surfaces, cushioning effects of, 455, 456, 496 electric field lines on, 556, 557 of mirrors, 657 Synchrotron particle accelerator, 841 System, 470 T Tail of a vector, 70–75 Tangent, 24, 25 Tangent function, 535–537 Tangential line, 242f–244 Taylor, Richard, 845 Technologies, 614, 615, 619, 646 Telescopes, 682f Telluric currents, 610 Tension, 132, 134, 135, 264, 356, 463 Terminal velocity, 61 Tesla (T), 585, 834 Test charge, 546, 547f, 548f Thales, 512 Thin lens equation, 680, 681 Thomson, George Paget, 729f Thomson, Joseph John, 754, 757, 758 Thomson, William (also Lord Kelvin), 702f, 703 Threshold frequency, 712, 713, 718 Time, 455–466 Tip of a vector, 70–75 Torsion balance, 205 Total internal reflection, 672 Trajectory, 103 Translational kinetic energy, 302 Transmission electron microscope, 727 Transmutation, 806 Transverse pulse,
401 Transverse waves, 401, 406, 408, 695f Triboelectric series, 518f Trough, 394, 395, 397f, 408 True weight, 222, 223 True weightlessness, 228 Tuned mass damper, 385, 386f Tuning, 424 Turnbull, Wallace Rupert, 166 U Ultraviolet catastrophe, 705 Ultraviolet rays, 637f, 638t Uniform circular motion, 242 Uniform motion, 13, 21–28, 31–44, 104 Uniformly accelerated motion, 25, 52, 104 Universal gravitational constant (G), 204–207, 524 Universal wave equation, 408, 424, 645, 648, 669, 670, 676 Up quark, 845, 846t Uranium-235 fission, 819f V Vacuum, 666, 667t, 668 Van Allen belt, 597 Van de Graaff generator, 560 Vectors, 6–10, 70–75, 77, 78, 83, 84, 127, 449, 451 adding, 71–73, 80–82, 86–89, 489–495, 550, 552 analyzing electrostatic forces, 532–537 subtracting, 73 Velocity, 10, 12–18, 21–28, 31–44, 46–51, 53, 56–62, 91–100, 139 in circular motion, 242–244, 247t in momentum, 448–452, 474 of a mass-spring system, 367, 368 Velocity-time graphs, 21–28, 31–44, 46–50, 62 Vertex, 657, 658 Vertical inversion, 656 Vertical projectiles, 58–62 Virtual image, 654, 659, 660, 662, 680 Virtual particles, 837 Visible ray, 709f Visible spectrum, 637, 638t Volt, 564 Volta, Alessandro, 564 Voltage (also Electric potential), 564, 565 Voltmeter, 604 von Fraunhofer, Josef, 771 Voyager missions, 213, 214 W Water, 666–669 Watt (W), 324 Watt, James, 324 Wave, 394, 395–409, 411–427, 428–434, 639 Wave (also Point) source, 395, 397f, 398 Wave equation, 726, 727 Wave front, 395, 398, 684 Wave model, 639, 640, 669
, 684–698 Wave patterns, 731 Wave train, 395, 417 Wavelength, 395, 397f, 408, 409, 424, 427, 429–432, 636, 637, 676t and angle of diffraction, 690, 691 and Snell’s law, 669, 670 Wavelet, 684 Wave-particle duality, 726, 737–740 Weak nuclear force, 804, 838t Weight (see also Apparent weight; True weight), 128, 197, 198, 216, 219, 220 Weightlessness, 228 Weinberg, Steven, 848 Wheel, 242f, 243 White light, 675–677 Wilson, Charles Thomas Rees, 831 Wind velocity, 92–97 Work function, 712t, 713, 718 Work, 293–304, 306–309, 320, 321, 324, 560–562 and electric potential energy, 563, 567 Work-energy theorem, 307, 308 X X rays, 637f, 638t, 709f, 721, 722 x vector component, 77, 86–89, 105–111, 134, 135 Y y vector component, 77, 86–89, 105–111, 134, 135 Young, Thomas, 639f, 685, 640, 691 Young’s double-slit experiment, 685, 686, 738–740 Z Zero electric potential energy, 562 Zero net forces, 307 Zero reference point, 561, 562 Zweig, George, 845 904 Indexing is changing. Q: In each picture in the Figure 1.1, what is moving and how is its position changing? A: The train and all its passengers are speeding straight down a track to the next station. The man and his bike are racing along a curving highway. The geese are ﬂying over their wetland environment. The meteor is shooting through the atmosphere toward Earth, burning up as it goes. Frame of Reference There’s more to motion than objects simply changing position. You’ll see why when you consider the following example. Assume that the school bus pictured in the Figure 1.2 passes by you as you stand on the sidewalk. It’s obvious to you that the bus is moving, but what about to the children inside the bus? The bus isn’t moving relative to them, and if they look at the
other children sitting on the bus, they won’t appear to be moving either. If the ride 1 www.ck12.org FIGURE 1.1 FIGURE 1.2 is really smooth, the children may only be able to tell that the bus is moving by looking out the window and seeing you and the trees whizzing by. This example shows that how we perceive motion depends on our frame of reference. Frame of reference refers to something that is not moving with respect to an observer that can be used to detect motion. For the children on the bus, if they use other children riding the bus as their frame of reference, they do not appear to be moving. But if they use objects outside the bus as their frame of reference, they can tell they are moving. The video at the URL below illustrates other examples of how frame of reference is related to motion. http://www.youtube.com/watch?v=7FYBG5GSklU MEDIA Click image to the left for more content. Q: What is your frame of reference if you are standing on the sidewalk and see the bus go by? How can you tell that the bus is moving? A: Your frame of reference might be the trees and other stationary objects across the street. As the bus goes by, it momentarily blocks your view of these objects, and this helps you detect the bus’ motion. 2 www.ck12.org Summary Chapter 1. Motion • Motion is deﬁned as a change of position. • How we perceive motion depends on our frame of reference. Frame of reference refers to something that is not moving with respect to an observer that can be used to detect motion. Vocabulary • frame of reference: Something that is not moving with respect to an observer that can be used to detect motion. • motion: Change in position. Practice Do the frame of reference activity at the following URL. Watch the introduction and then do the nine trials. Repeat any trial you answer incorrectly until you get the correct answer. http://www.amnh.org/learn/pd/physical_science/week2/frame_reference.html Review 1. How is motion deﬁned in science? 2. Describe an original example that shows how frame of reference inﬂuences the perception of motion. References 1. Train: John H. Gray; Bike: Flickr:DieselDemon; Geese: Don McCullough; Meteor: Ed Sweeney (Flickr:Navicore).
. CC BY 2.0 2. Bus: Flickr:torbakhopper; Children: Flickr:woodleywonderworks.. CC BY 2.0 3 CHAPTER 2 Position and Displacement www.ck12.org • Deﬁne and give an example of a frame of reference. • Describe the difference between distance and displacement. • Identify the position, distance, and displacements in various descriptions of motions. In stockcar races, the winners frequently travel a distance of 500 miles but at the end of the race, their displacement is only a few feet from where they began. Position, Distance, and Displacement In order to study how something moves, we must know where it is. For straight line motion, it is easy to visualize the object on a number line. The object may be placed at any point on the number line either in the positive numbers or the negative numbers. In making the zero mark the reference point, you have chosen a frame of reference. The position of an object is the separation between the object and the reference point. It is common to choose the original position of the object to be on the zero mark. When an object moves, we often refer to the amount it moves as the distance. Distance does not need a reference point and does not need a direction. If an automobile moves 50 kilometers, the distance traveled is 50 kilometers regardless of the starting point or the direction of movement. If we wish to ﬁnd the ﬁnal position of the automobile, however, just having the distance traveled will not allow us to determine the ﬁnal position. In order to ﬁnd the ﬁnal position of the object, we need to know the starting point and the direction of the motion. The change in the position of the object is called its displacement. The displacement must include a direction because the ﬁnal position may be either in the positive or negative direction along the number line from the initial position. The displacement is a vector quantity and vectors are discussed in another section. Summary • The length traveled by an object moving in any direction or even changing direction is called distance. 4 www.ck12.org Chapter 2. Position and Displacement • The location of an object in a frame of reference is called position. • For straight line motion, positions can be shown using a number line. • The separation between original and ﬁnal position is called displacement. Practice The following url is
for a discussion of the difference between distance and displacement. http://www.tutorvista.com/content/physics/physics-i/motion/distance-and-displacement.php Use this resource to answer the questions that follow. MEDIA Click image to the left for more content. 1. What is the vector equivalent of the scalar “distance”? 2. What is the vector equivalent of the scalar “speed”? Review 1. Explain the difference between distance and displacement in your own words. 2. Suppose that John lives on a square block that is 180 yards per side, and in the evenings, he walks with his dog around the block after dinner for a little exercise. (a) If John walks once around the block, what distance does he travel? (b) If John walks around the block, what is his displacement at the end? 3. Joanna’s house is 8000 feet due west of her school. If her house is assigned the position of zero and her school is assigned the possition of +8000, what would Joanna’s position be if she walked 100 feet west of her house? • distance: The space between two objects but this is not adequate when considering the distance travelled. The distance travelled cannot be negative and can never get smaller –in this sense, distance is the total length of path traversed by the moving body irrespective of direction. • displacement: The vector from the initial position to a subsequent position assumed by a body. References 1. Image copyright Action Sports Photography, 2013. http://www.shutterstock.com. Used under license from Shutterstock.com 5 CHAPTER 3 • Distinguish between velocity and speed. • Represent velocity with vector arrows. • Describe objects that have different velocities. • Show how to calculate average velocity when direction is constant. www.ck12.org Velocity Ramey and her mom were driving down this highway at 45 miles per hour, which is the speed limit on this road. As they approached this sign, Ramey’s mom put on the brakes and started to slow down so she could safely maneuver the upcoming curves in the road. This speed limit sign actually represents two components of motion: speed and direction. Speed and Direction Speed tells you only how fast or slow an object is moving. It doesn’t tell you the direction the object is moving. The measure of both speed and direction is called velocity. Velocity is a vector. A
vector is measurement that includes both size and direction. Vectors are often represented by arrows. When using an arrow to represent velocity, the length of the arrow stands for speed, and the way the arrow points indicates the direction. If you’re still not sure of the difference between speed and velocity, watch the cartoon at this URL: http://www.youtube.com/watch?v=mDcaeO0WxBI MEDIA Click image to the left for more content. 6 www.ck12.org Chapter 3. Velocity Using Vector Arrows to Represent Velocity The arrows in the Figure 3.1 represent the velocity of three different objects. Arrows A and B are the same length but point in different directions. They represent objects moving at the same speed but in different directions. Arrow C is shorter than arrow A or B but points in the same direction as arrow A. It represents an object moving at a slower speed than A or B but in the same direction as A. FIGURE 3.1 Differences in Velocity Objects have the same velocity only if they are moving at the same speed and in the same direction. Objects moving at different speeds, in different directions, or both have different velocities. Look again at arrows A and B from the Figure 3.1. They represent objects that have different velocities only because they are moving in different directions. A and C represent objects that have different velocities only because they are moving at different speeds. Objects represented by B and C have different velocities because they are moving in different directions and at different speeds. Q: Jerod is riding his bike at a constant speed. As he rides down his street he is moving from east to west. At the end of the block, he turns right and starts moving from south to north, but he’s still traveling at the same speed. Has his velocity changed? A: Although Jerod’s speed hasn’t changed, his velocity has changed because he is moving in a different direction. Q: How could you use vector arrows to represent Jerod’s velocity and how it changes? A: The arrows might look like this (see Figure 3.2): FIGURE 3.2 7 Calculating Average Velocity You can calculate the average velocity of a moving object that is not changing direction by dividing the distance the object travels by the time it takes to travel that distance. You would use this formula: www.ck12.org velocity = distance time This is the same formula
that is used for calculating average speed. It represents velocity only if the answer also includes the direction that the object is traveling. Let’s work through a sample problem. Toni’s dog is racing down the sidewalk toward the east. The dog travels 36 meters in 18 seconds before it stops running. The velocity of the dog is: velocity = distance time 36 m 18 s = 2 m/s east = Note that the answer is given in the SI unit for velocity, which is m/s, and it includes the direction that the dog is traveling. Q: What would the dog’s velocity be if it ran the same distance in the opposite direction but covered the distance in 24 seconds? A: In this case, the velocity would be: velocity = = distance time 36 m 24 s = 1:5 m/s west Summary • Velocity is a measure of both speed and direction of motion. Velocity is a vector, which is a measurement that includes both size and direction. • Velocity can be represented by an arrow, with the length of the arrow representing speed and the way the arrow points representing direction. • Objects have the same velocity only if they are moving at the same speed and in the same direction. Objects moving at different speeds, in different directions, or both have different velocities. • The average velocity of an object moving in a constant direction is calculated with the formula: velocity = distance time. The SI unit for velocity is m/s, plus the direction the object is traveling. Vocabulary • vector: Measure such as velocity that includes both size and direction; may be represented by an arrow. • velocity: Measure of both speed and direction of motion. 8 www.ck12.org Practice Chapter 3. Velocity At the following URL, review how to calculate speed and velocity, and work through the sample problems. Then solve the 10 practice problems. http://www2.franciscan.edu/academic/mathsci/mathscienceintegation/MathScienc eIntegation-827.htm Review 1. What is velocity? 2. How does velocity differ from speed? Why is velocity a vector? 3. Explain how an arrow can be used to represent velocity. 4. Use vector arrows to represent the velocity of a car that travels north at 50 mi/h and then travels east at 25 mi/h. 5. Another car travels northwest for 2 hours and covers a distance of 90 miles. What is the average velocity of the car? References 1
. Christopher Auyeung (CK-12 Foundation); Compass: Seamus McGill.. CC BY-NC 3.0; Compass: Public Domain 2... CC BY-NC 3.0 9 www.ck12.org Average Velocity CHAPTER 4 • Explain the difference between speed and velocity. • Deﬁne the concept of average velocity. • Given displacement and time, calculate average velocity. • Solve for any variable in the equation Vave = Dx Dt Test Pilot Neil Armstrong (later to become a famous astronaut) is seen here next to the X-15 ship after a research ﬂight. Armstrong made his ﬁrst X-15 ﬂight on November 30, 1960. This was the ﬁrst X-15 ﬂight to use the ball nose, which provided accurate measurement of air speed at hypersonic speeds. The servo-actuated ball nose can be seen in this photo in front of Armstrong’s right hand. The X-15 employed a non-standard landing gear. It had a nose gear with a wheel and tire, but the main landing consisted of skids mounted at the rear of the vehicle. In the photo, the left skid is visible, as are marks on the lakebed from both skids. Because of the skids, the rocket-powered aircraft could only land on a dry lakebed, not on a concrete runway. The X-15 weighed about 14,000 lb empty and approximately 34,000 lb at launch. The X-15 was ﬂown over a period of nearly 10 years – June 1959 to Oct. 1968 – and set the world’s unofﬁcial speed record of 4,520 mph. Average Velocity The terms speed and velocity are used interchangeably in ordinary language. In physics, however, we make a distinction between the two. Essentially both words refer to how fast an object is moving. Speed is the number we read off the speedometer of a car. It indicates how fast the car is moving at any instant but given no indication of the direction it is moving. For a particular time interval, average speed would be calculated by dividing the distance travelled by the time interval of travel. Velocity, in physics, is a vector, meaning that it must have a direction as well as a magnitude. Furthermore, the average velocity is deﬁned in terms of displacement rather than distance. Average 10 www.ck12.
org Chapter 4. Average Velocity velocity would be calculated by dividing the displacement by the time interval where displacement is the change in position of the object. To show the distinction, we could calculate the average speed and the average velocity of a person who walks 50 m to the east, then turns around and walks 50 m to the west. The total time interval is 20 seconds. The distance traveled in this trip is 100 m but the displacement is zero. The average speed would be calculated by dividing 100 m by 20 s with a result of 5 m/s. The average velocity, on the other hand, would be calculated by dividing 0 m by 20 s giving a result of 0 m/s. Neither average speed nor average velocity implies a constant rate of motion. That is to say, an object might travel at 10 m/s for 10 s and then travel at 20 m/s for 5 s and then travel at 100 m/s for 5s. This motion would cover a distance of 700 m in 20 s and the average speed would be 35 m/s. We would report the average speed during this 20 s interval to be 35 m/s and yet at no time during the interval was the speed necessarily 35 m/s. The concept of constant velocity is very different from average velocity. If an object traveled at 35 m/s for 20 s, it would travel the same distance in the same time as the previous example but in the second case, the speed of the object would always be 35 m/s. Example: The position of a runner as a function of time is plotted as moving along the x-axis of a coordinate system. During a 3.00 s time interval, the runner’s position changes from x1 = 50:0 m to x2 = 30:5 m. What was the runner’s average velocity. Solution: Displacement = 30:5 m 50:0 m = 19:5 m (the object was traveling back toward zero) Dt = 3:00 s vave = Dx Dt = 19:5 m 3:00 s = 6:50 m/s Summary • Average speed is distance divided by time. • Average velocity is displacement divided by time. Practice The url below is a physics classroom discussion of speed versus velocity with a short animation. http://www.physicsclassroom.com/Class/1DKin/U1L1d.cfm Use this resource to answer the questions that follow. http://www.youtube
.com/watch?v=BWP1tN7PZps MEDIA Click image to the left for more content. 1. The velocity versus time graph in the video is divided into six sections. In how many of these sections is the velocity constant? 2. In how many sections of the graph is the velocity zero? 3. What does the area under the curve of a velocity versus time graph represent? 11 www.ck12.org Review 1. On a one day vacation, Jane traveled 340 miles in 8.0 hours. What was her average speed? 2. An object on a number line moved from x = 12 m to x = 124 m and moved back to x = 98 m. The time interval for all the motion was 10. s. What was the average velocity of the object? 3. An object on a number line moved from x = 15 cm to x = 165 cm and then moved back to x = 25 cm all in a time of 100 seconds. (a) What was the average velocity of the object? (b) What was the average speed of the object? • speed: Distance travelled per unit time. • velocity: A vector measurement of the rate and direction of motion or, in other terms, the rate and direction of the change in the position of an object. References 1. Courtesy of NASA. http://commons.wikimedia.org/wiki/File:Pilot_Neil_Armstrong_and_X-15.jpg. Public Domain 12 www.ck12.org Chapter 5. Instantaneous Velocity CHAPTER 5 Instantaneous Velocity • Deﬁne instantaneous velocity. • Plot and interpret position vs time graphs. • Determine the slope of a curve on a position vs time graph. In a footrace such as the one shown here, the initial velocity of a runner is zero. The runner increases his velocity out of the starting blocks and his velocity continues to increase as the race proceeds. For the well-trained athlete, his highest velocity is maintained through the ﬁnish line. Instantaneous Velocity The instantaneous velocity of an object is the precise velocity at a given moment. It is a somewhat difﬁcult quantity to determine unless the object is moving with constant velocity. If the object is moving with constant velocity, then the instantaneous velocity at every instant, the average velocity, and the constant velocity are all exactly the same. Position vs Time Graphs Consider a position versus time graph for an object starting at t = 0
and x = 0 that has a constant velocity of 80. m/s. 13 www.ck12.org The velocity of an object can be found from a position vs time graph. On a position vs time graph, the displacement The ratio of is the vertical separation between two points and the time interval is the horizontal separation. displacement to time interval is the average velocity. The ratio of the vertical separation to the horizontal separation is also the slope of the line. Therefore, the slope of straight line is the average velocity. The slope at any given time is the instantaneous velocity. For the motion pictured above, slope = rise run = Dd Dt = 400: m 5:0 s = 80: m/s For accelerated motion (the velocity is constantly changing), the position vs time graph will be a curved line. The slope of the curved line at any point will be the instantaneous velocity at that time. If we were using calculus, the slope of a curved line could be calculated. Since we are not using calculus, we can only approximate the slope of curved line by laying a straight edge along the curved line and guessing at the slope. 14 www.ck12.org Chapter 5. Instantaneous Velocity In the image above, the red line is the position vs time graph and the blue line is an approximated slope for the line at t = 2:5 seconds. The rise for this slope is approximately 170 m and the time interval (run) is 4.0 seconds. Therefore, the approximated slope is 43 m/s. Summary • The slope of a position versus time graph is the velocity. For a constant velocity motion, the slope gives the constant velocity, the average velocity, and the instantaneous velocity at every point. For constant acceleration motion, the slope of the position versus time curve gives only the instantaneous velocity at that point. Practice Draw a velocity versus time graph for an object whose constant velocity is 15 m/s and whose position starts at x = 0 when t = 0. Graph the motion for the ﬁrst 5.0 seconds. Use this resource to answer the questions that follow. http://www.youtube.com/watch?v=sujsb5ZlM8o MEDIA Click image to the left for more content. 1. In the graph on the video, what is graphed on the vertical axis? 2. What is graphed on the horizontal axis. 3. What does the slope of this graph represent? Review 1. For the motion graphed
in the position versus time graph shown above, what is the average velocity in the time interval 1 to 3 seconds? 2. For the motion graphed in the position versus time graph shown above, what is the average velocity in the time interval 3 to 4 seconds? 3. For the motion graphed in the position versus time graph shown above, what is the average velocity in the time interval 5 to 6 seconds? 15 • instantaneous velocity: The velocity of an object at any given instant. www.ck12.org References 1. Image copyright Denis Kuvaev, 2013. http://www.shutterstock.com. Used under license from Shutterstock.com 2. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 3. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 4. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 16 www.ck12.org Chapter 6. Average Acceleration CHAPTER 6 Average Acceleration • Deﬁne average acceleration. • Given initial velocity, ﬁnal velocity and time, calculate acceleration. • Given three of initial velocity, acceleration, time, and ﬁnal velocity, calculate the fourth. End of an era. The Space Shuttle Atlantis blasts off on mission STS-125, the ﬁnal mission to service and upgrade the Hubble Space Telescope, one of NASA’s greatest legacies and triumphs. Canceled in the wake of the Columbia tragedy and then reinstated, the only mission not to go to the international space station post-accident will see seven astronauts undertake one of the most ambitious shuttle missions in history, with ﬁve spacewalks to install new and replace old components on Hubble. It will be the closing chapter in one of the original purposes of the shuttle. Average Acceleration An object whose velocity is changing is said to be accelerating. Average acceleration, a is deﬁned as the rate of change of velocity, or the change in velocity per unit time. A symbol with a bar over it is read as average –so a-bar is average acceleration. Example: A car accelerates along a straight road from rest to 60. km/h in 5.0 s. What is the magnitude of its average acceleration? Solution: This is read as kilometers per hour per second. In general, it is undesirable to have to different units for the same quantity in
a unit expression. For example, in this case, it is undesirable to have two different units for time (hours and seconds) in the same unit expression. To eliminate this problem, we would convert the hour units to seconds. If we converted the original 60. km/h to m/s, it would be 17 m/s. Then the acceleration would be 3.4 m/s2. Example: An automobile is moving along a straight highway in the positive direction and the driver puts on If the initial velocity is 15.0 m/s and 5.0 s is required to slow down to 5.0 m/s, what was the car’s the brakes. acceleration? 17 www.ck12.org Solution: a = Dv Dt = 10: m/s 5:0 s = 2:0 m/s/s Summary • Average acceleration is the rate of change of velocity, or the change in velocity per unit time. Practice The following url has a lesson on the difference between average and instantaneous acceleration and practice calculating average acceleration. http://www.brighthubeducation.com/homework-math-help/102434-deﬁnition-and-how-to-calculate-acceleration/ Review 1. The velocity of a car increases from 2.0 m/s to 16.0 m/s in a time period of 3.5 s. What was the average acceleration? 2. If an automobile slows from 26 m/s to 18 m/s in a period of 4.0 s, what was the average acceleration? 3. If a runner increases his velocity from 0 m/s to 20 m/s in 2.0 s, what was his average acceleration? 4. If a runner decreases his velocity from 20 m/s to 10 m/s in 2.0 s, what was his average acceleration? • average acceleration: The change in velocity over the change in time. References 1. Courtesy of NASA. http://spaceﬂight.nasa.gov/gallery/images/shuttle/sts-125/html/sts125-s-025.html. Public Domain 18 www.ck12.org Chapter 7. Uniform Acceleration CHAPTER 7 Uniform Acceleration • Deﬁne uniform acceleration. • Given initial velocity, acceleration, and time, calculate ﬁnal velocity. Wingtip vortices are often thought to be a type of contrail but are
actually produced from a different process. During very speciﬁc weather conditions you may see vapor trails form at the rear of the wingtips of jet aircraft on takeoff or landing. This phenomenon occurs due to a decrease in pressure and temperature as the wing generates lift. The image is an F-35 departing from Elgin Air Force Base in Florida. Uniform Acceleration Acceleration that does not change in time is called uniform or constant acceleration. The velocity at the beginning of the time interval is called initial velocity, vi, and the velocity at the end of the time interval is called ﬁnal velocity, v f. In a velocity versus time graph for uniform acceleration, the slope of the line is the acceleration. The equation that describes the curve is v f = vi + at. Example: velocity? If an automobile with a velocity of 4.0 m/s accelerates at a rate of 4.0 m/s2 for 2.5 s, what is the ﬁnal Solution: v f = vi + at = 4:0 m/s + (4:0 m/s2)(2:5 s) = 4:0 m/s + 10: m/s = 14 m/s Example: If a cart slows from 22.0 m/s to 4.0 m/s with an acceleration of -2.0 m/s2, how long does it require? Solution: t = v f vi a = 18 m/s 2:0 m/s2 = 9:0 s 19 www.ck12.org Summary • Acceleration that does not change in time is uniform or constant acceleration. • The equation relating initial velocity, ﬁnal velocity, time, and acceleration is v f = vi + at. Practice The following url has instruction in one dimensional uniformly accelerated motion and it also has a series of practice problems. http://dallaswinwin.com/Motion_in_One_Dimension/uniform_accelerated_motion.htm Review 1. If an object has zero acceleration, does that mean it has zero velocity? Give an example. 2. If an object has zero velocity, does that mean it has zero acceleration? Give an example. 3. If the acceleration of a motorboat is 4.0 m/s2, and the motorboat starts from rest, what is its velocity after 6.0 s? 4. The friction of the water on a boat produces an acceleration of -10
. m/s2. If the boat is traveling at 30. m/s and the motor is shut off, how long it take the boat to slow down to 5.0 m/s? • uniform acceleration: Acceleration that does not change in time is uniform or constant acceleration. References 1. Courtesy of Senior Airman Julianne Showalter/U.S. Air Force. http://www.af.mil/news/story.asp?id=1232 61835. Public Domain 20 www.ck12.org Chapter 8. Displacement During Constant Acceleration CHAPTER 8 Displacement During Constant Acceleration • Plot and interpret a velocity vs time graph. • Find the area under a curve on a velocity vs time graph and calculate the displacement from such a graph. • Calculate the displacement of an object undergoing uniform acceleration when given two of the three quanti- ties acceleration, time, velocity. Long distance runners try to maintain constant velocity with very little acceleration or deceleration because acceleration requires more energy than simply maintaining velocity. Displacement During Constant Acceleration When the acceleration is constant, there are three equations that relate displacement to two of the other three It is absolutely vital that you do NOT quantities we use to describe motion –time, velocity, and acceleration. try to use these equations when the acceleration is NOT constant. Fortunately, there are quite a few cases of motion where the acceleration is constant. One of the most common, if we ignore air resistance, are objects falling due to gravity. When an object is moving with constant velocity, the displacement can be found by multiplying the velocity by the time interval. d = vt If the object is moving with constant acceleration, the velocity in that equation is replaced with the average velocity. The average velocity for a uniformly accelerated object can be found by adding the beginning and ﬁnal velocities and dividing by 2. vave = 1 2 (v f + vi) The distance, then, for uniformly accelerating motion can be found by multiplying the average velocity by the time. 21 d = 1 2 (v f + vi)(t) (Equation 1) We know that the ﬁnal velocity for constantly accelerated motion can be found by multiplying the acceleration times time and adding the result to the initial velocity, v f = vi + at. The second equation that relates, displacement, time, initial velocity, and ﬁnal velocity is generated by substituting into equation 1. www.ck12.org
d = 1 2 (v f + vi)(t vit but v f = vi + at and substituting for v f yields d = 1 2 vit + d = vit + 1 2 1 2 at2 (t)(vi + at) = 1 2 vit + 1 2 vit + at2 1 2 (Equation 2) The third equation is formed by combining v f = vi + at and d = 1 and then substitute into the second equation, we get 2 (v f + vi)(t). If we solve the ﬁrst equation for t d = 1 2 (v f + vi) v f vi a = 1 2 v2 f v2 i a And solving for v f 2 yields v f 2 = vi 2 + 2ad (Equation 3) Keep in mind that these three equations are only valid when acceleration is constant. velocity can be set to zero and that simpliﬁes the three equations considerably. In many cases, the initial With both constant acceleration and initial velocity of zero = 2ad: d = at2 and v f Example: Suppose a planner is designing an airport for small airplanes. Such planes must reach a speed of 56 m/s before takeoff and can accelerate at 12.0 m/s2. What is the minimum length for the runway of this airport? Solution: The acceleration in this problem is constant and the initial velocity of the airplane is zero, therefore, we can use the equation v f 2a = (56 m/s)2 d = v f (2)(12:0 m/s2 2 = 2ad and solve for d. = 130 m ) 2 Example: How long does it take a car to travel 30.0 m if it accelerates from rest at a rate of 2.00 m/s2? Solution: The acceleration in this problem is constant and the initial velocity is zero, therefore, we can use d = 1 solved for t. r s 2 at2 t = 2d a = (2)(30:0 m) 2:00 m/s2 = 5:48 s Example: A baseball pitcher throws a fastball with a speed of 30.0 m/s. Assuming the acceleration is uniform and the distance through which the ball is accelerated is 3.50 m. What is the acceleration? 22 www.ck12.org Chapter 8. Displacement During Constant Acceleration Solution: Since the acceleration is uniform and the initial velocity is zero, we can use v f 2
= 2ad solved for a. a = v2 f 2d = (30:0 m/s)2 (2)(3:50 m) = 900: m2=s2 7:00 m = 129 m/s2 Suppose we plot the velocity versus time graph for an object undergoing uniform acceleration. In this ﬁrst case, we will assume the object started from rest. If the object has a uniform acceleration of 6.0 m/s2 and started from rest, then each succeeding second, the velocity will increase by 6.0 m/s. Here is the table of values and the graph. In displacement versus time graphs, the slope of the line is the velocity of the object and in this case of velocity versus time graph, the slope of the line is the acceleration. If you take any segment of this line and determine the Dy to Dx ratio, you will get 6.0 m/s2 which we know to be the constant acceleration of this object. The area of a triangle is calculated by multiplying one-half the base times the height. The area under the curve in the image above is the area of the triangle shown below. 23 www.ck12.org The area of this triangle would be calculated by area = 1 2 The distance traveled by an object accelerating uniformly from rest at 6.0 m/s2 would be displacement = 1 (6:0 s)(36 m/s) = 108 m. 2 at2. Therefore, the displacement of this object in the ﬁrst 6 seconds of travel would be displacement = 1 2 (6:0 m/s2)(6:0 s)2 = 108 m. In fact, the area underneath the curve in a velocity versus time graph is always equal to the displacement that occurs during that time interval. Summary • There are three equations relating displacement to two of the other three quantities we use to describe motion –time, velocity, and acceleration: – d = 1 2 – d = vit + 1 2 = vi – v f (v f + vi)(t) (Equation 1) 2 at2 (Equation 2) 2 + 2ad (Equation 3) • When the initial velocity of the object is zero, these three equations become: (v f )(t) (Equation 1’) – d = 1 2 – d = 1 2 at2 (Equation 2’) 2 = 2ad (Equation 3’) – v f
• The slope of a velocity versus time graph is the acceleration of the object. • The area under the curve of a velocity versus time graph is the displacement that occurs during the given time interval. Practice Use this resource to answer the questions that follow. MEDIA Click image to the left for more content. 1. For the example in the video, what acceleration is used? 2. What time period is used in the example? 3. What does the slope of the line in the graph represent? 4. What does the area under the curve of the line represent? Review 1. An airplane accelerates with a constant rate of 3.0 m/s2 starting at a velocity of 21 m/s. If the distance traveled during this acceleration was 535 m, what is the ﬁnal velocity? 2. An car is brought to rest in a distance of 484 m using a constant acceleration of -8.0 m/s2. What was the velocity of the car when the acceleration ﬁrst began? 3. An airplane starts from rest and accelerates at a constant 3.00 m/s2 for 20.0 s. What is its displacement in this time? 4. A driver brings a car to a full stop in 2.0 s. 24 www.ck12.org Chapter 8. Displacement During Constant Acceleration (a) If the car was initially traveling at 22 m/s, what was the acceleration? (b) How far did the car travel during braking? References 1. Image copyright Maridav, 2013. http://www.shutterstock.com. Used under license from Shutterstock.com 2. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 3. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 25 CHAPTER 9 Acceleration Due to Gravity www.ck12.org • Solve problems of the motion of objects uniformly accelerated by gravity. In the absence of air resistance, all objects fall toward the earth with the same acceleration. Man, however, make maximum use of air resistance in the construction of parachutes for both entertainment and military use. The image at left was taken during a 2008 Graduation demonstration jump by the U.S. Army Parachute Team. The 2008 team contained the ﬁrst amputee member and the largest number of females in history. Acceleration Due to Gravity One of the most common examples of uniformly accelerated
motion is that an object allowed to fall vertically to the earth. In treating falling objects as uniformly accelerated motion, we must ignore air resistance. Galileo’s original statement about the motion of falling objects is: At a given location on the earth and in the absence of air resistance, all objects fall with the same uniform acceleration. We call this acceleration due to gravity on the earth and we give it the symbol g. The value of g is 9.80 m/s2. All of the equations involving constant acceleration can be used for falling bodies but we insert g wherever “a” appeared and the value of g is always 9.80 m/s2. Example: A rock is dropped from a tower 70.0 m high. How far will the rock have fallen after 1.00 s, 2.00 s, and 3.00 s? Assume the distance is positive downward. 26 www.ck12.org Chapter 9. Acceleration Due to Gravity Solution: We are looking for displacement and we have time and acceleration. Therefore, we can use d = 1 Displacement after 1:00 s = 1 2 Displacement after 2:00 s = 1 2 Displacement after 3:00 s = 1 2 (9:80 m/s2)(1:00 s)2 = 4:90 m (9:80 m/s2)(2:00 s)2 = 19:6 m (9:80 m/s2)(3:00 s)2 = 44:1 m 2 at2. Example: (a) A person throws a ball upward into the air with an initial velocity of 15.0 m/s. How high will it go before it comes to rest? (b) How long will the ball be in the air before it returns to the person’s hand? Solution: In part (a), we know the initial velocity (15.0 m/s), the ﬁnal velocity (0 m/s), and the acceleration -9.80 m/s2. We wish to solve for the displacement, so we can use v f d = v f 2 + 2ad and solve for d. 2a = (0 m/s)2(15:0 m/s)2 2vi = 11:5 m 2 = vi 2 (2)(9:80 m/s2 ) There are a number of methods by which we can solve part (b). Probably the easiest is to divide
the distance traveled by the average velocity to get the time going up and then double this number since the motion is symmetrical –that is, time going up equals the time going down. The average velocity is half of 15.0 m/s or 7.5 m/s and dividing this into the distance of 11.5 m yields 1.53 seconds. This is the time required for the ball to go up and the time for the ball to come down will also be 1.53 s, so the total time for the trip up and down is 3.06 seconds. Example: A car accelerates with uniform acceleration from 11.1 m/s to 22.2 m/s in 5.0 s. acceleration and (b) how far did it travel during the acceleration? (a) What was the Dt = 22:2 m/s11:1 m/s Solution: (a) a = Dv (b) We can ﬁnd the distance traveled by d = vit + 1 average velocity and multiply it by the time. = 2:22 m/s2 5:0 s 2 at2 and we can also ﬁnd the distance traveled by determining the d = vit + at2 1 2 = (11:1 m/s)(5:0 s) + = 55:5 m + 27:8 m = 83 m 1 2 (2:22 m/s2)(5:0 s)2 d = (vave)(t) = (16:6 m/s)(5:0 s) = 83 m Example: A stone is dropped from the top of a cliff. It is seen to hit the ground after 5.5 s. How high is the cliff? Solution: d = vit + 1 2 at2 = (0 m/s)(5:5 s) + 1 2 (9:80 m/s2)(5:5 s)2 = 150 m Summary • At a given location on the earth and in the absence of air resistance, all objects fall with the same uniform acceleration. • We call this acceleration the acceleration due to gravity on the earth and we give it the symbol g. • The value of g is 9.80 m/s2. 27 Practice This url shows a video of a discussion and demonstration of the acceleration due to gravity. http://www.youtube.com/watch?v=izXGpivLvgY www.ck12.org MEDIA Click image to the
left for more content. Review 1. A baseball is thrown vertically into the air with a speed of 24.7 m/s. (a) How high does it go? (b) How long does the round trip up and down require? 2. A salmon jumps up a waterfall 2.4 m high. With what minimum speed did the salmon leave the water below to reach the top? 3. A kangaroo jumps to a vertical height of 2.8 m. How long will it be in the air before returning to earth? • acceleration due to gravity: The acceleration experienced by a body in free fall in a gravitational ﬁeld. References 1. Courtesy of Donna Dixon/U.S. Military. http://commons.wikimedia.org/wiki/File:Flickr_-_The_U.S._Arm y_-_U.S._Army_Parachute_Team_graduates_first_wounded_warrior_and_largest_female_class_%282%29.jp g. Public Domain 28 www.ck12.org Chapter 10. Graphing Motion CHAPTER 10 Graphing Motion Students will learn how to graph motion vs time. Speciﬁcally students will learn how to take the slope of a graph and relate that to the instantaneous velocity or acceleration for position or velocity graphs, respectively. Finally students will learn how to take the area of a velocity vs time graph in order to calculate the displacement. Students will learn how to graph motion vs time. Speciﬁcally students will learn how to take the slope of a graph and relate that to the instantaneous velocity or acceleration for position or velocity graphs, respectively. Finally students will learn how to take the area of a velocity vs time graph in order to calculate the displacement. Key Equations For a graph of position vs. time. The slope is the rise over the run, where the rise is the displacement and the run is the time. thus, Slope = vavg = Dx Dt Note: Slope of the tangent line for a particular point in time = the instantaneous velocity For a graph of velocity vs. time. The slope is the rise over the run, where the rise is the change in velocity and the run is the time. thus, Slope = aavg = Dv Dt Note: Slope of the tangent line for a particular point in time = the instantaneous acceleration Guidance • One must ﬁrst
read a graph correctly. For example on a position vs. time graph (thus the position is graphed on the y-axis and the time on the x-axis) for a given a data point, go straight down from it to get the time and straight across to get the position. • If there is constant acceleration the graph x vs. t produces a parabola. The slope of the x vs. t graph equals the instantaneous velocity. The slope of a v vs. t graph equals the acceleration. • The slope of the graph v vs. t can be used to ﬁnd acceleration; the area of the graph v vs. t can be used to ﬁnd displacement. Welcome to calculus! What is a Graph Watch this Explanation MEDIA Click image to the left for more content. 29 www.ck12.org MEDIA Click image to the left for more content. MEDIA Click image to the left for more content. MEDIA Click image to the left for more content. Time for Practice 1. The position graph below is of the movement of a fast turtle who can turn on a dime. a. Sketch the velocity vs. time graph of the turtle below. 30 www.ck12.org Chapter 10. Graphing Motion b. Explain what the turtle is doing (including both speed and direction) from: i) 0-2s. ii) 2-3s. iii) 3-4s. c. How much distance has the turtle covered after 4s? d. What is the turtle’s displacement after 4s? 2. Draw the position vs. time graph that corresponds to the velocity vs. time graph below. You may assume a starting position x0 = 0. Label the yaxis with appropriate values. 3. The following velocity-time graph represents 10 seconds of actress Halle Berry’s drive to work (it’s a rough morning). 31 a. Fill in the tables below –remember that displacement and position are not the same thing! www.ck12.org 32 www.ck12.org Chapter 10. Graphing Motion TABLE 10.1: Displacement (m) Acceleration(m=s2) Instantaneous Time (s) 0 sec Position (m) 0 m 2 sec 4 sec 5 sec 9 sec 10 sec Interval (s) 0-2 sec 2-4 sec 4-5 sec 5-9 sec 9-10 sec b. On the axes below, draw an acceleration
-time graph for the car trip. Include numbers on your acceleration axis. c. On the axes below, draw a position-time graph for the car trip. Include numbers on your position axis. Be sure to note that some sections of this graph are linear and some curve –why? 4. Two cars are drag racing down El Camino. At time t = 0, the yellow Maserati starts from rest and accelerates at 10 m=s2. As it starts to move it’s passed by a ’63 Chevy Nova (cherry red) traveling at a constant velocity of 30 m/s. a. On the axes below, show a line for each car representing its speed as a function of time. Label each line. 33 www.ck12.org b. At what time will the two cars have the same speed (use your graph)? (or curve) for each car representing its position as a function of time. Label each curve. c. On the axes below, draw a line d. At what time would the two cars meet (other than at the start)? Answers: 1c. 25 m 1d. -5 m 2. discuss in class 3. discuss in class 4b. 3 sec 4d. 6 sec 34 Physics Unit 3 (Vectors) Patrick Marshall Ck12 Science Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) www.ck12.org To access a customizable version of this book, as well as other interactive content, visit www.ck12.org AUTHORS Patrick Marshall Ck12 Science CK-12 Foundation is a non-proﬁt organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Using an open-content, web-based collaborative model termed the FlexBook®, CK-12 intends to pioneer the generation and distribution of high-quality educational content that will serve both as core text as well as provide an adaptive environment for learning, powered through the FlexBook Platform®. Copyright © 2014 CK-12 Foundation, www.ck12.org The names “CK-12” and “CK12” and associated logos and the terms “FlexBook®” and “FlexBook Platform®” (collectively “CK-12 Marks”) are trademarks and service marks of CK-12 Foundation and are
protected by federal, state, and international laws. Any form of reproduction of this book in any format or medium, in whole or in sections must include the referral attribution link http://www.ck12.org/saythanks (placed in a visible location) in addition to the following terms. Except as otherwise noted, all CK-12 Content (including CK-12 Curriculum Material) is made available to Users in accordance with the Creative Commons Attribution-Non-Commercial 3.0 Unported (CC BY-NC 3.0) License (http://creativecommons.org/ licenses/by-nc/3.0/), as amended and updated by Creative Commons from time to time (the “CC License”), which is incorporated herein by this reference. Complete terms can be found at http://www.ck12.org/terms. Printed: February 4, 2014 iii Contents www.ck12.org Contents 1 Graphical Methods of Vector Addition 2 Vector Addition 1 5 iv www.ck12.org Chapter 1. Graphical Methods of Vector Addition CHAPTER 1 Graphical Methods of Vector Addition • Differentiate between scalars and vectors. • Graphically add vectors in one dimension by placing the vectors head to toe on a number line. • Deﬁne resultant. • Graphically add vectors in two dimensions by placing them head to toe on a two-dimensional coordinate system. Successfully shooting a basketball requires a subconscious understanding of the vectors involved in how the basketball moves through the air. The vertical and horizontal vectors must be perfectly organized if the ball is to pass through the basket. Graphical Methods Vector Addition In physics, a quantity, such as mass, length, or speed, that is completely speciﬁed by its magnitude and has no direction is called a scalar. A vector, on the other hand, is a quantity possessing both magnitude and direction. A vector quantity can be represented by an arrow-tipped line segment. The length of the line, drawn to scale, represents the magnitude of the quantity. The direction of the arrow indicates the direction of the vector. Not only can vectors be represented graphically, but they can also be added graphically. For one dimensional vector addition, the ﬁrst vector is placed on a number line with the tail of the vector on the origin. The second vector is placed with its tail exactly on the arrow head of the ﬁrst vector. The sum of the two vectors
is the vector that begins at the origin and ends at the arrow head of the ﬁnal added vector. Consider the following two vectors. 1 www.ck12.org The red vector has a magnitude of 11 in the positive direction on the number line. The blue vector has a magnitude of -3 in the negative direction on the number line. In order to add these two vectors, we place one of the vectors on a number line and then the second vector is placed on the same number line such that its origin is on the arrow head of the ﬁrst vector. The sum of these two vectors is the vector that begins at the origin of the ﬁrst vector (the red one) and ends at the arrow head of the blue vector. So the sum of these two vectors is the purple vector as shown below. The vector sum of the ﬁrst two vectors is a vector that begins at the origin and has a magnitude of 8 units in the positive direction. If we were adding three or four vectors all in one dimension, we would continue to place them head to toe in sequence on the number line. The sum would be the vector that begins at the beginning of the ﬁrst vector and goes to the ending of the ﬁnal vector. Adding Vectors in Two Dimensions In the following image, vectors A and B represent the two displacements of a person who walked 90. m east and then 50. m north. We want to add these two vectors to get the vector sum of the two movements. The graphical process for adding vectors in two dimensions is to place the tail of the second vector on the arrow head of the ﬁrst vector as shown above. The sum of the two vectors is the vector that begins at the origin of the ﬁrst vector and goes to the ending of the second vector, as shown below. 2 www.ck12.org Chapter 1. Graphical Methods of Vector Addition If we are using totally graphic means of adding these vectors, the magnitude of the sum would be determined by measuring the length of the sum vector and comparing it to the original standard. We would also use a compass to measure the angle of the summation vector. If we are using calculation means, we can determine the inverse tangent of 50 units divided by 90 units and get the angle of 29° north of east. The length of the sum vector can also be determined mathematically by the Pythagorean theorem,
a2 + b2 = c2. In this case, the length of the hypotenuse would be the square root of (8100 + 2500) or 103 units. If three or four vectors are to be added by graphical means, we would continue to place each new vector head to toe with the vectors to be added until all the vectors were in the coordinate system and then the sum vector would be the vector goes from the origin of the ﬁrst vector to the arrowhead of the last vector. The magnitude and direction of the sum vector would be measured. Summary • Scalars are quantities, such as mass, length, or speed, that are completely speciﬁed by magnitude and has no direction. • Vectors are quantities possessing both magnitude and direction and can be represented by an arrow; the direction of the arrow indicates the direction of the quantity and the length of the arrow is proportional to the magnitude. • Vectors that are in one dimension can be added arithmetically. • Vectors that are in two dimensions are added geometrically. • When vectors are added graphically, graphs must be done to scale and answers are only as accurate as the graphing. Practice Video on the graphical method of adding vectors. http://www.youtube.com/watch?v=_Vppxdho6JU MEDIA Click image to the left for more content. 3 Review 1. On the following number line, add the vector 7.5 m/s and the vector -2.0 m/s. www.ck12.org 2. On a sheet of graph paper, add a vector that is 4.0 N due east and a vector that is 3.0 N due north. • scalar: A quantity, such as mass, length, or speed, that is completely speciﬁed by its magnitude and has no direction. • vector: A quantity possessing both magnitude and direction, represented by an arrow the direction ofwhich indicates the direction of the quantity and the length of which is proportional to the magnitude. • vector addition: The process of ﬁnding one vector that is equivalent to the result of the successive application of two or more given vectors. References 1. Ofﬁcial White House photo by Pete Souza. http://commons.wikimedia.org/wiki/File:Barack_Obama_play ing_basketball.jpg. Public Domain 2. CK-12 Foundation - Richard Parsons
.. CC-BY-NC-SA 3.0 3. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 4. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 5. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 6. CK-12 Foundation - CC-BY-NC-SA 3.0.. CC-BY-NC-SA 3.0 7. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 4 www.ck12.org Chapter 2. Vector Addition CHAPTER 2 Vector Addition • Describe the independence of perpendicular vectors. • Resolve vectors into axial components. • Deﬁne resultant. • Add vectors using geometric and trigonometric methods. Vector Addition Adding Vectors in Two Dimensions In the following image, vectors A and B represent the two displacements of a person who walked 90. m east and then 50. m north. We want to add these two vectors to get the vector sum of the two movements. The graphical process for adding vectors in two dimensions is to place the tail of the second vector on the arrow head of the ﬁrst vector as shown above. The sum of the two vectors is the vector that begins at the origin of the ﬁrst vector and goes to the ending of the second vector, as shown below. If we are using totally graphic means of adding these vectors, the magnitude of the sum would be determined by measuring the length of the sum vector and comparing it to the original standard. We would also use a compass to measure the angle of the summation vector. If we are using calculation means, we can determine the inverse tangent of 50 units divided by 90 units and get the angle of 29° north of east. The length of the sum vector can also be determined mathematically by the Pythagorean 5 www.ck12.org theorem, a2 + b2 = c2. In this case, the length of the hypotenuse would be the square root of (8100 + 2500) or 103 units. If three or four vectors are to be added by graphical means, we would continue to place each new vector head to toe with the vectors to be added until all the vectors were in the coordinate system and then the sum vector would be the vector goes from the origin of the ﬁ
rst vector to the arrowhead of the last vector. The magnitude and direction of the sum vector would be measured. Mathematical Methods of Vector Addition We can add vectors mathematically using trig functions, the law of cosines, or the Pythagorean theorem. If the vectors to be added are at right angles to each other, we would assign them to the sides of a right triangle and calculate the sum as the hypotenuse of the right triangle. We would also calculate the direction of the sum vector by using an inverse sin or some other trig function. Suppose, however, that we wish to add two vectors that are not at right angles to each other. Let’s consider the vectors in the following images. The two vectors we are to add is a force of 65 N at 30° north of east and a force of 35 N at 60° north of west. We know that vectors in the same dimension can be added by regular arithmetic. Therefore, we can resolve each of these vectors into components that lay on the axes –pictured below. We can resolve each of the vectors into two components. The components are on the axes lines. The resolution of vectors reduces each vector to a component on the north-south axis and a component on the east-west axis. We can now mathematically determine the magnitude of the components and add then arithmetically because they are in the same dimension. Once we have added the components, we will once again have only two vectors that are perpendicular to each other and can be the legs of a right triangle. The east-west component of the ﬁrst vector is (65 N)(cos 30°) = (65 N)(0.866) = 56.3 N north The north-south component of the ﬁrst vector is (65 N)(sin 30°) = (65 N)(0.500) = 32.5 N north 6 www.ck12.org Chapter 2. Vector Addition The east-west component of the second vector is (35 N)(cos 60°) = (35 N)(0.500) = 17.5 N west The north-south component of the second vector is (35 N)(sin 60°) = (35 N)(0.866) = 30.3 N north The sum of the two east-west components is 56.3 N - 17.5 N = 38.8 N east The sum of the two north-south components is 32.5 N + 30.
3 N = 62.8 N north We can now consider those two vectors to be the sides of a right triangle and use the Pythagorean Theorem to ﬁnd the length of the hypotenuse and use a trig function to ﬁnd its direction. p c = sin x = 62:8 38:82 + 62:82 = 74 N 74 so x = sin1 0:84 so x = 58 The direction of the sum vector is 74 N at 58° north of east. Perpendicular vectors have no components in the other direction. For example, if a boat is ﬂoating down a river due south, and you are paddling the boat due east, the eastward vector has no component in the north-south direction and therefore, has no effect on the north-south motion. If the boat is ﬂoating down the river at 5 miles/hour south and you paddle the boat eastward at 5 miles/hour, the boat continues to ﬂoat southward at 5 miles/hour. The eastward motion has absolutely no effect on the southward motion. Perpendicular vectors have NO effect on each other. Example Problem: A motorboat heads due east at 16 m/s across a river that ﬂows due north at 9.0 m/s. (a) What is the resultant velocity of the boat? (b) If the river is 135 m wide, how long does it take the boat to reach the other side? (c) When the boat reaches the other side, how far downstream will it be? Solution: Sketch: (a) Since the two motions are perpendicular to each other, they can be assigned to the legs of a right triangle and the hypotenuse (resultant) calculated. c = p a2 + b2 = q (16 m/s)2 + (9:0 m/s)2 = 18 m/s sin q = 9:0 18 = 0:500 and therefore q = 30 The resultant is 18 m/s at 30° north of east. 7 www.ck12.org (b) The boat is traveling across the river at 16 m/s due to the motor. The current is perpendicular and therefore has no effect on the speed across the river. The time required for the trip can be determined by dividing the distance by the velocity. t = d = 8:4 s v = 135 m 16 m/s (c) The boat is
traveling across the river for 8.4 seconds and therefore, it is also traveling downstream for 8.4 seconds. We can determine the distance downstream the boat will travel by multiplying the speed downstream by the time of the trip. ddownstream = (vdownstream)(t) = (9:0 m/s)(8:4 s) = 76 m Summary • Vectors can be added mathematically using geometry and trigonometry. • Vectors that are perpendicular to each other have no effect on each other. • Vector addition can be accomplished by resolving into axial components those vectors that are to be added, adding up the axial components, and then combining the two axial components. Practice A video demonstrating the component method of vector addition. http://www.youtube.com/watch?v=nFDzRWw08Ew MEDIA Click image to the left for more content. Review 1. A hiker walks 11 km due north from camp and then turns and walks 11 km due east. (a) What is the total distance walked by the hiker? (b) What is the displacement (on a straight line) of the hiker from the camp? 2. While ﬂying due east at 33 m/s, an airplane is also being carried due north at 12 m/s by the wind. What is the plane’s resultant velocity? 3. Two students push a heavy crate across the ﬂoor. John pushes with a force of 185 N due east and Joan pushes with a force of 165 N at 30° north of east. What is the resultant force on the crate? 4. An airplane ﬂying due north at 90. km/h is being blown due west at 50. km/h. What is the resultant velocity of the plane? 5. A golf ball is struck with a golf club and travels in a parabolic curve. The horizontal distance traveled by the golf ball is 240 meters and the time of ﬂight is 4.00 seconds. What was the initial velocity magnitude and direction? • axial component: A component situated in or on an axis. • resolution of vectors: Any vector directed at an angle to the horizontal (or the vertical) can be thought of as having two parts (or components) that lie on the axes (one horizontal and one vertical). The process of identifying these two components is known as the resolution of the vector. 8 Chapter 2. Vector Addition www.ck12.org
References 1. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 2. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 3. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 4. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 5. CK-12 Foundation - Richard Parsons.. CC-BY-NC-SA 3.0 9 Physics Unit 4 (Two Dimensional Motion) Patrick Marshall Jean Brainard, Ph.D. Ck12 Science James Dann, Ph.D. Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) AUTHORS Patrick Marshall Jean Brainard, Ph.D. Ck12 Science James Dann, Ph.D. CONTRIBUTORS Chris Addiego Antonio De Jesus López www.ck12.org To access a customizable version of this book, as well as other interactive content, visit www.ck12.org CK-12 Foundation is a non-proﬁt organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Using an open-content, web-based collaborative model termed the FlexBook®, CK-12 intends to pioneer the generation and distribution of high-quality educational content that will serve both as core text as well as provide an adaptive environment for learning, powered through the FlexBook Platform®. Copyright © 2014 CK-12 Foundation, www.ck12.org The names “CK-12” and “CK12” and associated logos and the terms “FlexBook®” and “FlexBook Platform®” (collectively “CK-12 Marks”) are trademarks and service marks of CK-12 Foundation and are protected by federal, state, and international laws. Any form of reproduction of this book in any format or medium, in whole or in sections must include the referral attribution link http://www.ck12.org/saythanks (placed in a visible location) in addition to the following terms. Except as otherwise noted, all CK-12 Content (including CK-12 Curriculum Material) is made available to Users in accordance with the Creative Commons Attribution-Non-Commercial 3.0 Unported (CC BY-
NC 3.0) License (http://creativecommons.org/ licenses/by-nc/3.0/), as amended and updated by Creative Commons from time to time (the “CC License”), which is incorporated herein by this reference. Complete terms can be found at http://www.ck12.org/terms. Printed: February 4, 2014 iii Contents www.ck12.org Contents Projectile Motion Projectile Motion for an Object Launched Horizontally Projectile Motion for an Object Launched at an Angle Projectile Motion Problem Solving 1 4 7 11 1 2 3 4 iv www.ck12.org Chapter 1. Projectile Motion CHAPTER 1 Projectile Motion • Describe projectile motion and state when it occurs. • Give examples of projectile motion. The archer in the opening image is aiming his arrow a little bit above the bull’s eye of the target, rather than directly at it. Why doesn’t he aim at the bull’s eye instead? The answer is projectile motion. Combining Forces When the archer releases the bowstring, the arrow will be ﬂung forward toward the top of the target where she’s aiming. But another force will also act on the arrow in a different direction. The other force is gravity, and it will pull the arrow down toward Earth. The two forces combined will cause the arrow to move in the curved path shown in the Figure 1.1. This type of motion is called projectile motion. It occurs whenever an object curves down toward the ground because it has both a horizontal force and the downward force of gravity acting on it. Because of projectile motion, to hit the bull’s eye of a target with an arrow, you actually have to aim for a spot above the bull’s eye. You can see in theFigure 1.2 what happens if you aim at the bull’s eye instead of above it. 1 www.ck12.org FIGURE 1.1 FIGURE 1.2 Another Example of Projectile Motion You can probably think of other examples of projectile motion. One is shown in the Figure 1.3. The cannon shoots a ball straight ahead, giving it horizontal motion. At the same time, gravity pulls the ball down toward the ground. FIGURE 1.3 Q: How would you show the force of gravity on the cannon ball in the Figure 1.3? A: You would add a line pointing straight down from the cannon to
the ground. To get a better feel for projectile motion, try these interactive animations: • http://phet.colorado.edu/en/simulation/projectile-motion • http://jersey.uoregon.edu/vlab/ (Click on the applet “Cannon.”) Summary • Projectile motion is movement of an object in a curved path toward the ground because it has both a horizontal force and the downward force of gravity acting on it. 2 www.ck12.org Chapter 1. Projectile Motion • Examples of objects that have projectile motion include arrows and cannon balls. Vocabulary • projectile motion: Motion of an object that has initial horizontal velocity but is also pulled down toward Earth by gravity. Practice Play the game at the following URL by shooting the cannon at a stationary target. Experiment with three variablespower, height of barrel, and angle of barrelyou ﬁnd at least three different combinations of variables that allow the cannon ball to hit the target. Record the values for the three combinations of variables. Then summarize what you learned by doing the activity. http://www.science-animations.com/support-ﬁles/projektielbeweging.swf Review 1. What is projectile motion? When does it occur? 2. How might knowledge of projectile motion help you shoot baskets in basketball? References 1. Laura Guerin.. CC BY-NC 3.0 2. Laura Guerin.. CC BY-NC 3.0 3. Christopher Auyeung.. CC-BY-NC-SA 3.0 3 CHAPTER 2 Projectile Motion for an Object Launched Horizontally www.ck12.org • State the relationship between the vertical and horizontal velocities of a projectile launched horizontally. • Find the time for a horizontally launched projectile to strike the ground. • Calculate the range of a horizontally launched projectile. The activity of bike jumping, like other sports that involve vector motions in perpendicular directions, requires more physical practice than mathematical analysis. The laws of physics apply to the activity, however, whether the biker is aware of them or not. Projectile Motion for an Object Launched Horizontally Objects that are launched into the air are called projectiles. The path followed by an object in projectile motion is called a trajectory. The motion of a projectile is described in terms of its position, velocity, and acceleration. Our knowledge that perpendicular components of vectors do not affect each other allow us
to analyze the motion of projectiles. 4 www.ck12.org Chapter 2. Projectile Motion for an Object Launched Horizontally In the diagram, two balls (one red and one blue) are dropped at the same time. The red ball is released with no horizontal motion and the blue ball is dropped but also given a horizontal velocity of 10 m/s. As the balls fall to the ﬂoor, a photograph is taken every second so that in 5 seconds, we have 5 images of the two balls. Each vertical line on the diagram represents 5 m. Since the blue ball has a horizontal velocity of 10 m/s, you will see that for every second, the blue ball has moved horizontally 10 m. That is, in each second, the blue ball has increased its horizontal distance by 10 m. This horizontal motion is constant velocity motion. The red ball was dropped straight down with no horizontal velocity and therefore, in each succeeding second, the red ball falls straight down with no horizontal motion. The succeeding distances between seconds with the red ball motion indicates this motion is accelerated. A very important point here is that, the vertical motion of these two balls is identical. That is, they each fall exactly the same distance vertically in each succeeding second. The constant horizontal velocity of the blue ball has no effect on its accelerated vertical motion! Therefore, the vertical motion of the blue ball (the projectile) can be analyzed exactly the same as the vertical motion of the red ball. Example Problem: If an arrow if ﬁred from a bow with a perfectly horizontal velocity of 60.0 m/s and the arrow was 2.00 m above the ground when the it was released, how far will the arrow ﬂy horizontally before it strikes the ground? Solution: This problem is solved by determining how long it takes the arrow to fall to the ground in exactly the same manner as if the arrow was dropped with no horizontal velocity. Then the time required for the fall is multiplied by the horizontal velocity to get the horizontal distance. d = 1 2 at2 solved for t = s r 2d a = (2)(2:00 m) 9:80 m/s2 = 0:639 s The time required for the arrow to fall to the ground is the same time that the arrow ﬂies horizontally at 60.0 m/s, so dhorizontal = (vhorizontal)(time) = (60:0 m/s)(0:639 s) = 38:
3 m Example Problem: A rock was thrown horizontally from a 100.0 m high cliff. It strikes the ground 90.0 m from the base of the cliff. At what speed was it thrown? 5 Solution: We can calculate how long it takes for a rock to free fall 100.0 m and then divide this time into the horizontal distance to get the horizontal velocity. www.ck12.org s r 2d a = d t = 90:0 m 4:52 s t = v = (2)(100:0 m) 9:80 m/s2 = 4:52 s = 19:9 m/s Summary • Perpendicular components of vectors do not inﬂuence each other. • The horizontal motion of a projectile does not inﬂuence its free fall. Practice The following video discusses projectile motion for projectiles launched horizontally. http://www.youtube.com/watch?v=-uUsUaPJUc0 1. Why does speedy need to drive a convertible? 2. What is speedy doing in this video? 3. How does the horizontal velocity change during the fall? 4. How does the vertical velocity change during the fall? Review 1. If a bullet is ﬁred from a high powered riﬂe at the exact time a duplicate bullet is dropped by hand near the barrel of the riﬂe, which bullet will hit the ground ﬁrst? (a) the one dropped straight down (b) the one ﬁred horizontally (c) both will hit the ground at the same time 2. A cannon is ﬁred from the edge of a small cliff. The height of the cliff is 80.0 m. The cannon ball is ﬁred with a perfectly horizontal velocity of 80.0 m/s. How far will the cannon ball ﬂy horizontally before it strikes the ground? 3. A cliff diver running 3.60 m/s dives out horizontally from the edge of a vertical cliff and reaches the water below 2.00 s later. How high is the cliff and how far from the base of the cliff did the diver hit the water? • projectile motion: A form of motion where a particle (called a projectile) is thrown obliquely near the earth’s surface, it moves along a curved path under the action of gravity. The path followed by a projectile motion is called its trajectory. Projectile motion only occurs when
there is one force applied at the beginning of the trajectory after which there is no interference apart from gravity. • trajectory: The path followed by an object in projectile motion. References 1. Courtesy of PDPhoto.org. http://www.pdphoto.org/PictureDetail.php?mat=&pg=7672. Public Domain 2. CK-12 Foundation - Samantha Bacic.. CC-BY-NC-SA 3.0 6 www.ck12.org Chapter 3. Projectile Motion for an Object Launched at an Angle CHAPTER 3 Projectile Motion for an Object Launched at an Angle • The student will calculate the maximum height and range of projectiles launched at an angle given the initial velocity and angle. In the case of the human cannonball shown, all the vector and gravitational calculations must be worked out perfectly before the ﬁrst practice session. With this activity, you cannot afford trial and error –the ﬁrst miss might be the last trial. Projectile Motion for an Object Launched at an Angle When an object is projected from rest at an upward angle, its initial velocity can be resolved into two components. These two components operate independently of each other. The upward velocity undergoes constant downward acceleration which will result in it rising to a highest point and then falling backward to the ground. The horizontal motion is constant velocity motion and undergoes no changes due to gravity. As usual, the analysis of the motion involves dealing with the two motions independently. 7 www.ck12.org Example Problem: A cannon ball is ﬁred with an initial velocity of 100. m/s at an angle of 45° above the horizontal. What maximum height will it reach and how far will it ﬂy horizontally? Solution: The ﬁrst step in the analysis of this motion is to resolve the initial velocity into its vertical and horizontal components. viup = (100: m/s)(sin 45) = (100: m/s)(0:707) = 70:7 m/s vihorizontal = (100: m/s)(cos 45) = (100: m/s)(0:707) = 70:7 m/s We will deal with the vertical motion ﬁrst. The vertical motion is symmetrical. The object will rise up to its highest point and then fall back. The distance it travels up will be the same as the distance it falls down. The time it takes
to reach the top will be the same time it takes to fall back to its initial point. The initial velocity upward will be the same magnitude (opposite in direction) as the ﬁnal velocity when it returns to its original height. There are several ways we could approach the upward motion. We could calculate the time it would take gravity to bring the initial velocity to rest. Or, we could calculate the time it would take gravity to change the initial velocity from +70.7 m/s to -70.0 m/s. Yet another way would be to calculate the time for the height of the object to return to zero. v f = vi + at so t = v f vi a If we calculate the time required for the ball to rise up to its highest point and come to rest, the initial velocity is 70.7 m/s and the ﬁnal velocity is 0 m/s. Since we have called the upward velocity positive, then the acceleration must be negative or -9.80 m/s2. t = v f vi a = 0 m/s70:7 m/s 9:80 m/s2 = 7:21 s The maximum height reached can be calculated by multiplying the time for the upward trip by the average vertical velocity. The average upward velocity during the trip up is one-half the initial velocity. vupave = 1 height = (vupave)(tup) = (35:3 m/s)(7:21 s) = 255 m (70:7 m/s) = 35:3 m/s 2 Since this is the time required for the cannon ball to rise up to its highest point and come to rest, then the time required for the entire trip up and down would be double this value, or 14.42 s. The horizontal distance traveled during the ﬂight is calculated by multiplying the total time times the constant horizontal velocity. dhorizontal = (14:42 s)(70:7 m/s) = 1020 m Example Problem: A golf ball was knocked into the with an initial velocity of 4.47 m/s at an angle of 66° with the horizontal. How high did the ball go and how far did it ﬂy horizontally? Solution: viup = (4:47 m/s)(sin 66) = (4:47 m/s)(0:913) = 4:08 m/s vihor = (4:47 m
/s)(cos 66) = (4:47 m/s)(0:407) = 1:82 m/s 8 www.ck12.org Chapter 3. Projectile Motion for an Object Launched at an Angle a = 0 m/s4:08 m/s 9:80 m/s2 = 0:416 s tup = v f vi vupave = 1 height = (vupave)(tup) = (2:04 m/s)(0:416 s) = 0:849 m (4:08 m/s) = 2:04 m/s 2 ttotal trip = (2)(0:416 s) = 0:832 s dhorizontal = (0:832 s)(1:82 m/s) = 1:51 m Example Problem: Suppose a cannon ball is ﬁred downward from a 50.0 m high cliff at an angle of 45° with an initial velocity of 80.0 m/s. How far horizontally will it land from the base of the cliff? Solution: In this case, the initial vertical velocity is downward and the acceleration due to gravity will increase this downward velocity. vidown = (80:0 m/s)(sin 45) = (80:0 m/s)(0:707) = 56:6 m/s vihor = (80:0 m/s)(cos 45) = (80:0 m/s)(0:707) = 56:6 m/s d = vidownt + 1 2 at2 50:0 = 56:6t + 4:9t2 Changing to standard quadratic form yields 4:9t2 + 56:6t 50:0 = 0 This equation can be solved with the quadratic formula. The quadratic formula will produce two possible solutions for t: p t = b+ 56:6+ t = p b2 4ac b2 4ac and t = b 2a 2a p(56:6)2 (4)(4:9)(50) (2)(4:9) = 0:816 s The other solution to the quadratic formula yields a negative number which is clearly not a reasonable solution for this problem. dhorizontal = (0:816 s)(56:6 m/s) = 46:2 m Summary • When an object is projected from rest at an upward angle, its initial velocity can be resolved
into two components. These two components operate independently of each other. • The upward velocity undergoes constant downward acceleration which will result in it rising to a highest point and then falling backward to the ground. • The horizontal motion is constant velocity motion and undergoes no changes due to gravity. • The analysis of the motion involves dealing with the two motions independently. Practice The following video shows a motion analysis for projectile motion launched upward. http://www.youtube.com/watch?v=rMVBc8cE5GU MEDIA Click image to the left for more content. 9 www.ck12.org The following video shows the famous "shoot the monkey" demonstration. Use this resource to answer the questions that follow. http://www.youtube.com/watch?v=cxvsHNRXLjw In this demonstration, a stuffed toy is hung from a high support and is attached to the support by an electric switch. A golf ball cannon is aimed up at the “monkey” while it is hanging on the support. The cannon is designed such that It when the golf ball projectile leaves the barrel, it triggers the switch and releases the toy monkey from its perch. would seem (to the non-physicist) that the projectile will miss the monkey because the monkey will fall under the line of ﬁre. The physicist knows, however, that the projectile falls from its line of ﬁre by exactly the same amount that the monkey falls and therefore, the projectile will hit the monkey every time... in fact, it cannot miss. 1. What is the cannon ball in this video? 2. What is used as the monkey in this video? Review 1. A player kicks a football from ground level with a velocity of magnitude 27.0 m/s at an angle of 30.0° above the horizontal. (a) Find the time the ball is in the air. (b) Find the maximum height of the ball. (c) Find the horizontal distance the ball travels. 2. A person standing on top of a 30.0 m high building throws a ball with an initial velocity of 20. m/s at an angle of 20.0° below horizontal. How far from the base of the building will the ball land? 3. An arrow is ﬁred downward at an angle of 45 degrees from the top of a 200 m cliff with a velocity of 60.0 m/s. (a) How long will it take the arrow
to hit the ground? (b) How far from the base of the cliff will the arrow land? • trajectory: The ballistic trajectory of a projectile is the path that a thrown or launched projectile will take under the action of gravity, neglecting all other forces, such as air resistance, without propulsion. References 1. Flickr: JoshBerglund19. http://www.flickr.com/photos/tyrian123/1539636464/. CC-BY 2.0 2. CK-12 Foundation - Samantha Bacic.. CC-BY-NC-SA 3.0 10 www.ck12.org Chapter 4. Projectile Motion Problem Solving CHAPTER 4 Projectile Motion Problem Solving Students will learn how to use the equations of motion in two dimensions in order to solve problems for projectiles. It is necessary to understand how to break a vector into its x and y components. Students will learn how to use the equations of motion in two dimensions in order to solve problems for projectiles. It is necessary to understand how to break a vector into its x and y components. Key Equations Break the Initial Velocity Vector into its Components Apply the Kinematics Equations y(t) = yi + viyt 1 Vertical Direction 2 gt2 vy(t) = viy gt 2 2g(Dy) vy ay = g = 9:8m=s2 10m=s2 2 = v0y Horizontal Direction x(t) = xi + vixt vx(t) = vix ax = 0 11 www.ck12.org Guidance • To work these problems, separate the “Big Three” equations into two sets: one for the vertical direction, and one for the horizontal. Keep them separate. • The only variable that can go into both sets of equations is time; use time to communicate between the x and y components of the object’s motion. Example 1 CSI discovers a car at the bottom of a 72 m cliff. How fast was the car going if it landed 22m horizontally from the cliff’s edge? (Note that the cliff is ﬂat, i.e. the car came off the cliff horizontally). Question: v =? [m=s] Given: h = Dy = 72 m d = Dx = 22 m g = 10:0 m=s2 Equation: h = viyt + 1 2 gt2 and d = vixt Plug
n’ Chug: Step 1: Calculate the time required for the car to freefall from a height of 72 m. h = viyt + 1 s 2 gt2 but since viy = 0, the equation simpliﬁes to h = 1 s 2 gt2 rearranging for the unknown variable, t, yields t = 2h g = 2(72 m) 10:0 m=s2 = 3:79 s Step 2: Solve for initial velocity: vix = d 3:79 s = 5:80 m=s t = 22 m Answer: Example 2 5:80 m=s Question: A ball of mass m is moving horizontally with a speed of vi off a cliff of height h. How much time does it take the ball to travel from the edge of the cliff to the ground? Express your answer in terms of g (acceleration due to gravity) and h (height of the cliff). Solution: Since we are solving or how long it takes for the ball to reach ground, any motion in the x direction is not pertinent. To make this problem a little simpler, we will deﬁne down as the positive direction and the top of the cliff to be. In this solution we will use the equation y = 0 y(t) = yo + voyt + gt2 1 2. 12 www.ck12.org Chapter 4. Projectile Motion Problem Solving gt2 gt2 1 2 1 2 gt2 1 2 gt2 y(t) = yo + voyt + h = yo + voyt + h = 0 + voy + gt2 2 s 2h g start with the equation substitute h for y(t) because that’s the position of the ball when it hits the ground after time t substitute 0 for yobecause the ball starts at the top of the cliff substitute 0 for voy becauese the ball starts with no vertical component to it’s velocity simplify the equation solve for t Watch this Explanation MEDIA Click image to the left for more content. Time for Practice 1. A stone is thrown horizontally at a speed of 8:0 m=s from the edge of a cliff 80 m in height. How far from the base of the cliff will the stone strike the ground? 2. A toy truck moves off the edge of a table that is 1:25 m high and lands 0:40 m from the base of the table
. a. How much time passed between the moment the car left the table and the moment it hit the ﬂoor? b. What was the horizontal velocity of the car when it hit the ground? 3. A hawk in level ﬂight 135 m above the ground drops the ﬁsh it caught. If the hawk’s horizontal speed is 20:0 m=s, how far ahead of the drop point will the ﬁsh land? 4. A pistol is ﬁred horizontally toward a target 120 m away, but at the same height. The bullet’s velocity is 200 m=s. How long does it take the bullet to get to the target? How far below the target does the bullet hit? 5. A bird, traveling at 20 m=s, wants to hit a waiter 10 m below with his dropping (see image). In order to hit the waiter, the bird must release his dropping some distance before he is directly overhead. What is this distance? 13 www.ck12.org 6. Joe Nedney of the San Francisco 49ers kicked a ﬁeld goal with an initial velocity of 20 m=s at an angle of 60. a. How long is the ball in the air? Hint: you may assume that the ball lands at same height as it starts at. b. What are the range and maximum height of the ball? 7. A racquetball thrown from the ground at an angle of 45 and with a speed of 22:5 m=s lands exactly 2:5 s later on the top of a nearby building. Calculate the horizontal distance it traveled and the height of the building. 8. Donovan McNabb throws a football. He throws it with an initial velocity of 30 m=s at an angle of 25. How much time passes until the ball travels 35 m horizontally? What is the height of the ball after 0:5 seconds? (Assume that, when thrown, the ball is 2 m above the ground.) 9. Pablo Sandoval throws a baseball with a horizontal component of velocity of 25 m=s. After 2 seconds, the ball is 40 m above the release point. Calculate the horizontal distance it has traveled by this time, its initial vertical component of velocity, and its initial angle of projection. Also, is the ball on the way up or the way down at this moment in time? 10. Barry Bonds hits a 125 m(4500) home run that lands in
the stands at an altitude 30 m above its starting altitude. Assuming that the ball left the bat at an angle of 45 from the horizontal, calculate how long the ball was in the air. 11. A golfer can drive a ball with an initial speed of 40:0 m=s. If the tee and the green are separated by 100 m, but are on the same level, at what angle should the ball be driven? ( Hint: you should use 2 cos (x) sin (x) = sin (2x) at some point.) 12. How long will it take a bullet ﬁred from a cliff at an initial velocity of 700 m=s, at an angle 30 below the horizontal, to reach the ground 200 m below? 13. A diver in Hawaii is jumping off a cliff 45 m high, but she notices that there is an outcropping of rocks 7 m out at the base. So, she must clear a horizontal distance of 7 m during the dive in order to survive. Assuming the diver jumps horizontally, what is his/her minimum push-off speed? 14. If Monte Ellis can jump 1:0 m high on Earth, how high can he jump on the moon assuming same initial velocity that he had on Earth (where gravity is 1=6 that of Earth’s gravity)? 15. James Bond is trying to jump from a helicopter into a speeding Corvette to capture the bad guy. The car is going 30:0 m=s and the helicopter is ﬂying completely horizontally at 100 m=s. The helicopter is 120 m above the car and 440 m behind the car. How long must James Bond wait to jump in order to safely make it into the car? 14 www.ck12.org Chapter 4. Projectile Motion Problem Solving 16. A ﬁeld goal kicker lines up to kick a 44 yard (40 m) ﬁeld goal. He kicks it with an initial velocity of 22 m=s at an angle of 55. The ﬁeld goal posts are 3 meters high. a. Does he make the ﬁeld goal? b. What is the ball’s velocity and direction of motion just as it reaches the ﬁeld goal post (i.e., after it has traveled 40 m in the horizontal direction)? 17. In a football game a punter kicks the ball a horizontal distance of 43 yards (39 m). On TV, they track the hang
time, which reads 3:9 seconds. From this information, calculate the angle and speed at which the ball was kicked. (Note for non-football watchers: the projectile starts and lands at the same height. It goes 43 yards horizontally in a time of 3:9 seconds) Answers to Selected Problems 1. 32 m 2. a. 0:5 s b. 0:8 m=s 3. 104 m 4. t = 0:60 s; 1:8 m below target 5. 28 m. 6. a. 3:5 s. b. 35 m; 15 m 7. 40 m; 8:5 m 8. 1:3 seconds, 7:1 meters 9. 50 m; v0y = 30 m=s; 500; on the way up 10. 4:4 s 11. 19 12. 0:5 s 13. 2:3 m=s 14. 6 m 15. 1:4 seconds 16. a. yes b. 14 m=s @ 23 degrees from horizontal 17. 22 m=s @ 62 degrees 15 Physics Unit 5 (Forces and Newton’s Laws) Patrick Marshall Ck12 Science Jean Brainard, Ph.D. James H Dann, Ph.D. Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) AUTHORS Patrick Marshall Ck12 Science Jean Brainard, Ph.D. James H Dann, Ph.D. CONTRIBUTORS Chris Addiego Antonio De Jesus López www.ck12.org To access a customizable version of this book, as well as other interactive content, visit www.ck12.org CK-12 Foundation is a non-proﬁt organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Using an open-content, web-based collaborative model termed the FlexBook®, CK-12 intends to pioneer the generation and distribution of high-quality educational content that will serve both as core text as well as provide an adaptive environment for learning, powered through the FlexBook Platform®. Copyright © 2014 CK-12 Foundation, www.ck12.org The names “CK-12” and “CK12” and associated logos and the terms “FlexBook®” and “FlexBook Platform®” (collectively “CK-12 Marks
”) are trademarks and service marks of CK-12 Foundation and are protected by federal, state, and international laws. Any form of reproduction of this book in any format or medium, in whole or in sections must include the referral attribution link http://www.ck12.org/saythanks (placed in a visible location) in addition to the following terms. Except as otherwise noted, all CK-12 Content (including CK-12 Curriculum Material) is made available to Users in accordance with the Creative Commons Attribution-Non-Commercial 3.0 Unported (CC BY-NC 3.0) License (http://creativecommons.org/ licenses/by-nc/3.0/), as amended and updated by Creative Commons from time to time (the “CC License”), which is incorporated herein by this reference. Complete terms can be found at http://www.ck12.org/terms. Printed: February 4, 2014 iii Contents www.ck12.org 1 4 10 13 16 20 24 27 31 33 Contents 1 Newton’s First and Second Laws of Motion 2 Newton’s First Law 3 Newton’s Second Law 4 Newton’s Third Law of Motion 5 Types of Forces 6 Universal Law of Gravity 7 Mass versus Weight 8 9 Friction Free Body Diagrams 10 Problem Solving 1 iv www.ck12.org Chapter 1. Newton’s First and Second Laws of Motion CHAPTER 1 Newton’s First and Second Laws of Motion • Deﬁne force. • State the fundamental units for the Newton. • State Newton’s First Law of Motion. • Given two of the three values in F = ma, calculate the third. This image is of Buzz Aldrin, one of the ﬁrst men to walk on the moon. Apollo 11 was the spaceﬂight that landed the ﬁrst humans, Neil Armstrong and Buzz Aldrin, on the Moon on July 20, 1969. Armstrong became the ﬁrst to step onto the lunar surface 6 hours later on July 21. This accomplishment could not have occurred without a thorough understanding of forces and acceleration. Newton’s First and Second Laws of Motion What is a force? A force can be deﬁned as a push or pull. When you place a book on a table, the book pushes downward on the table and the table pushes upward on the book. The two forces are equal and there is

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