A more ordinary example of conservation of momentum than a

What average club speed would double the average force?

When a person is involved in a car accident, why is the likelihood of injury greater in a head-on collision as opposed to being hit from behind? Answer using the concepts of relative velocity, momentum, and average force.

Would fi ring a heavier arrow necessarily increase the recoil velocity? Explain, using the result of Quick Quiz 6.1.

If the mass of both vehicles were doubled, how would the fi nal velocity be affected? The change in kinetic energy?

List three ways mechanical energy can be lost from the system in this experiment.

In this example, is it possible to adjust the initial velocities of the balls so that both are at rest after the collision? Explain

In this example, is it possible to adjust the initial velocities of the balls so that both are at rest after the collision? Explain

If the car and van had identical mass and speed, what would the resultant angle have been?

What initial normal force would be exerted on an astronaut of mass m in a rocket traveling vertically upward with an acceleration a? Answer symbolically in terms of the positive quantities m, g, and a.

A soccer player runs up behind a 0.450-kg soccer ball traveling at 3.20 m/s and kicks it in the same direction as it is moving, increasing its speed to 12.8 m/s. What magnitude impulse did the soccer player deliver to the ball? (a) 2.45 kg # m/s (b) 4.32 kg # m/s (c) 5.61 kg # m/s (d) 7.08 kg # m/s (e) 9.79 kg # m/s

A 57.0-g tennis ball is traveling straight at a player at 21.0 m/s. The player volleys the ball straight back at 25.0 m/s. If the ball remains in contact with the racket for 0.060 s, what average force acts on the ball? (a) 22.6 kg # m/s2 (b) 32.5 kg # m/s2 (c) 43.7 kg # m/s2 (d) 72.1 kg # m/s2 (e) 102 kg # m/s2

A car of mass m traveling at speed v crashes into the rear of a truck of mass 2m that is at rest and in neutral at an intersection. If the collision is perfectly inelastic, what is the speed of the combined car and truck after the collision? (a) v (b) v/2 (c) v/3 (d) 2v (e) None of these

A small china bowl having kinetic energy E is sliding along a frictionless countertop when a server, with perfect timing, places a rice ball into the bowl as it passes him. If the bowl and rice ball have the same mass, what is the kinetic energy of the system thereafter? (a) 2E (b) E (c) E/2 (d) E/4 (e) E/8

In a game of billiards, a red billiard ball is traveling in the positive x-direction with speed v and the cue ball is traveling in the negative x-direction with speed 3v when the two balls collide head on. Which statement is true concerning their velocities subsequent to the collision? Neglect any effects of spin. (a) red ball: v; cue ball: 3v (b) red ball: v; cue ball: 2v (c) red ball: 3v; cue ball: v (d) red ball: v; cue ball: 3v (e) The velocities cant be determined without knowing the mass of each ball.

A 5-kg cart moving to the right with a speed of 6 m/s collides with a concrete wall and rebounds with a speed of 2 m/s. Is the change in momentum of the cart (a) 0, (b) 40 kg # m/s, (c) 240 kg # m/s, (d) 230 kg # m/s, or (e) 210 kg # m/s?

A 0.10-kg object moving initially with a velocity of 0.20 m/s eastward makes an elastic head-on collision with a 0.15-kg object initially at rest. What is the fi nal velocity of the 0.10-kg object after the collision? (a) 0.16 m/s eastward (b) 0.16 m/s westward (c) 0.040 m/s eastward (d) 0.040 m/s westward (e) None of these

A 0.004-kg bullet is fi red into a 0.200-kg block of wood at rest on a horizontal surface. After impact, the block with the embedded bullet slides 8.00 m before coming to rest. If the coeffi cient of friction is 0.400, what is the speed of the bullet before impact? (a) 96 m/s (b) 112 m/s (c) 286 m/s (d) 404 m/s (e) 812 m/s

The kinetic energy of a rocket is increased by a factor of eight after its engines are fi red, whereas its total mass is reduced by half through the burning of fuel. By what factor is the magnitude of its momentum changed? Hint: Use KE p2/2m. (a) 2 (b) 8 (c) 4 (d) 16 (e) 1

If two particles have equal momenta, are their kinetic energies equal? (a) yes, always (b) no, never (c) no, except when their masses are equal (d) no, except when their speeds are the same (e) yes, as long as they move along parallel lines

If two particles have equal kinetic energies, are their momenta equal? (a) yes, always (b) no, never (c) yes, as long as their masses are equal (d) yes, if both their masses and directions of motion are the same (e) no, unless they are moving perpendicular to each other

A rocket with total mass 3.00  105 kg leaves a launch pad at Cape Kennedy, moving vertically with an acceleration of 36.0 m/s2. If the speed of the exhausted gases is 4.50  103 m/s, at what rate is the rocket initially burning fuel? (a) 3.05  103 kg/s (b) 2.40  103 kg/s (c) 7.50  102 kg/s (d) 1.50  103 kg/s (e) None of these

A batter bunts a pitched baseball, blocking the ball without swinging. (a) Can the baseball deliver more kinetic energy to the bat and batter than the ball carries initially? (b) Can the baseball deliver more momentum to the bat and batter than the ball carries initially? Explain each of your answers.

Americans will never forget the terrorist attack on September 11, 2001. One commentator remarked that the force of the explosion at the Twin Towers of the World Trade Center was strong enough to blow glass and parts of the steel structure to small fragments. Yet the television coverage showed thousands of sheets of paper fl oating down, many still intact. Explain how that could be.

In perfectly inelastic collisions between two objects, there are events in which all of the original kinetic energy is transformed to forms other than kinetic. Give an example of such an event.

If two objects collide and one is initially at rest, is it possible for both to be at rest after the collision? Is it possible for only one to be at rest after the collision? Explain.

A ball of clay of mass m is thrown with a speed v against a brick wall. The clay sticks to the wall and stops. Is the principle of conservation of momentum violated in this example?

A skater is standing still on a frictionless ice rink. Her friend throws a Frisbee straight at her. In which of the following cases is the largest momentum transferred to the skater? (a) The skater catches the Frisbee and holds onto it. (b) The skater catches the Frisbee momentarily, but then drops it vertically downward. (c) The skater catches the Frisbee, holds it momentarily, and throws it back to her friend.

A more ordinary example of conservation of momentum than a rocket ship occurs in a kitchen dishwashing machine. In this device, water at high pressure is forced out of small holes on the spray arms. Use conservation of momentum to explain why the arms rotate, directing water to all the dishes.

A large bedsheet is held vertically by two students. A third student, who happens to be the star pitcher on the baseball team, throws a raw egg at the sheet. Explain why the egg doesnt break when it hits the sheet, regardless of its initial speed. (If you try this, make sure the pitcher hits the sheet near its center, and dont allow the egg to fall on the fl oor after being caught.)

Your physical education teacher throws you a tennis ball at a certain velocity, and you catch it. You are now given the following choice: The teacher can throw you a medicine ball (which is much more massive than the tennis ball) with the same velocity, the same momentum, or the same kinetic energy as the tennis ball. Which option would you choose in order to make the easiest catch, and why?

If two automobiles collide, they usually do not stick together. Does this mean the collision is elastic? Explain why a head-on collision is likely to be more dangerous than other types of collisions.

A sharpshooter fi res a rifl e while standing with the butt of the gun against his shoulder. If the forward momentum of a bullet is the same as the backward momentum of the gun, why isnt it as dangerous to be hit by the gun as by the bullet?

An air bag infl ates when a collision occurs, protecting a passenger (the dummy in Figure CQ6.12) from serious injury. Why does the air bag soften the blow? Discuss the physics involved in this dramatic photograph.

In golf, novice players are often advised to be sure to follow through with their swing. Why does this make the ball travel a longer distance? If a shot is taken near the green, very little follow-through is required. Why?

An open box slides across a frictionless, icy surface of a frozen lake. What happens to the speed of the box as water from a rain shower falls vertically downward into the box? Explain.

Calculate the magnitude of the linear momentum for the following cases: (a) a proton with mass 1.67  1027 kg, moving with a speed of 5.00  106 m/s; (b) a 15.0-g bullet moving with a speed of 300 m/s; (c) a 75.0-kg sprinter running with a speed of 10.0 m/s; (d) the Earth (mass 5.98  1024 kg) moving with an orbital speed equal to 2.98  104 m/s.

A stroboscopic photo of a club hitting a golf ball, such as the photo shown in Figure 6.3, was made by Harold Edgerton in 1933. The ball was initially at rest, and the club was shown to be in contact with the club for about 0.002 0 s. Also, the ball was found to end up with a speed of 2.0  102 ft/s. Assuming that the golf ball had a mass of 55 g, find the average force exerted by the club on the ball.

A pitcher claims he can throw a 0.145-kg baseball with as much momentum as a 3.00-g bullet moving with a speed of 1.50  103 m/s. (a) What must the baseballs speed be if the pitchers claim is valid? (b) Which has greater kinetic energy, the ball or the bullet?

A 0.10-kg ball is thrown straight up into the air with an initial speed of 15 m/s. Find the momentum of the ball (a) at its maximum height and (b) halfway to its maximum height.

A baseball player of mass 84.0 kg running at 6.70 m/s slides into home plate. (a) What magnitude impulse is delivered to the player by friction? (b) If the slide lasts 0.750 s, what average friction force is exerted on the player?

Show that the kinetic energy of a particle of mass m is related to the magnitude of the momentum p of that particle by KE p2/2m. Note: This expression is invalid for particles traveling at speeds near that of light.

An object has a kinetic energy of 275 J and a momentum of magnitude 25.0 kg m/s. Find the speed and mass of the object.

An estimated force vs. time curve for a baseball struck by a bat is shown in Figure P6.8. From this curve, determine (a) the impulse delivered to the ball and (b) the average force exerted on the ball.

A 0.280-kg volleyball approaches a player horizontally with a speed of 15.0 m/s. The player strikes the ball with her fist and causes the ball to move in the opposite direction with a speed of 22.0 m/s. (a) What impulse is delivered to the ball by the player? (b) If the players fist is in contact with the ball for 0.060 0 s, find the magnitude of the average force exerted on the players fist.

A man claims he can safely hold on to a 12.0-kg child in a head-on collision with a relative speed of 120-mi/h lasting for 0.10 s as long as he has his seat belt on. (a) Find the magnitude of the average force needed to hold onto the child. (b) Based on the result to part (a), is the mans claim valid? (c) What does the answer to this problem say about laws requiring the use of proper safety devices such as seat belts and special toddler seats?

A ball of mass 0.150 kg is dropped from rest from a height of 1.25 m. It rebounds from the floor to reach a height of 0.960 m. What impulse was given to the ball by the floor?

A tennis player receives a shot with the ball (0.060 0 kg) traveling horizontally at 50.0 m/s and returns the shot with the ball traveling horizontally at 40.0 m/s in the opposite direction. (a) What is the impulse delivered to the ball by the racket? (b) What work does the racket do on the ball?

A car is stopped for a traffic signal. When the light turns green, the car accelerates, increasing its speed from 0 to 5.20 m/s in 0.832 s. What are the magnitudes of the linear impulse and the average total force experienced by a 70.0-kg passenger in the car during the time the car accelerates?

A 0.500-kg football is thrown toward the east with a speed of 15.0 m/s. A stationary receiver catches the ball and brings it to rest in 0.020 0 s. (a) What is the impulse delivered to the ball as its caught? (b) What is the average force exerted on the receiver?

The force shown in the force vs. time diagram in Figure P6.15 acts on a 1.5-kg object. Find (a) the impulse of the force, (b) the final velocity of the object if it is initially at rest, and (c) the final velocity of the object if it is initially moving along the x-axis with a velocity of 2.0 m/s.

A force of magnitude Fx acting in the x-direction on a 2.00-kg particle varies in time as shown in Figure P6.16. Find (a) the impulse of the force, (b) the final velocity of the particle if it is initially at rest, and (c) the final velocity of the particle if it is initially moving along the x-axis with a velocity of 2.00 m/s.

The forces shown in the force vs. time diagram in Figure P6.17 act on a 1.5-kg particle. Find (a) the impulse for the interval from t 0 to t 3.0 s and (b) the impulse for the interval from t 0 to t 5.0 s. (c) If the forces act on a 1.5-kg particle that is initially at rest, find the particles speed at t 3.0 s and at t 5.0 s.

A 3.00-kg steel ball strikes a massive wall at 10.0 m/s at an angle of 60.0 with the plane of the wall. It bounces off the wall with the same speed and angle (Fig. P6.18). If the ball is in contact with the wall for 0.200 s, what is the average force exerted by the wall on the ball?

The front 1.20 m of a 1 400-kg car is designed as a crumple zone that collapses to absorb the shock of a collision. If a car traveling 25.0 m/s stops uniformly in 1.20 m, (a) how long does the collision last, (b) what is the magnitude of the average force on the car, and (c) what is the acceleration of the car? Express the acceleration as a multiple of the acceleration of gravity.

A pitcher throws a 0.15-kg baseball so that it crosses home plate horizontally with a speed of 20 m/s. The ball is hit straight back at the pitcher with a final speed of 22 m/s. (a) What is the impulse delivered to the ball? (b) Find the average force exerted by the bat on the ball if the two are in contact for 2.0  103 s.

High-speed stroboscopic photographs show that the head of a 200-g golf club is traveling at 55 m/s just before it strikes a 46-g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 40 m/s. Find the speed of the golf ball just after impact.

A rifle with a weight of 30 N fi res a 5.0-g bullet with a speed of 300 m/s. (a) Find the recoil speed of the rifle. (b) If a 700-N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle.

A 45.0-kg girl is standing on a 150-kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.50 m/s to the right relative to the plank. (a) What is her velocity relative to the surface of the ice? (b) What is the velocity of the plank relative to the surface of the ice?

A 730-N man stands in the middle of a frozen pond of radius 5.0 m. He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 1.2-kg physics textbook horizontally toward the north shore at a speed of 5.0 m/s. How long does it take him to reach the south shore?

An astronaut in her space suit has a total mass of 87.0 kg, including suit and oxygen tank. Her tether line loses its attachment to her spacecraft while shes on a spacewalk. Initially at rest with respect to her spacecraft, she throws her 12.0-kg oxygen tank away from her spacecraft with a speed of 8.00 m/s to propel herself back toward it (Fig. P6.25). (a) Determine the maximum distance she can be from the craft and still return within 2.00 min (the amount of time the air in her helmet remains breathable). (b) Explain in terms of Newtons laws of motion why this strategy works.

A cannon is mounted on a railroad flatcar, the muzzle elevated to 30.0 and pointed in the direction of the track. The cannon fi res a 1.00metric-ton projectile at 1.00 km/s. (a) If the flatcar and cannon together have a mass of 36.0 metric tons (not including the projectile), what is the initial recoil speed of the flatcar? (b) In this problem, it appears that momentum in the y-direction is not conserved. Explain what happens to it.

A 65.0-kg person throws a 0.045 0-kg snowball forward with a ground speed of 30.0 m/s. A second person, with a mass of 60.0 kg, catches the snowball. Both people are on skates. The first person is initially moving forward with a speed of 2.50 m/s, and the second person is initially at rest. What are the velocities of the two people after the snowball is exchanged? Disregard friction between the skates and the ice.

Two ice skaters are holding hands at the center of a frozen pond when an argument ensues. Skater A shoves skater B along a horizontal direction. Identify (a) the horizontal forces acting on A and (b) those acting on B. (c) Which force is greater, the force on A or the force on B? (d) Can conservation of momentum be used for the system of A and B? Defend your answer. (e) If A has a mass of 0.900 times that of B, and B begins to move away with a speed of 2.00 m/s, find the speed of A.

A man of mass m1 70.0 kg is skating at v1 8.00 m/s behind his wife of mass m2 50.0 kg, who is skating at v2 4.00 m/s. Instead of passing her, he inadvertently collides with her. He grabs her around the waist, and they maintain their balance. (a) Sketch the problem with before-and-after diagrams, representing the skaters as blocks. (b) Is the collision best described as elastic, inelastic, or perfectly inelastic? Why? (c) Write the general equation for conservation of momentum in terms of m1, v1, m2, v2, and final velocity vf. (d) Solve the momentum equation for vf. (e) Substitute values, obtaining the numerical value for vf, their speed after the collision.

An archer shoots an arrow toward a 300-g target that is sliding in her direction at a speed of 2.50 m/s on a smooth, slippery surface. The 22.5-g arrow is shot with a speed of 35.0 m/s and passes through the target, which is stopped by the impact. What is the speed of the arrow after passing through the target?

Gayle runs at a speed of 4.00 m/s and dives on a sled, initially at rest on the top of a frictionless, snow-covered hill. After she has descended a vertical distance of 5.00 m, her brother, who is initially at rest, hops on her back, and they continue down the hill together. What is their speed at the bottom of the hill if the total vertical drop is 15.0 m? Gayles mass is 50.0 kg, the sled has a mass of 5.00 kg, and her brother has a mass of 30.0 kg.

A 75.0-kg ice skater moving at 10.0 m/s crashes into a stationary skater of equal mass. After the collision, the two skaters move as a unit at 5.00 m/s. Suppose the average force a skater can experience without breaking a bone is 4 500 N. If the impact time is 0.100 s, does a bone break?

A railroad car of mass 2.00  104 kg moving at 3.00 m/s collides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 1.20 m/s. (a) What is the speed of the three coupled cars after the collision? (b) How much kinetic energy is lost in the collision?

A railroad car of mass M moving at a speed v1 collides and couples with two coupled railroad cars, each of the same mass M and moving in the same direction at a speed v2. (a) What is the speed vf of the three coupled cars after the collision in terms of v1 and v2? (b) How much kinetic energy is lost in the collision? Answer in terms of M, v1, and v2.

Consider the ballistic pendulum device discussed in Example 6.5 and illustrated in Figure 6.12. (a) Determine the ratio of the momentum immediately after the collision to the momentum immediately before the collision. (b) Show that the ratio of the kinetic energy immediately after the collision to the kinetic energy immediately before the collision is m1/(m1 + m2).

A 7.0-g bullet is fi red into a 1.5-kg ballistic pendulum. The bullet emerges from the block with a speed of 200 m/s, and the block rises to a maximum height of 12 cm. Find the initial speed of the bullet.

In a Broadway performance, an 80.0-kg actor swings from a 3.75-m-long cable that is horizontal when he starts. At the bottom of his arc, he picks up his 55.0-kg costar in an inelastic collision. What maximum height do they reach after their upward swing?

Two shuffl eboard disks of equal mass, one orange and the other yellow, are involved in a perfectly elastic glancing collision. The yellow disk is initially at rest and is struck by the orange disk moving initially to the right at 5.00 m/s. After the collision, the orange disk moves in a direction that makes an angle of 37.0 with its initial direction. Meanwhile, the velocity vector of the yellow disk is perpendicular to the postcollision velocity vector of the orange disk. Determine the speed of each disk after the collision.

A 0.030-kg bullet is fi red vertically at 200 m/s into a 0.15- kg baseball that is initially at rest. How high does the combined bullet and baseball rise after the collision, assuming the bullet embeds itself in the ball?

An 8.00-g bullet is fi red into a 250-g block that is initially at rest at the edge of a table of height 1.00 m (Fig. P6.40). The bullet remains in the block, and after the impact the block lands 2.00 m from the bottom of the table. Determine the initial speed of the bullet.

A 12.0-g bullet is fi red horizontally into a 100-g wooden block that is initially at rest on a frictionless horizontal surface and connected to a spring having spring constant 150 N/m. The bullet becomes embedded in the block. If the bulletblock system compresses the spring by a maximum of 80.0 cm, what was the speed of the bullet at impact with the block?

A 1 200-kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a 9 000-kg truck moving in the same direction at 20.0 m/s (Fig. P6.42). The velocity of the car right after the collision is 18.0 m/s to the east. (a) What is the velocity of the truck right after the collision? (b) How much mechanical energy is lost in the collision? Account for this loss in energy.

A 5.00-g object moving to the right at 20.0 cm/s makes an elastic head-on collision with a 10.0-g object that is initially at rest. Find (a) the velocity of each object after the collision and (b) the fraction of the initial kinetic energy transferred to the 10.0-g object.

A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass m1 48.0 kg travels in the positive x- direction at 12.0 m/s, and a second piece of mass m2 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m3 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities. (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2, and v3 and the sines and cosines of the angles, taking u to be the unknown angle. (c) Calculate the fi nal x-components of the momenta of m1 and m2. (d) Calculate the fi nal y-components of the momenta of m1 and m2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (f) Solve the two momentum equations for v3 cos u and v3 sin u, respectively, and use the identity cos2 u sin2 u 1 to obtain v3. (g) Divide the equation for v3 sin u by that for v3 cos u to obtain tan u, then obtain the angle by taking the inverse tangent of both sides. (h) In general, would three such pieces necessarily have to move in the same plane? Why?

A 25.0-g object moving to the right at 20.0 cm/s overtakes and collides elastically with a 10.0-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision.

A billiard ball rolling across a table at 1.50 m/s makes a head-on elastic collision with an identical ball. Find the speed of each ball after the collision (a) when the second ball is initially at rest, (b) when the second ball is moving toward the fi rst at a speed of 1.00 m/s, and (c) when the second ball is moving away from the fi rst at a speed of 1.00m/s.

A 90.0-kg fullback running east with a speed of 5.00 m/s is tackled by a 95.0-kg opponent running north with a speed of 3.00 m/s. (a) Why does the tackle constitute a perfectly inelastic collision? (b) Calculate the velocity of the players immediately after the tackle and (c) deter mine the mechanical energy that is lost as a result of the collision. Where did the lost energy go?

Identical twins, each with mass 55.0 kg, are on ice skates and at rest on a frozen lake, which may be taken as frictionless. Twin A is carrying a backpack of mass 12.0 kg. She throws it horizontally at 3.00 m/s to Twin B. Neglecting any gravity effects, what are the subsequent speeds of Twin A and Twin B?

A 2 000-kg car moving east at 10.0 m/s collides with a 3 000-kg car moving north. The cars stick together and move as a unit after the collision, at an angle of 40.0 north of east and a speed of 5.22 m/s. Find the speed of the 3 000-kg car before the collision.

Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 13.0 m/s toward the east, and the other is traveling north with speed v2i . Neither driver sees the other. The vehicles collide in the intersection and stick together, leaving parallel skid marks at an angle of 55.0 north of east. The speed limit for both roads is 35 mi/h, and the driver of the northward-moving vehicle claims he was within the limit when the collision occurred. Is he telling the truth?

A billiard ball moving at 5.00 m/s strikes a stationary ball of the same mass. After the collision, the fi rst ball moves at 4.33 m/s at an angle of 30 with respect to the original line of motion. (a) Find the velocity (magnitude and direction) of the second ball after collision. (b) Was the collision inelastic or elastic?

In research in cardiology and exercise physiology, it is often important to know the mass of blood pumped by a persons heart in one stroke. This information can be obtained by means of a ballistocardiograph. The instrument works as follows: The subject lies on a horizontal pallet fl oating on a fi lm of air. Friction on the pallet is negligible. Initially, the momentum of the system is zero. When the heart beats, it expels a mass m of blood into the aorta with speed v, and the body and platform move in the opposite direction with speed V. The speed of the blood can be determined independently (for example, by observing an ultrasound Doppler shift). Assume that the bloods speed is 50.0 cm/s in one typical trial. The mass of the subject plus the pallet is 54.0 kg. The pallet moves 6.00  105 m in 0.160 s after one heartbeat. Calculate the mass of blood that leaves the heart. Assume that the mass of blood is negligible compared with the total mass of the person. This simplifi ed example illustrates the principle of ballistocardiography, but in practice a more sophisticated model of heart function is used.

Most of us know intuitively that in a head-on collision between a large dump truck and a subcompact car, you are better off being in the truck than in the car. Why is this? Many people imagine that the collision force exerted on the car is much greater than that exerted on the truck. To substantiate this view, they point out that the car is crushed, whereas the truck is only dented. This idea of unequal forces, of course, is false; Newtons third law tells us that both objects are acted upon by forces of the same magnitude. The truck suffers less damage because it is made of stronger metal. But what about the two drivers? Do they experience the same forces? To answer this question, suppose that each vehicle is initially moving at 8.00 m/s and that they undergo a perfectly inelastic headon collision. Each driver has mass 80.0 kg. Including the masses of the drivers, the total masses of the vehicles are 800 kg for the car and 4 000 kg for the truck. If the collision time is 0.120 s, what force does the seat belt exert on each driver?

Consider a frictionless track as shown in Figure P6.54. A block of mass m1 5.00 kg is released from . It makes a head-on elastic collision at with a block of mass m2 10.0 kg that is initially at rest. Calculate the maximum height to which m1 rises after the collision.

A 2.0-g particle moving at 8.0 m/s makes a perfectly elastic head-on collision with a resting 1.0-g object. (a) Find the speed of each particle after the collision. (b) Find the speed of each particle after the collision if the stationary particle has a mass of 10 g. (c) Find the fi nal kinetic energy of the incident 2.0-g particle in the situations described in parts (a) and (b). In which case does the incident particle lose more kinetic energy?

A bullet of mass m and speed v passes completely through a pendulum bob of mass M as shown in Figure P6.56. The bullet emerges with a speed of v/2. The pendulum bob is suspended by a stiff rod of length and negligible mass. What is the minimum value of v such that the bob will barely swing through a complete vertical circle?

An 80-kg man standing erect steps off a 3.0-m-high diving platform and begins to fall from rest. The man again comes to a rest 2.0 s after reaching the water. What average force did the water exert on him?

A 0.400-kg blue bead slides on a curved frictionless wire, starting from rest at point in Figure P6.58 (page 188). At point , the bead collides elastically with a 0.600-kg blue ball at rest. Find the maximum height the blue ball rises as it moves up the wire.

A ball of mass 0.500 kg is dropped from a height of 2.00 m. It bounces against the ground and rises to a height of 1.40 m. If the ball was in contact with the ground for 0.080 0 s, what average force did the ground exert on the ball?

An unstable nucleus of mass 1.7  1026 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m1 5.0  1027 kg, moves in the positive y-direction with speed v1 6.0  106 m/s. Another particle, of mass m2 8.4  1027 kg, moves in the positive x-direction with speed v2 4.0  106 m/s. Find the magnitude and direction of the velocity of the third particle.

Two blocks of masses m1 and m2 approach each other on a horizontal table with the same constant speed, v0, as measured by a laboratory observer. The blocks undergo a perfectly elastic collision, and it is observed that m1 stops but m2 moves opposite its original motion with some constant speed, v. (a) Determine the ratio of the two masses, m1/ m2. (b) What is the ratio of their speeds, v/v0?

Two blocks of masses m1 2.00 kg and m2 4.00 kg are each released from rest at a height of 5.00 m on a frictionless track, as shown in Figure P6.62, and undergo an elastic head-on collision. (a) Determine the velocity of each block just before the collision. (b) Determine the velocity of each block immediately after the collision. (c) Determine the maximum heights to which m1 and m2 rise after the collision.

A 0.500-kg block is released from rest at the top of a frictionless track 2.50 m above the top of a table. It then collides elastically with a 1.00-kg object that is initially at rest on the table, as shown in Figure P6.63. (a) Determine the velocities of the two objects just after the collision. (b) How high up the track does the 0.500-kg object travel back after the collision? (c) How far away from the bottom of the table does the 1.00-kg object land, given that the table is 2.00 m high? (d) How far away from the bottom of the table does the 0.500-kg object eventually land?

Two objects of masses m and 3m are moving toward each other along the x-axis with the same initial speed v0. The object with mass m is traveling to the left, and the object with mass 3m is traveling to the right. They undergo an elastic glancing collision such that m is moving downward after the collision at right angles from its initial direction. (a) Find the fi nal speeds of the two objects. (b) What is the angle u at which the object with mass 3m is scattered?

A small block of mass m1 0.500 kg is released from rest at the top of a curved wedge of mass m2 3.00 kg, which sits on a frictionless horizontal surface as in Figure P6.65a. When the block leaves the wedge, its velocity is measured to be 4.00 m/s to the right, as in Figure P6.65b. (a) What is the velocity of the wedge after the block reaches the horizontal surface? (b) What is the height h of the wedge?

A cue ball traveling at 4.00 m/s makes a glancing, elastic collision with a target ball of equal mass that is initially at rest. The cue ball is defl ected so that it makes an angle of 30.0 with its original direction of travel. Find (a) the angle between the velocity vectors of the two balls after the collision and (b) the speed of each ball after the collision.

A cannon is rigidly attached to a carriage, which can move along horizontal rails, but is connected to a post by a large spring, initially unstretched and with force constant k 2.00  104 N/m, as in Figure P6.67. The cannon res a 200-kg projectile at a velocity of 125 m/s directed 45.0 above the horizontal. (a) If the mass of the cannon and its carriage is 5 000 kg, fi nd the recoil speed of the cannon. (b) Determine the maximum extension of the spring. (c) Find the maximum force the spring exerts on the carriage. (d) Consider the system consisting of the cannon, the carriage, and the shell. Is the momentum of this system conserved during the fi ring? Why or why not?

The force platform is a tool that is used to analyze the performance of athletes by measuring the vertical force as a function of time that the athlete exerts on the ground in performing various activities. A simplifi ed force vs. time graph for an athlete performing a standing high jump is shown in Figure P6.68. The athlete started the jump at t 0.0 s. How high did this athlete jump?

A neutron in a reactor makes an elastic head-on collision with a carbon atom that is initially at rest. (The mass of the carbon nucleus is about 12 times that of the neutron.) (a) What fraction of the neutrons kinetic energy is transferred to the carbon nucleus? (b) If the neutrons initial kinetic energy is 1.6  1013 J, fi nd its fi nal kinetic energy and the kinetic energy of the carbon nucleus after the collision.

Two blocks collide on a frictionless surface. After the collision, the blocks stick together. Block A has a mass M and is initially moving to the right at speed v. Block B has a mass 2M and is initially at rest. System C is composed of both blocks. (a) Draw a free-body diagram for each block at an instant during the collision. (b) Rank the magnitudes of the horizontal forces in your diagram. Explain your reasoning. (c) Calculate the change in momentum of block A, block B, and system C. (d) Is kinetic energy conserved in this collision? Explain your answer. (This problem is courtesy of Edward F. Redish. For more such problems, visit http://www.physics.umd.edu/perg.)

(a) A car traveling due east strikes a car traveling due north at an intersection, and the two move together as a unit. A property owner on the southeast corner of the intersection claims that his fence was torn down in the collision. Should he be awarded damages by the insurance company? Defend your answer. (b) Let the eastward- moving car have a mass of 1 300 kg and a speed of 30.0 km/h and the northward-moving car a mass of 1 100 kg and a speed of 20.0 km/h. Find the velocity after the collision. Are the results consistent with your answer to part (a)?

A 60-kg soccer player jumps vertically upwards and heads the 0.45-kg ball as it is descending vertically with a speed of 25 m/s. If the player was moving upward with a speed of 4.0 m/s just before impact, what will be the speed of the ball immediately after the collision if the ball rebounds vertically upwards and the collision is elastic? If the ball is in contact with the players head for 20 ms, what is the average acceleration of the ball? (Note that the force of gravity may be ignored during the brief collision time.)

A tennis ball of mass 57.0 g is held just above a basketball of mass 590 g. With their centers vertically aligned, both balls are released from rest at the same time, to fall through a distance of 1.20 m, as shown in Figure P6.73. (a) Find the magnitude of the downward velocity with which the basketball reaches the ground. (b) Assume that an elastic collision with the ground instantaneously reverses the velocity of the basketball while the tennis ball is still moving down. Next, the two balls meet in an elastic collision. To what height does the tennis ball rebound?

A 20.0-kg toboggan with 70.0-kg driver is sliding down a frictionless chute directed 30.0 below the horizontal at 8.00 m/s when a 55.0-kg woman drops from a tree limb straight down behind the driver. If she drops through a vertical displacement of 2.00 m, what is the subsequent velocity of the toboggan immediately after impact?

Measuring the speed of a bullet. A bullet of mass m is fi red horizontally into a wooden block of mass M lying on a table. The bullet remains in the block after the collision. The coeffi cient of friction between the block and table is m, and the block slides a distance d before stopping. Find the initial speed v0 of the bullet in terms of M, m, m, g, and d.

A fl ying squid (family Ommastrephidae) is able to jump off the surface of the sea by taking water into its body cavity and then ejecting the water vertically downward. A 0.85-kg squid is able to eject 0.30 kg of water with a speed of 20 m/s. (a) What will be the speed of the squid immediately after ejecting the water? (b) How high in the air will the squid rise?

A 0.30-kg puck, initially at rest on a frictionless horizontal surface, is struck by a 0.20-kg puck that is initially moving along the x-axis with a velocity of 2.0 m/s. After the collision, the 0.20-kg puck has a speed of 1.0 m/s at an angle of u 53 to the positive x-axis. (a) Determine the velocity of the 0.30-kg puck after the collision. (b) Find the fraction of kinetic energy lost in the collision.

A 12.0-g bullet is fi red horizontally into a 100-g wooden block initially at rest on a horizontal surface. After impact, the block slides 7.5 m before coming to rest. If the coeffi cient of kinetic friction between block and surface is 0.650, what was the speed of the bullet immediately before impact?