Solution: Two ice skaters, with masses of 50 kg and 75 kg,

Rank in order, from largest to smallest, the momenta Pix through Psx of the objects presented in Figure Q9. l. Explain.

Starting from res t, object 1 is subject to a 12 N force for 2.0 s. Object 2, with twice the mass, is subject to a 15 N force for 3.0 s. Which object has the greater final speed? Explain.

A 0.2 kg plastic cart and a 20 kg lead cart can roll without friction on a horizontal surface. Equal forces are used to push both catts forward for a time of 1 s, starting from rest. After the force is removed at t = 1 s, is the momentum of the plastic cart greater than, less than, or equal to the momentum of the lead ca1t? Explain.

Two pucks, of mass m and 4m, lie on a frictionless table. Equal forces are used to push both pucks forward a distance of 1 m. a. Which puck takes longer to travel the d istance? Explain. b. Which puck has the greater momentum upon completing the distance? Explain.

A stationary fi recracker explodes into three pieces. One piece travels off to the east; a second travels to the north. Which of the vectors of Figure Q9.5 could be the velocity of the third piece? Explain.

Two students stand at rest, facing each other on frictionless skates. They then start tossing a heavy ball back and forth between them. Describe their subseq uent motion.

A 2 kg cart rolling to the right at 3 mis runs into a 3 kg cart rolling to the left. After the collision, both c arts are stationary. What was the original speed of the 3 kg cart?

Automobiles are designed with "crumple zones" intended to collapse in a colli sion. Why would a manufacturer design patt of a car so that it collapses in a coll ision?

You probably know that it feels better to catch a baseball if you are wearing a padded glove. Explain why this is so, using the ideas of momentum and impulse.

In the early days of rocketry, some people claimed that rockets couldn't fly in outer space as there was no air for the rockets to push against. Suppose you were an early investigator in the field of rocketry and met someone who made this argument. How would you convince the person that JC rockets could travel in space?

Two ice skaters, Megan and Jason, pus h off from each other on fric tionless ice. Jason's mass is twice that of Megan. a. Which skater, if either, experiences the greater impulse during the push? Explain. b. Which skater, if either, has the greater speed afte r the pushoff? Explain.

Suppose a rubber ball and a steel ba ll coll ide. Which, if either, receives the larger impulse? E xplain.

Whi le standing still on a basketball court, you throw the ball to a teammate. Why do you not move backward as a result? Is the law of conservation of momentum iolated?

To win a prize at the county fair, you' re trying to knock down a heavy bowling pin by hitting it with a thrown object. Should you choose to throw a rubber ball or a beanbag of equal size and weight? Explain.

Rank in order, from largest to smallest, the angular momenta L 1 through L5 of the balls shown in Figure Q9. l 5. Explain.

Monica stands at the edge of a circular platform that is slowly rotating on a frictionless ax le. She then wal ks toward the opposite edge, passing through the platform's center. Describe the motion of the platform as Monica makes her trip.

If the earth warms significantly, the polar ice caps will melt. Water will move from the poles, near the ea1th's rotation axis, and wi ll spread out around the globe. In principle, this will change the length of the day. Why? Will the length of the day increase or decrease?

The disks shown in Figure Q9. l 8 have equal mass. Is the angular momentum of disk 2, on the right, larger than, smaller than, or equal to the angular momentum of disk 1? Explain.

Curling is a sport played with 20 kg stones that slide across an ice surface. Suppose a c url ing stone sliding at 1 mis strikes another, stationary stone and comes to rest in 2 ms. Approximately how much force is there on the stone during the impact? A. 200 N B. 1000 N C. 2000 N D. 10,000 N

Two balls are hung from cords. The first ball, of mass 1.0 kg, is pulled to the side and released, reaching a speed of 2.0 mis at the bottom of its arc. Then, as shown in Figure Q9.20, it hits and sticks to another ball. The speed of the pair just after the collision is 1.2 mis. What is the mass of the second ball? A. 0.67 kg B. 2.0 kg C. 1.7 kg D. 1.0 kg

Figure Q9.2 l shows two blocks sl iding on a frictionless surface. Eventually the smaller block catches up with the larger one, collides with it, and sticks. What is the speed of the two blocks after the coll ision? A. ~n B. 4~6 C. ~ D. 5~M E. 2~

Two friends are sitting in a stationary canoe. At t = 3.0 s the person at the front tosses a sack to the person in the rear, who catches the sack 0.2 s later. Which plot in Figure Q9.22 shows the velocity of the boat as a function of time? Positive velocity is forward, negative velocity is backward. Neglect any drag force on the canoe from the water.

Two blocks, with masses m1 = 2.5 kg and m2 = 14 kg, approach each other along a horizontal, fri ctionless track. The initial velocities of the blocks are v1 = 12.0 mis to the right and v2 = 3.4 mis to the le ft. The two blocks then collide and stick together. Which of the graphs could represent the force of block 1 on block 2 during the collision?

A small puck is sliding to the right with momentum p; on a horizontal, frictionless surface, as shown in Figure Q9.24. A force is appl ied to the puck for a short time and its momentum afterward is Pr Which lettered arrow shows the direction of the impulse that was delivered to the puck?

A red ball, initially at rest, is simultaneously hit by a blue ball traveling from west to east at 3 mis and a green ball traveling east to west at 3 mis. All three balls have equal mass. Afterward, the red ball is traveling south and the green ball is moving to the east. ln which direction is the blue ball traveling?A. West B. North '/ C. Between north and west D. Between north and east E. Between south and west

A 4.0-m-diameter playground merry-go-round, with a moment of inertia of 400 kg m2 , is freely rotat ing with an angular velocity of 2.0 radls. Ryan, whose mass is 80 kg, runs on the ground around the outer edge of the merry-go-round in the opposite direction to its rotation. Still moving, he jumps directly onto the rim of the merry-go-round, bringing it (and himself) to a halt. How fa st was Ryan running when he jumped on? A. 2.0 mis B. 4.0 mis C. 5.0 mis D. 7.5 mis E. 10 mis

A disk rotates freely on a vertical axis with an angular velocity of 30 rpm. An identical disk rotates above it in the same direction about the same axis, but without touching the lower disk, at 20 rpm. The upper disk then drops onto the lower di sk. After a short time, because of friction , they rotate together. The fi nal angular velocity of the disks is A. 50 rpm B. 40 rpm C. 25 rpm D. 20 rpm E. 10 rpm

A 20 g ball of clay traveling east at 3.0 mis collides with a 30 g ball of clay traveling north at 2.0 mis. What are the speed and the direction of the resulting 50 g blob of clay?

Two particles collide and bounce apart. Figure P9.29 shows the initial momenta of both and the final momentum of particle 2. What is the final momentum of pa1ticle I? Show your answer by copying the figure and drawing the final momentum vector on the figure.

A 20 g ball of clay traveling east at 2.0 mis collides with a 30 g ball of clay traveling 30 south of west at 1.0 mis. What are the speed and direction of the resulting 50 g blob of clay?

A fi recracker in a coconut blows the coconut into three pieces. Two pieces of equal mass fly off south and west, perpendicular to each other, at 20 mis. The third piece has twice the mass of the other two. What are the speed and direction of the third piece?

What is the angular momentum of the moon around the earth? INT The moon's mass is 7.4 X 1022 kg and it orbits 3.8 x 108 m from the earth.

A little girl is going on the merry-go-round for the first time, and wants her47 kg motherto stand next to her on the ride, 2.6 m from the merry-go-round's center. If her mother's speed is 4.2 mis when the ride is in motion, what is her angular momentum around the center of the merry-go-round?

What is the angular momentum about the axle of the 500 g rotating bar in Figure P9.34?

What is the aogul ar momentum about the axle of the 2.0 kg, 4.0-cm-diameter rotatilJg disk in Figure P9.35?

Divers change their body position in midair while rotating about their center of mass. fn one dive, the diver leaves the board with her body nearly straight, then tucks into a somersault position. If the moment of inertia of the diver in a straight position is 14 kg m2 and in a tucked position is 4.0 kg m2 , by what factor is her angular velocity when tucked greater than when straight?

Ice skaters often end their performances with spin turns, BKl where they spin very fast about their center of mass with their arms folded in and legs together. Upon ending, their arms extend outward, proclaiming their fin ish. Not quite as noticeably, one leg goes out as we ll. Suppose that the moment of inertia of a skater with arms out and one leg extended is 3.2 kg m2 and for arms and legs in is 0.80 kg m2 If she starts out spi nning at 5.0 revls, what is her angular speed (in revls) when her arms and one leg open outward?

What is the impulse on a 3.0 kg particle that experiences the force described by the graph in Figure P9.38?

A 600 g air-track glider collides with a spring at one end of the track. Figure P9.39 shows the glider's velocity and the force exerted on the glider by the spring. How long is the glider in contact with the spring?

Far in space, where gravity is negligible, a 425 kg rocket traveling at 75.0 mis in the positive x-direction fi.res its engi nes. Figure P9.40 shows the thrust force as a function of time. The mass lost by the rocket during these 30.0 sis negligible. a. What impulse does the engine impart to the rocket? b. At what time does the rocket reach its maximum speed? What is the maximum speed?

A 200 g ball is dropped from a height of 2.0 m, bounces on a hard floor, and rebounds to a height of 1.5 m. Figure P9.4 I shows the impulse received from the floor. What maximum force does the floor exert on the ball?

A 200 g ball is dropped from a height of 2.0 m and bounces on a hard floor. The force on the ball from the floor is shown in Figure P9.42. How high does the ball rebound?

Figure P9.43 is a graph of the force exerted by the floor on a woman making a vettical jump. At what speed does she leave the ground? Hint: The force of the floor is not the only force acting on the woman.

A sled slides along a horizontal surface for which the coeffi cient of kinetic friction is 0.25. Its velocity at point A is 8.0 mis and at point B is 5.0 mis. Use the impulse-momentum theorem to find how long the sled takes to travel from A to B.

A 140 g baseball is moving horizontally to the right at 35 mis when it is hit by the bat. The ball fl ies off to the le ft at 55 mis, at an angle of 25 above the horizontal. What are the magnitude and direction of the impulse that the bat deli vers to the ball?

Squids rely on jet propulsion, a versatile technique to move around in water. A 1.5 kg squid at rest suddenly expels 0.1 0 kg of water backward to quic kly get itself moving forward at 3.0 mis. If other forces (such as the drag force on the squid) are ignored, what is the speed with which the squid expels the water?

The flowers of the bunchbeny plant open with astonishing force and speed, causing the pollen grains to be ejected out of the flower in a mere 0.30 ms at an acceleration of 2.5 x I 04 mls2. If the acceleration is constant, what impulse is delivered to a pollen grain with a mass of 1.0 x I 0-1 g?

a. With what speed are polle n grains ejected from a bunch- berry flower? See Problem 47 for information. b. Suppose that I 000 ejected pollen grains slam into the abdomen of a 5.0 g bee that is hovering just above the flower. If the collision is petfectly inelastic, what is the bee's speed immediately afterward? Is the bee li kely to notice?

A tennis player swi ngs her 1000 g rac ket with a speed of I 0 mis. She hits a 60 g tennis ball that was approaching her at a speed of 20 mis. The ball rebounds at 40 mis. a. How fast is her racket moving immediately after the impact? You can ignore the interaction of the racket with her hand for the brief duration of the collision. b. Tf the tennis ball and racket are in contact for I 0 ms, what is the average force that the racket exerts on the ball?

A 20 g ball of clay is thrown horizontally at 30 mis toward a l.O kg block sitting at rest on a frictionless surface. The clay hi ts and sticks to the block. a. What is the speed of the block and clay right after the collision? b. Use the block's initial and final speeds to calculate the impulse the clay e xerts on the block. c. Use the c lay's initial and final speeds to calculate the impulse the block exerts on the clay. d. Does Jblockon cly = - Jclyonblock?

Dan is gliding on his skateboard at 4.0 mis. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.0 mis. How fast is Dan going as his feet hit the ground? Dan's mass is 50 kg and the skateboard 's mass is 5.0 kg.

James and Sarah stand on a stationary cart with fri ctionless wheels. The total mass of the cart and riders is 130 kg. At the same instant, James throws a 1.0 kg ball to Sarah at 4.5 mis, while Sarah throws a 0.50 kg ball to James at 1.0 mis. (Both speeds are measured relative to the ground.) James's throw is to the right and Sarah's is to the left. a. While the two balls are in the air, what are the speed and direction of the cart and its riders? b. After the balls are caught, what are the speed and direction of the cart and riders?

Ethan, whose mass is 80 kg, stands at one end of a ve1y long, stationary wheeled cart that has a mass of 500 kg. He then starts sprinting toward the other end of the cart. He soon reaches his top speed of 8.0 mis, measured relat.ive to the cart. What is the speed of the cart when Ethan has reached his top speed?

A small cart rolls freely along the floor. As it rolls, balls of clay, each having one-fourth the mass of the cart, are dropped straight down onto the catt and stick to it. How many balls must be dropped until the cart is moving at less than one-third its initial speed?

Three identical train cars, coupled together, are rolling east at 2.0 mis. A fo utth car traveling east at 4 .0 mis catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. What is the speed of the five-car train?

A 110 kg linebacker running at 2.0 mis and an 82 kg quarterback running at 3.0 mis have a head-on colli sion in midair. The linebacker grabs and holds onto the quarterback. Who ends up moving forward after they hit? 57. II Most geologists believe that

Most geologists believe that the dinosaurs became ext.incl INT 65 million years ago when a large comet or asteroid struck the earth, throwing up so much dust that the sun was blocked out for a period of many months. Suppose an asteroid with a diameter of 2.0 km and a mass of 1.0 x I 013 kg hits the earth with an impact speed of 4.0 x I04 mis. a. What is the earth's recoil speed after such a collision? (Use a reference frame in which the earth was initially at rest.) b. What percentage is this of the earth's speed around the sun? (Use the astronomical data inside the back cover.)

Two ice skaters, with masses of 75 kg and 55 kg, stand facing each other on a 15-m-wide frozen river. The skaters push off against each other, glide backward straight toward the river's edges, and reach the edges at exactly the same time. How far did the 75 kg skater glide?

Two ice skaters, with masses of 50 kg and 75 kg, are at the center of a 60-m-diameter circular rink. The skaters push off against each other and glide to opposite edges of the rink. If the heavier skater reaches the edge in 20 s, how long does the lighter skater take to reach the edge?

One billiard ball is shot east at 2.00 mis. A second, identical billiard ball is shot west at 1.00 mis. The balls have a glancing collision, not a head-on collision, deflecting the second ball by 90 and sending it north at 1.41 mis. What are the speed and direction of the first ball after the collision?

A 10 g bullet is fired into a 10 kg wood block that is at rest on a wood table. The block, with the bullet embedded, slides 5.0 cm across the table. Whal was the speed of the bullet?

A typical raindrop is much more massive than a mosquito and falli ng much faster than a mosquito flies. How does a mosquito survive the impact? Recent research has found that the collision of a falling raindrop with a mosquito is a perfectly inelastic collision. That is, the mosquito is "swept up" by the raindrop and ends up traveling along with the raindrop. Once the relative speed between the mosquito and the raindrop is zero, the mosquito is able to detach itself from the drop and fly away. a. A hovering mosquito is hit by a raindrop that is 40 times as massive and fa lling at 8.2 mis, a typical raindrop speed. How fast is the raindrop, with the attached mosquito, falling immediately afterward if the coll ision is perfectly inelastic? b. Because a raindrop is "soft" and deformable, the collision duration is a relatively long 8.0 ms. What is the mosquito's average acceleration, in g's, during the collision? The peak acceleration is roughly twice the value you found, but the mosquito's rigid exoskeleton allows it to survive accelerations of this magnitude. Tn contrast, humans cannot survive an acceleration of more than about I Og.

A 15 g bullet is fired at 610 mis into a 4.0 kg block that sits at the edge of a 75-cm-high table. The bullet embeds itself in the block and carries it off the table. How far from the point directly below the table's edge does the block land?

A 1500 kg weather rocket accelerates upward at I 0.0 mls2 It explodes 2.00 s after liftoff and breaks into two fragments, one twice as massive as the other. Photos reveal that the lighter fragment traveled straight up and reached a maximum height of 530 m. What were the speed and direction of the heavier fragment just after the explosion?

Two 500 g blocks of wood are 2.0 m apart on a frictionless table. A 10 g bullet is fired at 400 mis toward the blocks. It passes all the way through the first block, then embeds itself in the second block. The speed of the first block immediately afterward is 6.0 mis. What is the speed of the second block after the bullet stops?

A 495 kg cannon fi res a I 0.0 kg cannonball with a speed of 2 11 mis relative to the muzzle. The cannon is on wheels that roll without friction. When the cannon fires, what is the speed of the cannonball relative to the ground?

Laura, whose mass is 35 kg, jumps horizontally off a 55 kg canoe at 1.5 mis relative to the canoe. What is the canoe's speed just after she jumps?

A spaceship of mass 2.0 x I 06 kg is cruising at a speed of 5.0 x I 06 mis when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.0 x 105 kg, is blown straight backward with a speed of 2.0 X I 06 mis. A second piece, with mass 8.0 X I 05 kg, continues frnward at 1.0 X l 06 mis. What are the direction and speed of the third piece?

At the county fair, Chris throws a 0.15 kg baseball at a 2.0 kg wooden milk bottle, hoping to knock it off its stand and win a prize. The ball bounces straight back at 20% of its incoming speed, knocking the bottle straight forward. What is the bottle's speed, as a percentage of the ball's incomi ng speed?

Figure P9.70 shows a collision between three balls of clay. The three hit simultaneously and stick together. What are the speed and direction of the resulting blob of clay?

The carbon isotope 14C is used for carbon dating of archeological artifacts. 14C (mass 2.34 x I0-26 kg) decays by the process known as beta decay in which the nucleus emits an electron (the beta particle) and a subatomic particle called a neutrino. In one such decay, the electron and the neutrino are emitted at right angles to each other. The electron (mass 9.1 1 x I0- 31 kg) has a speed of 5.00 x I 07 mis and the neutrino has a momentum of 8.00 x J0-24 kg mis. What is the recoil speed of the nucleus?

A 1.0-m-long massless rod is pivoted at one end and swings around in a circle on a frictionless table. A block with a hole through the center can slide in and out along the rod. I nitially, a small piece of wax holds the block 30 cm from the pivot. The block is spun at 50 rpm, then the temperature of the rod is slowly increased. When the wax melts, the block slides out to the end of the rod. What is the fi nal angular speed? Give your answer in rpm.

A 200 g puck revolves in a circle on a frictionless table at the end of a 50.0-cm-long string. The puck's angular momentum about the center of the circle is 3.00 kg m21s. What is the tension in the string?

Figure P9.74 shows a 100 g puck revolving at 100 rpm on a 20-cm-radius circle on a frictionless table. A string attached to the puck passes through a hole in the middle of the table. The end of the string below the table is then slowly pulled down until the puck is revolving in a JO-cm-radius ci rcle. How many revolutions per minute does the puck make at this new radi us?

A 2.0 kg, 20-cm-diameter turntable rotates at 100 rpm on fric tionless bearings. Two 500 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diagonal, and stick. What is the turntable's angular speed, in rpm, just after th is event?

Joey, from Example 9. 10, stands at rest at the outer edge of the frictionless merry-go-round of Figure 9.27. The merry-goround is also at rest. Joey then begins to run around the perimeter of the merry-go-round, finally reaching a constant speed, measured relative to the ground, of 5.0 mis. What is the final angular speed of the merry-go-round? 77. Ill A 3.0-m-diameter me1Ty-go-round with

A 3.0-m-diameter me1Ty-go-round with a mass of 250 kg is spinning at 20 rpm. John runs around the merry-go-round at 5.0 mis, in the same direction that it is turning, and jumps onto the outer edge. John's mass is 30 kg. What is the merry-goround's angular speed, in rpm, after John jumps on?

Disk A, with a mass of 2.0 kg and a radius of 40 cm, rotates clockwise about a frictionless ve1tical axle at 30 rev/s. Disk B, also 2.0 kg but with a radius of 20 cm, rotates counterclockwise about that same axle, but at a greater height than disk A, at 30 rev/s. Disk B slides down the axle until it lands on top of disk A, atier which they rotate together. After the collision, what is their common angular speed (in rev/s) and in which direction do they rotate?

What is the momentum of the club+ ball system right before the collision? A. 1.8 kg mis B. 8.0 kg mis C. 3220 kg mis D. 8000 kg mis

Immediately after the collision, the momentum of the club + ball system wjll be A. Less than before the collision. B. The same as before the collision. C. Greater than before the collision.

A manufacturer makes a golf ball that compresses more than a traditional golf ball when struck by a club. How will this affect the average force during the collision? A. The force will decrease. B. The force will not be affected. /.. C. The force will increase.

By approximately how much does the club head slow down as a result of hitting the ball? A. 4 mis B. 6 mis C. 14 mis D. 26 mis