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projectile : an object that travels through the air and experiences only acceleration due to gravity
https://openstax.org/books/college-physics-2e/pages/3-glossary
projectile motion : the motion of an object that is subject only to the acceleration of gravity
https://openstax.org/books/college-physics-2e/pages/3-glossary
range : the maximum horizontal distance that a projectile travels
https://openstax.org/books/college-physics-2e/pages/3-glossary
relative velocity : the velocity of an object as observed from a particular reference frame
https://openstax.org/books/college-physics-2e/pages/3-glossary
relativity : the study of how different observers moving relative to each other measure the same phenomenon
https://openstax.org/books/college-physics-2e/pages/3-glossary
resultant : the sum of two or more vectors
https://openstax.org/books/college-physics-2e/pages/3-glossary
resultant vector : the vector sum of two or more vectors
https://openstax.org/books/college-physics-2e/pages/3-glossary
scalar : a quantity with magnitude but no direction
https://openstax.org/books/college-physics-2e/pages/3-glossary
tail : the start point of a vector; opposite to the head or tip of the arrow
https://openstax.org/books/college-physics-2e/pages/3-glossary
trajectory : the path of a projectile through the air
https://openstax.org/books/college-physics-2e/pages/3-glossary
vector : a quantity that has both magnitude and direction; an arrow used to represent quantities with both magnitude and direction
https://openstax.org/books/college-physics-2e/pages/3-glossary
vector addition : the rules that apply to adding vectors together
https://openstax.org/books/college-physics-2e/pages/3-glossary
velocity : speed in a given direction
https://openstax.org/books/college-physics-2e/pages/3-glossary
The shortest path between any two points is a straight line. In two dimensions, this path can be represented by a vector with horizontal and vertical components.
https://openstax.org/books/college-physics-2e/pages/3-section-summary
The horizontal and vertical components of a vector are independent of one another. Motion in the horizontal direction does not affect motion in the vertical direction, and vice versa.
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Thegraphical method of adding vectorsAAandBBinvolves drawing vectors on a graph and adding them using the head-to-tail method. The resultant vectorRRis defined such thatA+B=RA+B=R. The magnitude and direction ofRRare then determined with a ruler and protractor, respectively.
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Thegraphical method of subtracting vectorBBfromAAinvolves adding the opposite of vectorBB, which is defined as−B−B. In this case,A–B=A+(–B)=RA–B=A+(–B)=R. Then, the head-to-tail method of addition is followed in the usual way to obtain the resultant vectorRR.
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Addition of vectors iscommutativesuch thatA+B=B+AA+B=B+A.
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Thehead-to-tail methodof adding vectors involves drawing the first vector on a graph and then placing the tail of each subsequent vector at the head of the previous vector. The resultant vector is then drawn from the tail of the first vector to the head of the final vector.
https://openstax.org/books/college-physics-2e/pages/3-section-summary
If a vectorAAis multiplied by a scalar quantitycc, the magnitude of the product is given bycAcA. Ifccis positive, the direction of the product points in the same direction asAA; ifccis negative, the direction of the product points in the opposite direction asAA.
https://openstax.org/books/college-physics-2e/pages/3-section-summary
The analytical method of vector addition and subtraction involves using the Pythagorean theorem and trigonometric identities to determine the magnitude and direction of a resultant vector.
https://openstax.org/books/college-physics-2e/pages/3-section-summary
The steps to add vectorsAAandBBusing the analytical method are as follows:Step 1: Determine the coordinate system for the vectors. Then, determine the horizontal and vertical components of each vector using the equationsAx=AcosθBx=BcosθAx=AcosθBx=BcosθandAy=AsinθBy=Bsinθ.Ay=AsinθBy=Bsinθ.Step 2: Add the horizon...
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Step 1: Determine the coordinate system for the vectors. Then, determine the horizontal and vertical components of each vector using the equations
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and
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Step 2: Add the horizontal and vertical components of each vector to determine the componentsRxRxandRyRyof the resultant vector,RR:
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and
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Step 3: Use the Pythagorean theorem to determine the magnitude,RR, of the resultant vectorRR:
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Step 4: Use a trigonometric identity to determine the direction,θθ, ofRR:
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Projectile motion is the motion of an object through the air that is subject only to the acceleration of gravity.
https://openstax.org/books/college-physics-2e/pages/3-section-summary
To solve projectile motion problems, perform the following steps:Determine a coordinate system. Then, resolve the position and/or velocity of the object in the horizontal and vertical components. The components of positionssare given by the quantitiesxxandyy, and the components of the velocityvvare given byvx=vcosθvx=...
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Determine a coordinate system. Then, resolve the position and/or velocity of the object in the horizontal and vertical components. The components of positionssare given by the quantitiesxxandyy, and the components of the velocityvvare given byvx=vcosθvx=vcosθandvy=vsinθvy=vsinθ, wherevvis the magnitude of the veloc...
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Analyze the motion of the projectile in the horizontal direction using the following equations:Horizontal motion(ax=0)Horizontal motion(ax=0)x=x0+vxtx=x0+vxtvx=v0x=vx=velocity is a constant.vx=v0x=vx=velocity is a constant.
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Analyze the motion of the projectile in the vertical direction using the following equations:Vertical Motion(assuming positive is upay=−g=−9.80m/s2)Vertical Motion(assuming positive is upay=−g=−9.80m/s2)y=y0+12(v0y+vy)ty=y0+12(v0y+vy)tvy=v0y−gtvy=v0y−gty=y0+v0yt−12gt2y=y0+v0yt−12gt2vy2=v0y2−2g(y−y0)...
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Recombine the horizontal and vertical components of location and/or velocity using the following equations:s=x2+y2s=x2+y2θ=tan−1(y/x)θ=tan−1(y/x)v=vx2+vy2v=vx2+vy2θv=tan−1(vy/vx).θv=tan−1(vy/vx).
https://openstax.org/books/college-physics-2e/pages/3-section-summary
The maximum heighthhof a projectile launched with initial vertical velocityv0yv0yis given byh=v0y22g.h=v0y22g.
https://openstax.org/books/college-physics-2e/pages/3-section-summary
The maximum horizontal distance traveled by a projectile is called therange. The rangeRRof a projectile on level ground launched at an angleθ0θ0above the horizontal with initial speedv0v0is given byR=v02sin2θ0g.R=v02sin2θ0g.
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Velocities in two dimensions are added using the same analytical vector techniques, which are rewritten asvx=vcosθvx=vcosθvy=vsinθvy=vsinθv=vx2+vy2v=vx2+vy2θ=tan−1(vy/vx).θ=tan−1(vy/vx).
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Relative velocity is the velocity of an object as observed from a particular reference frame, and it varies dramatically with reference frame.
https://openstax.org/books/college-physics-2e/pages/3-section-summary
Relativityis the study of how different observers measure the same phenomenon, particularly when the observers move relative to one another.Classical relativityis limited to situations where speed is less than about 1% of the speed of light (3000 km/s).
https://openstax.org/books/college-physics-2e/pages/3-section-summary
acceleration : the rate at which an object’s velocity changes over a period of time
https://openstax.org/books/college-physics-2e/pages/4-glossary
carrier particle : a fundamental particle of nature that is surrounded by a characteristic force field; photons are carrier particles of the electromagnetic force
https://openstax.org/books/college-physics-2e/pages/4-glossary
dynamics : the study of how forces affect the motion of objects and systems
https://openstax.org/books/college-physics-2e/pages/4-glossary
external force : a force acting on an object or system that originates outside of the object or system
https://openstax.org/books/college-physics-2e/pages/4-glossary
force : a push or pull on an object with a specific magnitude and direction; can be represented by vectors; can be expressed as a multiple of a standard force
https://openstax.org/books/college-physics-2e/pages/4-glossary
force field : a region in which a test particle will experience a force
https://openstax.org/books/college-physics-2e/pages/4-glossary
free-body diagram : a sketch showing all of the external forces acting on an object or system; the system is represented by a dot, and the forces are represented by vectors extending outward from the dot
https://openstax.org/books/college-physics-2e/pages/4-glossary
free-fall : a situation in which the only force acting on an object is the force due to gravity
https://openstax.org/books/college-physics-2e/pages/4-glossary
friction : a force past each other of objects that are touching; examples include rough surfaces and air resistance
https://openstax.org/books/college-physics-2e/pages/4-glossary
inertia : the tendency of an object to remain at rest or remain in motion
https://openstax.org/books/college-physics-2e/pages/4-glossary
inertial frame of reference : a coordinate system that is not accelerating; all forces acting in an inertial frame of reference are real forces, as opposed to fictitious forces that are observed due to an accelerating frame of reference
https://openstax.org/books/college-physics-2e/pages/4-glossary
law of inertia : see Newton’s first law of motion
https://openstax.org/books/college-physics-2e/pages/4-glossary
mass : the quantity of matter in a substance; measured in kilograms
https://openstax.org/books/college-physics-2e/pages/4-glossary
net external force : the vector sum of all external forces acting on an object or system; causes a mass to accelerate
https://openstax.org/books/college-physics-2e/pages/4-glossary
Newton’s first law of motion : a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force; also known as the law of inertia
https://openstax.org/books/college-physics-2e/pages/4-glossary
Newton’s second law of motion : the net external forceFnetFneton an object with massmmis proportional to and in the same direction as the acceleration of the object,aa, and inversely proportional to the mass; defined mathematically asa=Fnetma=Fnetm
https://openstax.org/books/college-physics-2e/pages/4-glossary
Newton’s third law of motion : whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that the first body exerts
https://openstax.org/books/college-physics-2e/pages/4-glossary
normal force : the force that a surface applies to an object to support the weight of the object; acts perpendicular to the surface on which the object rests
https://openstax.org/books/college-physics-2e/pages/4-glossary
system : defined by the boundaries of an object or collection of objects being observed; all forces originating from outside of the system are considered external forces
https://openstax.org/books/college-physics-2e/pages/4-glossary
tension : the pulling force that acts along a medium, especially a stretched flexible connector, such as a rope or cable; when a rope supports the weight of an object, the force on the object due to the rope is called a tension force
https://openstax.org/books/college-physics-2e/pages/4-glossary
thrust : a reaction force that pushes a body forward in response to a backward force; rockets, airplanes, and cars are pushed forward by a thrust reaction force
https://openstax.org/books/college-physics-2e/pages/4-glossary
weight : the forcewwdue to gravity acting on an object of massmm; defined mathematically as:w=mgw=mg, whereggis the magnitude and direction of the acceleration due to gravity
https://openstax.org/books/college-physics-2e/pages/4-glossary
Dynamicsis the study of how forces affect the motion of objects.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
Forceis a push or pull that can be defined in terms of various standards, and it is a vector having both magnitude and direction.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
External forcesare any outside forces that act on a body. Afree-body diagramis a drawing of all external forces acting on a body.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
Newton’s first law of motionstates that a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force. This is also known as thelaw of inertia.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
Inertiais the tendency of an object to remain at rest or remain in motion. Inertia is related to an object’s mass.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
Massis the quantity of matter in a substance.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
Acceleration,aa, is defined as a change in velocity, meaning a change in its magnitude or direction, or both.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
An external force is one acting on a system from outside the system, as opposed to internal forces, which act between components within the system.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
Newton’s second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
In equation form, Newton’s second law of motion isa=Fnetma=Fnetm.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
This is often written in the more familiar form:Fnet=maFnet=ma.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
The weightwwof an object is defined as the force of gravity acting on an object of massmm. The object experiences an acceleration due to gravitygg:w=mg.w=mg.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
If the only force acting on an object is due to gravity, the object is in free fall.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
Friction is a force that opposes the motion past each other of objects that are touching.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
Newton’s third law of motionrepresents a basic symmetry in nature. It states: Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that the first body exerts.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
Athrustis a reaction force that pushes a body forward in response to a backward force. Rockets, airplanes, and cars are pushed forward by a thrust reaction force.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
When objects rest on a surface, the surface applies a force to the object that supports the weight of the object. This supporting force acts perpendicular to and away from the surface. It is called a normal force,NN.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
When objects rest on a non-accelerating horizontal surface, the magnitude of the normal force is equal to the weight of the object:N=mg.N=mg.
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When objects rest on an inclined plane that makes an angleθθwith the horizontal surface, the weight of the object can be resolved into components that act perpendicular (w⊥w⊥) and parallel (w∥w∥)to the surface of the plane. These components can be calculated using:w∥=wsin(θ)=mgsin(θ)w∥=wsin(θ)=mgsin(θ...
https://openstax.org/books/college-physics-2e/pages/4-section-summary
The pulling force that acts along a stretched flexible connector, such as a rope or cable, is called tension,TT. When a rope supports the weight of an object that is at rest, the tension in the rope is equal to the weight of the object:T=mg.T=mg.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
In any inertial frame of reference (one that is not accelerated or rotated), Newton’s laws have the simple forms given in this chapter and all forces are real forces having a physical origin.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
To solve problems involving Newton’s laws of motion, follow the procedure described:Draw a sketch of the problem.Identify known and unknown quantities, and identify the system of interest. Draw a free-body diagram, which is a sketch showing all of the forces acting on an object. The object is represented by a dot, an...
https://openstax.org/books/college-physics-2e/pages/4-section-summary
Draw a sketch of the problem.
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Identify known and unknown quantities, and identify the system of interest. Draw a free-body diagram, which is a sketch showing all of the forces acting on an object. The object is represented by a dot, and the forces are represented by vectors extending in different directions from the dot. If vectors act in direction...
https://openstax.org/books/college-physics-2e/pages/4-section-summary
Write Newton’s second law in the horizontal and vertical directions and add the forces acting on the object. If the object does not accelerate in a particular direction (for example, thexx-direction) thenFnetx=0Fnetx=0. If the object does accelerate in that direction,Fnetx=maFnetx=ma.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
Check your answer. Is the answer reasonable? Are the units correct?
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Newton’s laws of motion can be applied in numerous situations to solve problems of motion.
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Some problems will contain multiple force vectors acting in different directions on an object. Be sure to draw diagrams, resolve all force vectors into horizontal and vertical components, and draw a free-body diagram. Always analyze the direction in which an object accelerates so that you can determine whetherFnet=maFn...
https://openstax.org/books/college-physics-2e/pages/4-section-summary
The normal force on an object is not always equal in magnitude to the weight of the object. If an object is accelerating, the normal force will be less than or greater than the weight of the object. Also, if the object is on an inclined plane, the normal force will always be less than the full weight of the object.
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Some problems will contain various physical quantities, such as forces, acceleration, velocity, or position. You can apply concepts from kinematics and dynamics in order to solve these problems of motion.
https://openstax.org/books/college-physics-2e/pages/4-section-summary
The various types of forces that are categorized for use in many applications are all manifestations of thefour basic forcesin nature.
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The properties of these forces are summarized inTable 4.1.
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Everything we experience directly without sensitive instruments is due to either electromagnetic forces or gravitational forces. The nuclear forces are responsible for the submicroscopic structure of matter, but they are not directly sensed because of their short ranges. Attempts are being made to show all four forces ...
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A force field surrounds an object creating a force and is the carrier of that force.
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deformation : change in shape due to the application of force
https://openstax.org/books/college-physics-2e/pages/5-glossary
drag force : FDFD, found to be proportional to the square of the speed of the object; mathematicallyFD∝v2FD∝v2FD=12CρAv2,FD=12CρAv2,whereCCis the drag coefficient,AAis the area of the object facing the fluid, andρρis the density of the fluid
https://openstax.org/books/college-physics-2e/pages/5-glossary
friction : a force that opposes relative motion or attempts at motion between systems in contact
https://openstax.org/books/college-physics-2e/pages/5-glossary
Hooke’s law : proportional relationship between the forceFFon a material and the deformationΔLΔLit causes,F=kΔLF=kΔL
https://openstax.org/books/college-physics-2e/pages/5-glossary
kinetic friction : a force that opposes the motion of two systems that are in contact and moving relative to one another
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