Problems

Note to Instructors: Most of the homework problems in this chapter are available for assignment via an on-line homework management program such as Wiley PLUS or WebAssign, and those marked with the icon are presented in a guided tutorial format that provides enhanced interactivity. See Preface for additional details.
ssm Solution is in the Student Solutions Manual.
This icon represents a biomedical application.
Section 7.1 Impulse–Momentum Theorem,

| 1 | ssm One average force has a magnitude that is three times as large as that of another average force . Both forces produce the same impulse. The average force acts for a time interval of 3.2 ms. For what time interval does the average force act?

| 2 | Interactive LearningWare 7.1 at provides a review of the concepts that are involved in this problem. A 62.0-kg person, standing on a diving board, dives straight down into the water. Just before striking the water, her speed is 5.50 m/s. At a time of 1.65 s after she enters the water, her speed is reduced to 1.10 m/s. What is the net average force (magnitude and direction) that acts on her when she is in the water?

| 3 | A golfer, driving a golf ball off the tee, gives the ball a velocity of + 38 m/s. The mass of the ball is 0.045 kg, and the duration of the impact with the golf club is . (a) What is the change in momentum of the ball? (b) Determine the average force applied to the ball by the club.

| 4 | A baseball () approaches a bat horizontally at a speed of 40.2 m/s (90 mi/h) and is hit straight back at a speed of 45.6 m/s (102 mi/h). If the ball is in contact with the bat for a time of 1.10 ms, what is the average force exerted on the ball by the bat? Neglect the weight of the ball, since it is so much less than the force of the bat. Choose the direction of the incoming ball as the positive direction.

| 5 | ssm A volleyball is spiked so that its incoming velocity of + 4.0 m/s is changed to an outgoing velocity of − 21 m/s. The mass of the volleyball is 0.35 kg. What impulse does the player apply to the ball?

| 6 | A space probe is traveling in outer space with a momentum that has a magnitude of . A retrorocket is fired to slow down the probe. It applies a force to the probe that has a magnitude of and a direction opposite to the probe’s motion. It fires for a period of 12 s. Determine the momentum of the probe after the retrorocket ceases to fire.

| 7 | A 46-kg skater is standing still in front of a wall. By pushing against the wall she propels herself backward with a velocity of − 1.2 m/s. Her hands are in contact with the wall for 0.80 s. Ignore friction and wind resistance. Find the magnitude and direction of the average force she exerts on the wall (which has the same magnitude, but opposite direction, as the force that the wall applies to her).

| 8 | Refer to Conceptual Example 3 as an aid in understanding this problem. A hockey goalie is standing on ice. Another player fires a puck () at the goalie with a velocity of + 65 m/s. (a) If the goalie catches the puck with his glove in a time of , what is the average force (magnitude and direction) exerted on the goalie by the puck? (b) Instead of catching the puck, the goalie slaps it with his stick and returns the puck straight back to the player with a velocity of − 65 m/s. The puck and stick are in contact for a time of . Now what is the average force exerted on the goalie by the puck? Verify that your answers to parts (a) and (b) are consistent with the conclusion of Conceptual Example 3.

* | 9 | Consult Interactive Solution 7.9 at for a review of problem-solving skills that are involved in this problem. A stream of water strikes a stationary turbine blade horizontally, as the drawing illustrates. The incident water stream has a velocity of + 16.0 m/s, while the exiting water stream has a velocity of − 16.0 m/s. The mass of water per second that strikes the blade is 30.0 kg/s. Find the magnitude of the average force exerted on the water by the blade.

* | 10 | A student () falls freely from rest and strikes the ground. During the collision with the ground, he comes to rest in a time of 0.010 s. The average force exerted on him by the ground is + 18 000 N, where the upward direction is taken to be the positive direction. From what height did the student fall? Assume that the only force acting on him during the collision is that due to the ground.

* | 11 | A 0.500-kg ball is dropped from rest at a point 1.20 m above the floor. The ball rebounds straight upward to a height of 0.700 m. What are the magnitude and direction of the impulse of the net force applied to the ball during the collision with the floor?

* | 12 | An 85-kg jogger is heading due east at a speed of 2.0 m/s. A 55-kg jogger is heading 32° north of east at a speed of 3.0 m/s. Find the magnitude and direction of the sum of the momenta of the two joggers.

| 13 | ssm www A golf ball strikes a hard, smooth floor at an angle of 30.0° and, as the drawing shows, rebounds at the same angle. The mass of the ball is 0.047 kg, and its speed is 45 m/s just before and after striking the floor. What is the magnitude of the impulse applied to the golf ball by the floor? (Hint: Note that only the vertical component of the ball’s momentum changes during impact with the floor, and ignore the weight of the ball.)

** | 14 | A dump truck is being filled with sand. The sand falls straight downward from rest from a height of 2.00 m above the truck bed, and the mass of sand that hits the truck per second is 55.0 kg/s. The truck is parked on the platform of a weight scale. By how much does the scale reading exceed the weight of the truck and sand?
Section 7.2 The Principle of Conservation of Linear Momentum

| 15 | Interactive LearningWare 7.2 at provides a review of the concepts that are important in this problem. For tests using a ballistocardiograph, a patient lies on a horizontal platform that is supported on jets of air. Because of the air jets, the friction impeding the horizontal motion of the platform is negligible. Each time the heart beats, blood is pushed out of the heart in a direction that is nearly parallel to the platform. Since momentum must be conserved, the body and the platform recoil, and this recoil can be detected to provide information about the heart. For each beat, suppose that 0.050 kg of blood is pushed out of the heart with a velocity of + 0.25 m/s and that the mass of the patient and platform is 85 kg. Assuming that the patient does not slip with respect to the platform, and that the patient and platform start from rest, determine the recoil velocity.

| 16 | A 55-kg swimmer is standing on a stationary 210-kg .oating raft. The swimmer then runs off the raft horizontally with a velocity of +4.6 m/s relative to the shore. Find the recoil velocity that the raft would have if there were no friction and resistance due to the water.

| 17 | ssm www A lumberjack () is standing at rest on one end of a floating log () that is also at rest. The lumberjack runs to the other end of the log, attaining a velocity of + 3.6 m/s relative to the shore, and then hops onto an identical floating log that is initially at rest. Neglect any friction and resistance between the logs and the water. (a) What is the velocity of the first log just before the lumberjack jumps off? (b) Determine the velocity of the second log if the lumberjack comes to rest on it.

| 18 | Concept Simulation 7.1 at illustrates the physics principles in this problem. An astronaut in his space suit and with a propulsion unit (empty of its gas propellant) strapped to his back has a mass of 146 kg. During a space-walk, the unit, which has been completely filled with propellant gas, ejects some gas with a velocity of + 32 m/s. As a result, the astronaut recoils with a velocity of − 0.39 m/s. After the gas is ejected, the mass of the astronaut (now wearing a partially empty propulsion unit) is 165 kg. What percentage of the gas propellant in the completely filled propulsion unit was depleted?

* | 19 | To view an interactive solution to a problem that is very similar to this one, go to and select Interactive Solution 7.19 A fireworks rocket is moving at a speed of 45.0 m/s. The rocket suddenly breaks into two pieces of equal mass, which fly off with velocities and , as shown in the drawing. What is the magnitude of (a) and (b) ?

* | 20 | Two ice skaters have masses m1 and m2 and are initially stationary. Their skates are identical. They push against one another, as in Figure 7-11, and move in opposite directions with different speeds. While they are pushing against each other, any kinetic frictional forces acting on their skates can be ignored. However, once the skaters separate, kinetic frictional forces eventually bring them to a halt. As they glide to a halt, the magnitudes of their accelerations are equal, and skater 1 glides twice as far as skater 2. What is the ratio m1/m2 of their masses?

* | 21 | ssm During July 1994 the comet Shoemaker–Levy 9 smashed into Jupiter in a spectacular fashion. The comet actually consisted of 21 distinct pieces, the largest of which had a mass of approximately and a speed of . Jupiter, the largest planet in the solar system, has a mass of and an orbital speed of . If this piece of the comet had hit Jupiter head-on, what would have been the change (magnitude only) in Jupiter’s orbital speed (not its final speed)?

* | 22 | The lead female character in the movie Diamonds Are Forever is standing at the edge of an offshore oil rig. As she fires a gun, she is driven back over the edge and into the sea. Suppose the mass of a bullet is 0.010 kg and its velocity is + 720 m/s. Her mass (including the gun) is 51 kg. (a) What recoil velocity does she acquire in response to a single shot from a stationary position, assuming that no external force keeps her in place? (b) Under the same assumption, what would be her recoil velocity if, instead, she shoots a blank cartridge that ejects a mass of at a velocity of + 720 m/s?

** | 23 | ssm Two people are standing on a 2.0-m-long platform, one at each end. The platform floats parallel to the ground on a cushion of air, like a hovercraft. One person throws a 6.0-kg ball to the other, who catches it. The ball travels nearly horizontally. Excluding the ball, the total mass of the platform and people is 118 kg. Because of the throw, this 118-kg mass recoils. How far does it move before coming to rest again?

** | 24 | A wagon is coasting at a speed vA along a straight and level road. When ten percent of the wagon’s mass is thrown off the wagon, parallel to the ground and in the forward direction, the wagon is brought to a halt. If the direction in which this mass is thrown is exactly reversed, but the speed of this mass relative to the wagon remains the same, the wagon accelerates to a new speed vB. Calculate the ratio vB/vA.
Section 7.3 Collisions in One Dimension,
Section 7.4 Collisions in Two Dimensions

| 25 | Kevin has a mass of 87 kg and is skating with in-line skates. He sees his 22-kg younger brother up ahead standing on the sidewalk, with his back turned. Coming up from behind, he grabs his brother and rolls off at a speed of 2.4 m/s. Ignoring friction, find Kevin’s speed just before he grabbed his brother.

| 26 | Multiple-Concept Example 7 presents a model for solving problems such as this one. A 1055-kg van, stopped at a traffic light, is hit directly in the rear by a 715-kg car traveling with a velocity of +2.25 m/s. Assume that the transmission of the van is in neutral, the brakes are not being applied, and the collision is elastic. What is the final velocity of (a) the car and (b) the van?

| 27 | ssm A golf ball bounces down a flight of steel stairs, striking several steps on the way down, but never hitting the edge of a step. The ball starts at the top step with a vertical velocity component of zero. If all the collisions with the stairs are elastic, and if the vertical height of the staircase is 3.00 m, determine the bounce height when the ball reaches the bottom of the stairs. Neglect air resistance.

| 28 | A projectile () is fired at and embeds itself in a target (). The target (with the projectile in it) flies off after being struck. What percentage of the projectile’s incident kinetic energy does the target (with the projectile in it) carry off after being struck?

| 29 | Consult Multiple-Concept Example 8 for background pertinent to this problem. A 2.50-g bullet, traveling at a speed of 425 m/s, strikes the wooden block of a ballistic pendulum, such as that in Figure 7-14. The block has a mass of 215 g. (a) Find the speed of the bullet/block combination immediately after the collision. (b) How high does the combination rise above its initial position?

| 30 | Multiple-Concept Example 9 reviews the concepts that play roles in this problem. The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 0.025 kg and is moving along the x axis with a velocity of + 5.5 m/s. It makes a collision with puck B, which has a mass of 0.050 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the angles shown in the drawing. Find the final speed of (a) puck A and (b) puck B.

| 31 | ssm Batman () jumps straight down from a bridge into a boat () in which a criminal is fleeing. The velocity of the boat is initially + 11 m/s. What is the velocity of the boat after Batman lands in it?

| 32 | Multiple-Concept Example 7 deals with some of the concepts that are used to solve this problem. A cue ball () is at rest on a frictionless pool table. The ball is hit dead center by a pool stick, which applies an impulse of + 1.50 N·s to the ball. The ball then slides along the table and makes an elastic head-on collision with a second ball of equal mass that is initially at rest. Find the velocity of the second ball just after it is struck.

* | 33 | Interactive Solution 7.33 at illustrates how to model a problem similar to this one. An automobile has a mass of 2100 kg and a velocity of + 17 m/s. It makes a rear-end collision with a stationary car whose mass is 1900 kg. The cars lock bumpers and skid off together with the wheels locked. (a) What is the velocity of the two cars just after the collision? (b) Find the impulse (magnitude and direction) that acts on the skidding cars from just after the collision until they come to a halt. (c) If the coefficient of kinetic friction between the wheels of the cars and the pavement is , determine how far the cars skid before coming to rest.

* | 34 | A mine car () rolls at a speed of 0.50 m/s on a horizontal track, as the drawing shows. A 150-kg chunk of coal has a speed of 0.80 m/s when it leaves the chute. Determine the velocity of the car/coal system after the coal has come to rest in the car.

* | 35 | ssm A 50.0-kg skater is traveling due east at a speed of 3.00 m/s. A 70.0-kg skater is moving due south at a speed of 7.00 m/s. They collide and hold on to each other after the collision, managing to move off at an angle south of east, with a speed of vf. Find (a) the angle and (b) the speed vf, assuming that friction can be ignored.

* | 36 | See Multiple-Concept Example 9 to review the approach used in problems of this type. Three guns are aimed at the center of a circle, and each fires a bullet simultaneously. The directions in which they fire are 120° apart. Two of the bullets have the same mass of and the same speed of 324 m/s. The other bullet has an unknown mass and a speed of 575 m/s. The bullets collide at the center and mash into a stationary lump. What is the unknown mass?

* | 37 | An electron collides elastically with a stationary hydrogen atom. The mass of the hydrogen atom is 1837 times that of the electron. Assume that all motion, before and after the collision, occurs along the same straight line. What is the ratio of the kinetic energy of the hydrogen atom after the collision to that of the electron before the collision?

** | 38 | A ball is dropped from rest at the top of a 6.10-m-tall building, falls straight downward, collides inelastically with the ground, and bounces back. The ball loses 10.0% of its kinetic energy every time it collides with the ground. How many bounces can the ball make and still reach a windowsill that is 2.44 m above the ground?

** | 39 | ssm Starting with an initial speed of 5.00 m/s at a height of 0.300 m, a 1.50-kg ball swings downward and strikes a 4.60-kg ball that is at rest, as the drawing shows. (a) Using the principle of conservation of mechanical energy, find the speed of the 1.50-kg ball just before impact. (b) Assuming that the collision is elastic, find the velocities (magnitude and direction) of both balls just after the collision. (c) How high does each ball swing after the collision, ignoring air resistance?

** | 40 | Multiple-Concept Example 7 outlines the general approach to problems like this one. Concept Simulation 7.2 at provides a view of this elastic collision. Two identical balls are traveling toward each other with velocities of − 4.0 and + 7.0 m/s, and they experience an elastic head-on collision. Obtain the velocities (magnitude and direction) of each ball after the collision.
Section 7.5 Center of Mass

| 41 | ssm The earth and moon are separated by a center-to-center distance of . The mass of the earth is and that of the moon is . How far does the center of mass lie from the center of the earth?

| 42 | Consider the two moving boxcars in Example 5. Determine the velocity of their center of mass (a) before and (b) after the collision. (c) Should your answer in part (b) be less than, greater than, or equal to the common velocity vf of the two coupled cars after the collision? Justify your answer.

| 43 | Interactive Solution 7.43 at presents a method for modeling this problem. The carbon monoxide molecule (CO) consists of a carbon atom and an oxygen atom separated by a distance of . The mass mC of the carbon atom is 0.750 times the mass mO of the oxygen atom, or . Determine the location of the center of mass of this molecule relative to the carbon atom.

* | 44 | The drawing shows a human figure approximately in a sitting position. For purposes of this problem, there are three parts to the figure, and the center of mass of each one is shown in the drawing. These parts are: (1) the torso, neck, and head () with a center of mass located on the y axis at a point 0.39 m above the origin, (2) the upper legs () with a center of mass located on the x axis at a point 0.17 m to the right of the origin, and (3) the lower legs and feet () with a center of mass located 0.43 m to the right of and 0.26 m below the origin. Find the x and y coordinates of the center of mass of the human figure. Note that the mass of the arms and hands (approximately 12% of the wholebody mass) has been ignored to simplify the drawing.

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