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any backing up and any change in radius due to wear? 4. (a) What is the period of rotation of Earth in seconds? (b) What is the angular velocity of Earth? (c) Given that Earth has a radius of 6.4×106 m at its equator, what is the linear velocity at Earth's surface? 5. A baseball pitcher brings his arm forward during a... |
horizontal circular path the riders follow has an 8.00 m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration whose magnitude is 1.50 times that due to gravity? 11. A runner taking part in the 200 m dash must run around the end of a track that has a circular arc with a ... |
c) An exceptional skater named Dick Button was able to spin much faster in the 1950s than anyone since—at about 9 rev/ s. What was the centripetal acceleration of the tip of his nose, assuming it is at 0.120 m radius? (d) Comment on the magnitudes of the accelerations found. It is reputed that Button ruptured small blo... |
gravity. (a) Assuming negligible friction, find the speed of the riders at the bottom of its arc, given the system's center of mass travels in an arc having a radius of 14.0 m and the riders are near the center of mass. (b) What is the centripetal acceleration at the bottom of the arc? (c) Draw a free body diagram of ... |
and taken at 30.0 m/s, assuming it is ideally banked? (b) Calculate the centripetal acceleration. (c) Does this acceleration seem large to you? 28. Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen in Figure 6.36. To be stable, the force exerted by the ground must be on a line ... |
loops are used in the latest roller coasters so that the radius of curvature gradually decreases to a minimum at the top. This means that the centripetal acceleration builds from zero to a maximum at the top and gradually decreases again. A circular loop would cause a jolting change in acceleration at entry, a disadva... |
ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). (a) Calculate the ideal speed to take a 100 m radius curve banked at 15.0º. (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 20.0 km/h? ... |
is even an effect, much less that an unknown force causes it.) 40. The existence of the dwarf planet Pluto was proposed based on irregularities in Neptune's orbit. Pluto was subsequently discovered near its predicted position. But it now appears that the discovery was fortuitous, because Pluto is small and the irregul... |
. Calculate the mass of the Sun based on data for Earth's orbit and compare the value obtained with the Sun's actual mass. 45. Find the mass of Jupiter based on data for the orbit of one of its moons, and compare your result with its actual mass. 46. Find the ratio of the mass of Jupiter to that of Earth based on data ... |
such things as a safe distance for the orbit. Although Eros is not spherical, calculate the acceleration due to gravity on its surface at a point an average distance from its center of mass. Your instructor may also wish to have you calculate the escape velocity from this point on Eros. Chapter 6 | Gravitation and Uni... |
7.2. Kinetic Energy and the Work-Energy Theorem 7.3. Gravitational Potential Energy 7.4. Conservative Forces and Potential Energy 7.5. Nonconservative Forces 7.6. Conservation of Energy 7.7. Power 7.8. Work, Energy, and Power in Humans 7.9. World Energy Use Connection for AP® Courses Energy plays an essential role bot... |
). An important aspect of energy is that the total amount of energy in the universe is constant. Energy can change forms, but it cannot appear from nothing or disappear without a trace. Energy is thus one of a handful of physical quantities that we say is 262 Chapter 7 | Work, Energy, and Energy Resources “conserved.” ... |
this chapter support: Big Idea 3 The interactions of an object with other objects can be described by forces. Enduring Understanding 3.E A force exerted on an object can change the kinetic energy of the object. Essential Knowledge 3.E.1 The change in the kinetic energy of an object depends on the force exerted on the ... |
will be able to: Learning Objectives • Explain how an object must be displaced for a force on it to do work. • Explain how relative directions of force and displacement of an object determine whether the work done on the object is positive, negative, or zero. The information presented in this section supports the foll... |
work done on a system that undergoes motion that is not one-way or that is in two or three dimensions, we divide the motion into one-way one-dimensional segments and add up the work done over each segment. = cos. (7.2) What is Work? The work done on a system by a constant force is the product of the component of the f... |
person carrying the briefcase This content is available for free at http://cnx.org/content/col11844/1.13 Chapter 7 | Work, Energy, and Energy Resources 265 on level ground in Figure 7.2(c) does no work on it, because the force is perpendicular to the motion. That is, cos 90º = 0, and so = 0. In contrast, when a force ... |
were dropped, then its displacement would be parallel to the force of gravity, which would do work on it, changing its state (it would fall to the ground). Calculating Work Work and energy have the same units. From the definition of work, we see that those units are force times distance. Thus, in SI units, work and en... |
day long, less than 10% of our food energy intake is used to do work and more than 90% is converted to thermal energy or stored as chemical energy in fat. 266 Chapter 7 | Work, Energy, and Energy Resources Applying the Science Practices: Boxes on Floors Plan and design an experiment to determine how much work you do o... |
and compare this to the area of a graph of force versus displacement for the duration of the push. They should be the same. 7.2 Kinetic Energy and the Work-Energy Theorem Learning Objectives By the end of this section, you will be able to: • Explain work as a transfer of energy and net work as the work done by the net... |
of the system. (S.P. 1.4, 2.2, 7.2) • 5.B.5.3 The student is able to predict and calculate from graphical data the energy transfer to or work done on an object or system from information about a force exerted on the object or system through a distance. (S.P. 1.5, 2.2, 6.4) Work Transfers Energy What happens to the wor... |
work is the work done by the net external force Fnet. In equation form, this is net = net cos where is the angle between the force vector and the displacement vector. Figure 7.3(a) shows a graph of force versus displacement for the component of the force in the direction of the displacement—that is, an cos vs. graph. ... |
do no work. Moreover, they are also equal in magnitude and opposite in direction so they cancel in calculating the net force. The net force arises solely from the horizontal applied force Fapp and the horizontal friction force f. Thus, as expected, the net force is parallel to the displacement, so that = 0º and cos = ... |
7 | Work, Energy, and Energy Resources 269 is the energy associated with translational motion. Kinetic energy is a form of energy associated with the motion of a particle, single body, or system of objects moving together. We are aware that it takes energy to get an object, like a car or the package in Figure 7.4, up ... |
that the unit of kinetic energy is the joule, the same as the unit of work, as mentioned when work was first defined. It is also interesting that, although this is a fairly massive package, its kinetic energy is not large at this relatively low speed. This fact is consistent with the observation that people can move p... |
the net force. Strategy and Concept for (a) This is a motion in one dimension problem, because the downward force (from the weight of the package) and the normal force have equal magnitude and opposite direction, so that they cancel in calculating the net force, while the applied force, friction, and the displacement ... |
can be calculated by either approach. Example 7.4 Determining Speed from Work and Energy Find the speed of the package in Figure 7.4 at the end of the push, using work and energy concepts. Strategy Here the work-energy theorem can be used, because we have just calculated the net work, net, and the initial kinetic ener... |
Furthermore, fr = ′ cos = – ′, where ′ is the distance it takes to stop. Thus, and so Discussion ′ = − fr = − −95.75 J 5.00 N, ′ = 19.2 m. (7.25) (7.26) This is a reasonable distance for a package to coast on a relatively friction-free conveyor system. Note that the work done by friction is negative (the force is in t... |
in this section. Let us calculate the work done in lifting an object of mass through a height, such as in Figure 7.5. If the object is lifted straight up at constant speed, then the force needed to lift it is equal to its weight. The work done on the mass is then. We define this to be the gravitational potential energ... |
b) As the weight moves downward, this gravitational potential energy is transferred to the cuckoo clock. More precisely, we define the change in gravitational potential energy ΔPEg to be ΔPEg =, (7.27) where, for simplicity, we denote the change in height by rather than the usual Δ. Note that is positive when the final... |
brought to zero in this situation by the work done on him by the floor as he stops. The initial PEg is transformed into KE as he falls. The work done by the floor reduces this kinetic energy to zero. Solution The work done on the person by the floor as he stops is given by = cos = −, (7.29) with a minus sign because t... |
reduced. (credit: Chris Samuel, Flickr) Example 7.7 Finding the Speed of a Roller Coaster from its Height (a) What is the final speed of the roller coaster shown in Figure 7.8 if it starts from rest at the top of the 20.0 m hill and work done by frictional forces is negligible? (b) What is its final speed (again assum... |
, This means that the final kinetic energy is the sum of the initial kinetic energy and the gravitational potential energy. Mass again cancels, and = 2 ∣ ∣ + 0 2. (7.40) This equation is very similar to the kinematics equation = 0 valid only for constant acceleration, whereas our equation above is valid for any path re... |
the 10-cm position on the ruler and let it roll down the ruler. When it hits the level surface, measure the time it takes to roll one meter. Now place the marble at the 20-cm and the 30-cm positions and again measure the times it takes to roll 1 m on the level surface. Find the velocity of the marble on the level surf... |
(S.P. 2.2, 6.4, 7.2) • 5.B.3.2 The student is able to make quantitative calculations of the internal potential energy of a system from a description or diagram of that system. (S.P. 1.4, 2.2) • 5.B.3.3 The student is able to apply mathematical reasoning to create a description of the internal potential energy of a sys... |
ball’s velocity, then determining its kinetic energy is simple. Note that this does require defining a reference frame in which to measure the velocity. Determining the ball’s potential energy also requires more information. You need to know its height above the ground, which requires a reference frame of the ground. ... |
path taken; it depends only on the stretch or squeeze in the final configuration. PEs = 1 (7.42) Figure 7.10 (a) An undeformed spring has no PEs stored in it. (b) The force needed to stretch (or compress) the spring a distance has a magnitude =, and the work done to stretch (or compress) it is 1 energy (PEs) in the sp... |
(7.46) (7.47) This equation means that the total kinetic and potential energy is constant for any process involving only conservative forces. That is, KE + PE = constant or KEi + PEi = KEf + PEf (conservative forces only), (7.48) where i and f denote initial and final values. This equation is a form of the work-energy... |
starts up the slope and (b) how fast it is going at the top of the slope. Figure 7.12 A toy car is pushed by a compressed spring and coasts up a slope. Assuming negligible friction, the potential energy in the spring is first completely converted to kinetic energy, and then to a combination of kinetic and gravitationa... |
53) This form of the equation means that the spring’s initial potential energy is converted partly to gravitational potential energy and partly to kinetic energy. The final speed at the top of the slope will be less than at the bottom. Solving for f and substituting known values gives f = 2 i − 2f 250.0 N/m 0.100 kg (0... |
, Energy, and Energy Resources 7.5 Nonconservative Forces By the end of this section, you will be able to: Learning Objectives • Define nonconservative forces and explain how they affect mechanical energy. • Show how the principle of conservation of energy can be applied by treating the conservative forces in terms of ... |
energy, which is dissipated as thermal energy, reducing its mechanical energy. Figure 7.15 compares the effects of conservative and nonconservative forces. We often choose to understand simpler systems such as that described in Figure 7.15(a) first before studying more complicated systems as in Figure 7.15(b). This co... |
a conservative force comes from a loss of gravitational potential energy, so that c = −ΔPE. Substituting this equation into the previous one and solving for nc gives nc = ΔKE + ΔPE. (7.57) This equation means that the total mechanical energy (KE + PE) changes by exactly the amount of work done by nonconservative force... |
level ground. Using energy considerations, calculate the distance the 65.0-kg baseball player slides, given that his initial speed is 6.00 m/s and the force of friction against him is a constant 450 N. Figure 7.17 The baseball player slides to a stop in a distance. In the process, friction removes the player’s kinetic... |
62) Solution The work done by friction is again nc = − ; initially the potential energy is PEi = ⋅ 0 = 0 and the kinetic energy is KEi = 1 2 ; the final energy contributions are KEf = 0 for the kinetic energy and PEf = = sin for the potential energy. 2i Substituting these values gives Solve this for to obtain 1 2i 2 + ... |
kinetic friction k of the cup on the table. The force of friction on the cup is k, where the normal force is just the weight of the cup plus the marble. The normal force and force of gravity do no work because they are perpendicular to the displacement of the cup, which moves horizontally. The work done by friction is... |
concepts of conservation of energy and the work-energy theorem to determine qualitatively and/or quantitatively that work done on a two-object system in linear motion will change the kinetic energy of the center of mass of the system, the potential energy of the systems, and/or the internal energy of the system. (S.P.... |
work can be included in this very general statement of conservation of energy. Kinetic energy is KE, work done by a conservative force is represented by PE, work done by nonconservative forces is nc, and all other energies are included as OE. This equation applies to all previous examples; in those situations OE was c... |
following systems are open or closed: a car, a spring-operated dart gun, and the system shown in Figure 7.15(a). A car is not a closed system. You add energy in the form of more gas in the tank (or charging the batteries), and energy is lost due to air resistance and friction. A spring-operated dart gun is not a close... |
or more of the terms is zero, simplifying its solution. Do not calculate c, the work done by conservative forces; it is already incorporated in the PE terms. Step 5. You have already identified the types of work and energy involved (in step 2). Before solving for the unknown, eliminate terms wherever possible to simpl... |
oules Big Bang Energy released in a supernova Fusion of all the hydrogen in Earth’s oceans Annual world energy use Large fusion bomb (9 megaton) 1 kg hydrogen (fusion to helium) 1 kg uranium (nuclear fission) Hiroshima-size fission bomb (10 kiloton) 90,000-ton aircraft carrier at 30 knots 1 barrel crude oil 1 ton TNT 1... |
spring laboratory. Hang masses from springs and adjust the spring stiffness and damping. You can even slow time. Transport the lab to different planets. A chart shows the kinetic, potential, and thermal energies for each spring. Figure 7.22 Masses and Springs (http://cnx.org/content/m55049/1.3/mass-spring-lab_en.jar) ... |
at http://cnx.org/content/col11844/1.13 Chapter 7 | Work, Energy, and Energy Resources 293 The work going into mechanical energy is = KE + PE. At the bottom of the stairs, we take both KE and PEg as initially zero; thus, = KEf + PEg = 1 given, we can calculate and then divide it by time to get power. 2 +, where is the... |
m2). A tiny fraction of this is retained by Earth over the long term. Our consumption rate of fossil fuels is far greater than the rate at which they are stored, so it is inevitable that they will be depleted. Power implies that energy is transferred, perhaps changing form. It is never possible to change one form compl... |
if its power consumption rate and time used are known. The higher the power consumption rate and the longer the appliance is used, the greater the cost of that appliance. The power consumption rate is = / = /, where is the energy supplied by the electricity company. So the energy consumed over a time is This content i... |
on only a few minutes per day. It would also not include electric clocks, in spite of their 24-hour-per-day usage, because they are very low power devices. It is sometimes possible to use devices that have greater efficiencies—that is, devices that consume less power to accomplish the same task. One example is the com... |
using more efficient room heaters, cars that have greater miles-pergallon ratings, energy-efficient compact fluorescent lights, etc. Since energy in an isolated system is not destroyed or created or generated, one might wonder why we need to be concerned about our energy resources, since energy is a conserved quantity... |
an object nonconservative force: a force whose work depends on the path followed between the given initial and final configurations nuclear energy: energy released by changes within atomic nuclei, such as the fusion of two light nuclei or the fission of a heavy nucleus potential energy: energy due to position, shape, ... |
theorem states that the net work net on a system changes its kinetic energy, net = 1 22 − 1 20 2. 7.3 Gravitational Potential Energy • Work done against gravity in lifting an object becomes potential energy of the object-Earth system. • The change in gravitational potential energy, ΔPEg, is ΔPEg =, with being the incr... |
.6 Conservation of Energy • The law of conservation of energy states that the total energy is constant in any process. Energy may change in form or be transferred from one system to another, but the total remains the same. • When all forms of energy are considered, conservation of energy is written in equation form as ... |
• Economic well-being is dependent upon energy use, and in most countries higher standards of living, as measured by GDP (Gross Domestic Product) per capita, are matched by higher levels of energy consumption per capita. • Even though, in accordance with the law of conservation of energy, energy can never be created o... |
is negligible, describe changes in the potential energy of a diving board as a swimmer dives from it, starting just before the swimmer steps on the board until just after his feet leave it. 11. Define mechanical energy. What is the relationship of mechanical energy to nonconservative forces? What happens to mechanical... |
in Humans 21. Explain why it is easier to climb a mountain on a zigzag path rather than one straight up the side. Is your increase in gravitational potential energy the same in both cases? Is your energy consumption the same in both? 22. Do you do work on the outside world when you rub your hands together to warm them... |
force is directly proportional to speed, how many gallons will be used to drive 108 km at a speed of 28.0 m/s? 5. Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º with the horizontal. (See Figure 7.35.) He exerts a force of 500 N on the crate parallel to ... |
90.0 km/h in a distance of 120 m (a fairly typical distance for a non-panic stop). (b) Suppose instead the car hits a concrete abutment at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a). 13. A car’s bumper is designed to withstand a... |
, if he encounters a headwind that exerts an average force of 30.0 N against him. 7.3 Gravitational Potential Energy 16. A hydroelectric power facility (see Figure 7.38) converts the gravitational potential energy of water behind a dam to electric energy. (a) What is the gravitational potential energy relative to the g... |
even small hills.) To demonstrate this, find the final speed and the time taken for a skier who skies 70.0 m along a 30º slope neglecting friction: (a) Starting from rest. (b) Starting with an initial speed of 2.50 m/s. (c) Does the answer surprise you? Discuss why it is still advantageous to get a running start in ve... |
TV tube? (These electrons were not dangerous in themselves, but they did create dangerous x rays. Later model tube TVs had shielding that absorbed x rays before they escaped and exposed viewers.) 27. Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above ... |
for several hours at a stretch, perhaps by pedaling a mechanism that drives an electric generator. Neglecting any problems of generator efficiency and practical considerations such as resting time: (a) How many people would it take to run a 4.00-kW electric clothes dryer? (b) How many people would it take to replace a... |
height, but the full 10,000 kg is accelerated. (b) What does it cost, if electricity is $0.0900 per kW ⋅ h? 40. (a) What is the available energy content, in joules, of a battery that operates a 2.00-W electric clock for 18 months? (b) How long can a battery that can supply 8.00104 J run a pocket calculator that consum... |
the 93.0 kcal of energy in a 10.0-g pat of butter? (b) How many flights is this if each flight has 16 stairs? 45. (a) What is the power output in watts and horsepower of a 70.0-kg sprinter who accelerates from rest to 10.0 m/s in 3.00 s? (b) Considering the amount of power generated, do you think a well-trained athlet... |
of a jogger’s leg, if his leg has a mass of 13.0 kg, a speed of 6.00 m/s, and stops in a distance of 1.50 cm. (Be certain to include the weight of the 75.0-kg jogger’s body.) (b) Compare this force with the weight of the jogger. 54. (a) Calculate the energy in kJ used by a 55.0-kg woman who does 50 deep knee bends in ... |
44 exerts an average horizontal backward force of 80.0 N with his arm during each 1.80 m long stroke. (a) What is his work output in each 310 Chapter 7 | Work, Energy, and Energy Resources stroke? (b) Calculate the power output of his arms if he does 120 strokes per minute. long time? Discuss why exercise is necessary ... |
fat. (These proportions neglect the mass of bulk and nondigestible materials consumed.) 7.9 World Energy Use 60. Integrated Concepts (a) Calculate the force the woman in Figure 7.46 exerts to do a push-up at constant speed, taking all data to be known to three digits. (b) How much work does she do if her center of mas... |
�s maximum range on level ground? 64. Integrated Concepts (a) What force must be supplied by an elevator cable to produce an acceleration of 0.800 m/s2 against a 200-N frictional force, if the mass of the loaded elevator is 1500 kg? (b) How much work is done by the cable in lifting the elevator 20.0 m? (c) What is the ... |
descend stairs at a faster rate for a nearly unlimited time in spite of the fact that very similar forces are exerted going down as going up. (This points to a fundamentally different process for descending versus climbing stairs.) 68. Construct Your Own Problem Consider humans generating electricity by pedaling a dev... |
. A crane is lifting construction materials from the ground to an elevation of 60 m. Over the first 10 m, the motor linearly increases the force it exerts from 0 to 10 kN. It exerts that constant force for the next 40 m, and then winds down to 0 N again over the last 10 m, as shown in the figure. What is the total work... |
model drag car is being accelerated along its track from rest by a motor with a force of 75 N, but there is a drag force of 30 N due to the track. What is the kinetic energy after 2 m of travel? a. 90 J This content is available for free at http://cnx.org/content/col11844/1.13 b. 150 J c. 210 J d. 60 J 13. You are lau... |
9.0 m/s. What is the kinetic energy? If you then learn that it is 4.0 m above the ground, what is the total mechanical energy relative to the ground? a. 78 J, 3 J b. 160 J, 81 J c. 81 J, 160 J d. 81 J, 3 J 21. You have a 120-g yo-yo that you are swinging at 0.9 m/s. How much energy does it have? How high can it get ab... |
imes. One particular clock has three masses: 4.0 kg, 4.0 kg, and 6.0 kg. They can drop 1.3 meters. How much energy does the clock use in a week? a. 51 J b. 76 J c. 127 J d. 178 J 28. A water tower stores not only water, but (at least part of) the energy to move the water. How much? Make reasonable estimates for how muc... |
an object pushed across a rough surface. Explain why this happens. What are the differences between these systems? 35. A child has two red wagons, with the rear one tied to the front by a stretchy rope (a spring). If the child pulls on the front wagon, the ____ increases. a. kinetic energy of the wagons b. potential e... |
8 LINEAR MOMENTUM AND COLLISIONS Figure 8.1 Each rugby player has great momentum, which will affect the outcome of their collisions with each other and the ground. (credit: ozzzie, Flickr) Chapter Outline 8.1. Linear Momentum and Force 8.2. Impulse 8.3. Conservation of Momentum 8.4. Elastic Collisions in One Dimension... |
all systems under all circumstances, energy, charge, linear momentum, and angular momentum are conserved. Essential Knowledge 5.D.1 In a collision between objects, linear momentum is conserved. In an elastic collision, kinetic energy is the same before and after. Essential Knowledge 5.D.2 In a collision between object... |
icized, boldfaced, and has an arrow is a vector.) In both parts of this example, the magnitude of momentum can be calculated directly from the definition of momentum given in the equation, which becomes = (8.3) when only magnitudes are considered. Solution for (a) To determine the momentum of the player, substitute the... |
be stated in its most broadly applicable form in terms of momentum. Momentum continues to be a key concept in the study of atomic and subatomic particles in quantum mechanics. This statement of Newton’s second law of motion includes the more familiar Fnet =a as a special case. We can derive this form as follows. First... |
(f – i) 0.057 kg = = 3.306 kg · m/s ≈ 3.3 kg · m/s (58 m/s – 0 m/s) Now the magnitude of the net external force can determined by using net = Δ Δ : net = Δ Δ = 3.306 kg ⋅ m/s 5.0×10−3 s = 661 N ≈ 660 N, (8.13) (8.14) Δ Δ (8.15) (8.16) where we have retained only two significant figures in the final step. Discussion Th... |
mine the average effective force using graphical representation. • Calculate average force and impulse given mass, velocity, and time. The information presented in this section supports the following AP® learning objectives and science practices: • 3.D.2.1 The student is able to justify the selection of routines for th... |
same as the change in momentum. Δp = FnetΔ, (8.18) Impulse: Change in Momentum Change in momentum equals the average net external force multiplied by the time this force acts. Δp = FnetΔ (8.19) The quantity Fnet Δ is given the name impulse. There are many ways in which an understanding of impulse can save lives, or at... |
•m/s (8.20) (8.21) We are assuming that the initial velocity is −3.0 m/s. We have established that the force exerted by the barrier is in the positive direction, so the initial velocity of the block must be in the negative direction. Since the final momentum of the block is zero, the impulse is equal to the change in m... |
in the direction. Therefore the wall exerts a force on the ball in the direction. The second ball continues with the same momentum component in the direction, but reverses its -component of momentum, as seen by sketching a diagram of the angles involved and keeping in mind the proportionality between velocity and mome... |
curve has units of momentum and is equal to the impulse or change in momentum between times 1 and 2. That area is equal to the area inside the 322 Chapter 8 | Linear Momentum and Collisions rectangle bounded by eff, 1, and 2. Thus the impulses and their effects are the same for both the actual and effective forces. Fi... |
a ball while keeping your hands still. Hit water in a tub with your full palm. After the water has settled, hit the water again by diving your hand with your fingers first into the water. (Your full palm represents a swimmer doing a belly flop and your diving hand represents a swimmer doing a dive.) Explain what happe... |
principle of the conservation of linear momentum, predict an outcome of the experiment using the principle, analyze data generated by that experiment whose uncertainties are expressed numerically, and evaluate the match between the prediction and the outcome. (S.P. 4.2, 5.1, 5.3, 6.4) • 5.D.2.1 The student is able to ... |
car (labeled 2) is bumped by the trailing car (labeled 1). The only unbalanced force on each car is the force of the collision. (Assume that the effects due to friction are negligible.) Car 1 slows down as a result of the collision, losing some momentum, while car 2 speeds up and gains some momentum. We shall now show... |
number of objects in it. In equation form, the conservation of momentum principle for an isolated system is written or ptot = constant, ptot = p′tot, (8.34) (8.35) (8.36) (8.37) (8.38) (8.39) This content is available for free at http://cnx.org/content/col11844/1.13 Chapter 8 | Linear Momentum and Collisions 325 where... |
the two carts move with equal speeds v in opposite directions towards the center of mass. Again, they have an elastic collision, so after the collision, they exchange velocities (each cart moving in the opposite direction of its initial motion with the same speed). As the two carts approach, the center of mass is exac... |
vs. time compare to a graph of the momentum of the system vs. time? 326 Chapter 8 | Linear Momentum and Collisions Perhaps an easier way to see that momentum is conserved for an isolated system is to consider Newton’s second law in terms of momentum, Fnet = Δptot Δ. For an isolated system, Fnet = 0 ; thus, Δptot = 0, ... |
if the basketball ball is held above and in contact with the tennis ball? Making Connections: Take-Home Investigation—Two Tennis Balls in a Ballistic Trajectory Tie two tennis balls together with a string about a foot long. Hold one ball and let the other hang down and throw it in a ballistic trajectory. Explain your ... |
ify your prediction. • How will you measure the momentum of each object? • Should you have two objects in motion or one object bouncing off a rigid surface? • Should you verify the relationship mathematically or graphically? • How will you estimate the uncertainty of your measurements? How will you express this uncerta... |
a target particle. In experiments seeking evidence for quarks, electrons were observed to occasionally scatter straight backward from a proton. 328 Chapter 8 | Linear Momentum and Collisions 8.4 Elastic Collisions in One Dimension Learning Objectives By the end of this section, you will be able to: • Describe an elast... |
for missing variables, and calculate their values. (S.P. 2.1, 2.2) • 5.D.1.6 The student is able to make predictions of the dynamical properties of a system undergoing a collision by application of the principle of linear momentum conservation and the principle of the conservation of energy in situations in which an e... |
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