Solved: Hitting a Golf BallConsider a golf club hitting a

Problem 1CQ Rank in order, from largest to smallest, the momenta of the objects presented in Figure Q9.1 . Explain.

Problem 1P At what speed do a bicycle and its rider, with a combined mass of 100 kg, have the same momentum as a 1500 kg car traveling at 1.0 m/s?

Problem 2CQ Starting from rest, 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.

Problem 2P A 57 g tennis ball is served at 45 m/s. If the ball started from rest, what impulse was applied to the ball by the racket?

Problem 3P A student throws a 120 g snowball at 7.5 m/s at the side of the schoolhouse, where it hits and sticks. What is the magnitude of the average force on the wall if the duration of the collision is 0.15 s?

Problem 3CQ 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 carts 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 cart? Explain.

Problem 4CQ Two pucks, of mass m and 4 m , 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 distance? Explain. b. Which puck has the greater momentum upon completing the distance? Explain.

Problem 4P In Figure P9.4 , what value of gives an impulse of 6.0 N . s?

Problem 5CQ A stationary firecracker 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.

Problem 5P A sled and rider, gliding over horizontal, frictionless ice at 4.0 m/s, have a combined mass of 80 kg. The sled then slides over a rough spot in the ice, slowing down to 3.0 m/s. What impulse was delivered to the sled by the friction force from the rough spot?

Problem 6CQ 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 subsequent motion.

Problem 6P Use the impulse-momentum theorem to find how long a stone falling straight down takes to increase its speed from 5.5 m/s to 10.4 m/s.

Problem 7CQ Two particles collide, one of which was initially moving and the other initially at rest. a. Is it possible for both particles to be at rest after the collision? Give an example in which this happens, or explain why it can’t happen. ________________ b. Is it possible for one particle to be at rest after the collision? Give an example in which this happens, or explain why it can’t happen.

Problem 7P a. A 2.0 kg object is moving to the right with a speed of 1.0 m/s when it experiences the force shown in Figure P9.7 a. What are the object’s speed and direction after the force ends? b. Answer this question for the force shown in Figure P9.7 b.

Problem 8CQ Automobiles are designed with “crumple zones” intended to collapse in a collision. Why would a manufacturer design part of a car so that it collapses in a collision?

Problem 8P A 60 g tennis ball with an initial speed of 32 m/s hits a wall and rebounds with the same speed. Figure P9.8 shows the force of the wall on the ball during the collision. What is the value of , the maximum value of the contact force during the collision?

Problem 9CQ 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.

Problem 9P A child is sliding on a sled at 1.5 m/s to the right. You stop the sled by pushing on it for 0.50 s in a direction opposite to its motion. If the mass of the child and sled is 35 kg, what average force do you need to apply to stop the sled? Use the concepts of impulse and momentum.

Problem 10CQ 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 rockets could travel in space?

Problem 10P An ice hockey puck slides along the ice at 12 m/s. A hockey stick delivers an impulse of 4.0 kg . m/s, causing the puck to move off in the opposite direction with the same speed. What is the mass of the puck?

Problem 11CQ Two ice skaters, Megan and Jason, push off from each other on frictionless 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 after the pushoff? Explain.

Problem 11P As part of a safety investigation, two 1400 kg cars traveling at 20 m/s are crashed into different barriers. Find the average forces exerted on (a) the car that hits a line of water barrels and takes 1.5 s to stop, and (b) the car that hits a concrete barrier and takes 0.10 s to stop.

Problem 12CQ Suppose a rubber ball and a steel ball collide. Which, if either, receives the larger impulse? Explain.

Problem 12P In a Little League baseball game, the 145 g ball reaches the batter with a speed of 15.0 m/s. The batter hits the ball, and it leaves his bat with a speed of 20.0 m/s in exactly the opposite direction. a. What is the magnitude of the impulse delivered by the bat to the ball? b. If the bat is in contact with the ball for 1.5 ms, what is the magnitude of the average force exerted by the bat on the ball?

Problem 13CQ While 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 violated?

Problem 13P A small, 100 g cart is moving at 1.20 m/s on a frictionless track when it collides with a larger, 1.00 kg cart at rest. After the collision, the small cart recoils at 0.850 m/s. What is the speed of the large cart after the collision?

Problem 14CQ 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.

Problem 14P A man standing on very slick ice fires a rifle horizontally. The mass of the man together with the rifle is 70 kg, and the mass of the bullet is 10 g. If the bullet leaves the muzzle at a speed of 500 m/s, what is the final speed of the man?

Problem 15CQ Rank in order, from largest to smallest, the angular momenta of the balls shown in Figure Q9.15 . Explain.

Problem 15P A 2.7 kg block of wood sits on a frictionless table. A 3.0 g bullet, fired horizontally at a speed of 500 m/s, goes completely through the block, emerging at a speed of 220 m/s. What is the speed of the block immediately after the bullet exits?

Problem 16CQ Figure 16 shows two masses held together by a thread on a rod that is rotating about its center with angular velocity to. If the thread breaks, the masses will slide out to the ends of the rod. If that happens, will the rod’s angular velocity increase, decrease, or remain unchanged? Explain. Figure 16

Problem 16P A strong man is compressing a lightweight spring between two weights. One weight has a mass of 2.3 kg, the other a mass of 5.3 kg. He is holding the weights stationary, but then he loses his grip and the weights fly off in opposite directions. The lighter of the two is shot out at a speed of 6.0 m/s. What is the speed of the heavier weight?

Problem 17CQ If the earth warms significantly, the polar ice caps will melt. Water will move from the poles, near the earth’s rotation axis, and will 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?

Problem 17P A 10,000 kg railroad car is rolling at 2.00 m/s when a 4000 kg load of gravel is suddenly dropped in. What is the car’s speed just after the gravel is loaded?

Problem 18CQ The disks shown in Figure Q9.18 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.

Problem 18P A 5000 kg train car, with its top open, is rolling on frictionless rails at 22.0 m/s when it starts pouring rain. A few minutes later, the car’s speed is 20.0 m/s. What mass of water has collected in the car?

Problem 19MCQ Curling is a sport played with 20 kg stones that slide across an ice surface. Suppose a curling stone sliding at 1 m/s 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

Problem 19P A 50.0 kg archer, standing on frictionless ice, shoots a 40 g arrow at a speed of 60 m/s. What is the recoil speed of the archer?

Problem 20MCQ 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 m/s 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 m/s. What is the mass of the second ball? A. 0.67 kg B. 2.0 kg C. 1.7 kg D. 1.0 kg

Problem 20P A 9.5 kg dog takes a nap in a canoe and wakes up to find the canoe has drifted out onto the lake but now is stationary. He walks along the length of the canoe at 0.50 m/s, relative to the water, and the canoe simultaneously moves in the opposite direction at 0.15 m/s. What is the mass of the canoe?

Problem 21MCQ Figure Q9.21 shows two blocks sliding 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 collision?

Problem 21P A 300 g bird flying along at 6.0 m/s sees a 10 g insect heading straight toward it with a speed of 30 m/s. The bird opens its mouth wide and enjoys a nice lunch. What is the bird’s speed immediately after swallowing?

Problem 22MCQ 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.

Problem 22P A 71 kg baseball player jumps straight up to catch a hard-hit ball. If the 140 g ball is moving horizontally at 28 m/s, and the catch is made when the ballplayer is at the highest point of his leap, what is his speed immediately after stopping the ball?

Problem 23MCQ

Problem 23P A kid at the junior high cafeteria wants to propel an empty milk carton along a lunch table by hitting it with a 3.0 g spit ball. If he wants the speed of the 20 g carton just after the spit ball hits it to be 0.30 m/s, at what speed should his spit ball hit the carton?

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

Problem 24P The parking brake on a 2000 kg Cadillac has failed, and it is rolling slowly, at 1 mph, toward a group of small children. Seeing the situation, you realize you have just enough time to drive your 1000 kg Volkswagen head-on into the Cadillac and save the children. With what speed should you impact the Cadillac to bring it to a halt?

Problem 25MCQ A red ball, initially at rest, is simultaneously hit by a blue ball traveling from west to east at 3 m/s and a green ball traveling east to west at 3 m/s. All three balls have equal mass. Afterward, the red ball is traveling south and the green ball is moving to the east. In 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

Problem 25P A 2.0 kg block slides along a frictionless surface at 1.0 m/s. A second block, sliding at a faster 4.0 m/s, collides with the first from behind and sticks to it. The final velocity of the combined blocks is 2.0 m/s. What was the mass of the second block?

Problem 26MCQ A 24 g, 3-cm-diameter thin, hollow sphere rotates at 30 rpm about a vertical, frictionless axis through its center. A4 g bug stands at the top of the sphere. He then walks along the surface of the sphere until he reaches its “equator.” When he reaches the equator, the sphere is rotating at A. 15 rpm B. 24 rpm C. 30 rpm D. 37 rpm E. 45 rpm

Problem 26P A 20 g ball of clay traveling east at 3.0 m/s collides with a 30 g ball of clay traveling north at 2.0 m/s. What are the speed and the direction of the resulting 50 g blob of clay?

Problem 27MCQ A 5.0 kg solid cylinder of radius 12 cm rotates with ?i =3.7 rad/s about an axis through its center. A torque of 0.040 N · m is applied to the cylinder for 5.0 s. By how much does the cylinder’s angular momentum change? A. 0.12kg · m2/s B. 0.20kg · m2/s C. 0.38kg · m2/s D. 0.52kg · m2/s E. 0.88kg · m2/s

Problem 27P 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 particle 1? Show your answer by copying the figure and drawing the final momentum vector on the figure.

Problem 28P 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 particle 1? Show your answer by copying the figure and drawing the final momentum vector on the figure.

Problem 29P A firecracker 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 m/s. The third piece has twice the mass of the other two. What are the speed and direction of the third piece?

Problem 30P What is the angular momentum of the moon around the earth? The moon’s mass is from the earth.

Problem 31P A little girl is going on the merry-go-round for the first time, and wants her 47 kg mother to 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 m/s when the ride is in motion, what is her angular momentum around the center of the merry-go-round?

Problem 32P What is the angular momentum about the axle of the 500 g rotating bar in Figure P9.34?

Problem 33P What is the angular momentum about the axle of the 2.0 kg, 4.0-cm-diameter rotating disk in Figure P9.35?

Problem 34P Divers change their body position in midair while rotating about their center of mass. In 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 , by what factor is her angular velocity when tucked greater than when straight?

Problem 35P Ice skaters often end their performances with spin turns, 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 finish. Not quite as noticeably, one leg goes out as well. Suppose that the moment of inertia of a skater with arms out and one leg extended is and for arms and legs in is . If she starts out spinning at 5.0 rev/s, what is her angular speed (in rev/s) when her arms and one leg open outward?

Problem 36GP What is the impulse on a 3.0 kg particle that experiences the force described by the graph in Figure P9.38?

Problem 37GP 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?

Problem 38GP Far in space, where gravity is negligible, a 425 kg rocket traveling at 75.0 m/s in the positive x-direction fires its engines. Figure P9.40 shows the thrust force as a function of time. The mass lost by the rocket during these 30.0 s is 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?

Problem 39GP 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 P9.41 shows the impulse received from the floor. What maximum force does the floor exert on the ball?

Problem 40GP 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?

Problem 41GP Figure P9.43 is a graph of the force exerted by the floor on a woman making a vertical jump. At what speed does she leave the ground? Hint: The force of the floor is not the only force acting on the woman.

Problem 42GP A sled slides along a horizontal surface for which the coefficient of kinetic friction is 0.25. Its velocity at point A is 8.0 m/s and at point B is 5.0 m/s. Use the impulse-momentum theorem to find how long the sled takes to travel from A to B.

Problem 43GP A 140 g baseball is moving horizontally to the right at 35 m/s when it is hit by the bat. The ball flies off to the left at 55 m/s, at an angle of 25° above the horizontal. What are the magnitude and direction of the impulse that the bat delivers to the ball?

Problem 44GP Squids rely on jet propulsion, a versatile technique to move around in water. A 1.5 kg squid at rest suddenly expels 0.10 kg of water backward to quickly get itself moving forward at 3.0 m/s. If other forces (such as the drag force on the squid) are ignored, what is the speed with which the squid expels the water?

Problem 45GP The flowers of the bunchberry 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 . If the acceleration is constant, what impulse is delivered to a pollen grain with a mass of ?

Problem 46GP a. With what speed are pollen grains ejected from a bunchberry flower? See Problem 47 for information. b. Suppose that 1000 ejected pollen grains slam into the abdomen of a 5.0 g bee that is hovering just above the flower. If the collision is perfectly inelastic, what is the bee’s speed immediately afterward? Is the bee likely to notice? Reference: Problem 47: The flowers of the bunchberry 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 . If the acceleration is constant, what impulse is delivered to a pollen grain with a mass of ?

Problem 47GP A tennis player swings her 1000 g racket with a speed of 10 m/s. She hits a 60 g tennis ball that was approaching her at a speed of 20 m/s. The ball rebounds at 40 m/s. 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. If the tennis ball and racket are in contact for 10 ms, what is the average force that the racket exerts on the ball?

Problem 48GP A 20 g ball of clay is thrown horizontally at 30 m/s toward a 1.0 kg block sitting at rest on a frictionless surface. The clay hits 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 exerts on the block. c. Use the clay’s initial and final speeds to calculate the impulse the block exerts on the clay. d. Does ?

Problem 49GP Dan is gliding on his skateboard at 4.0 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.0 m/s. 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.

Problem 50GP James and Sarah stand on a stationary cart with frictionless 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 m/s, while Sarah throws a 0.50 kg ball to James at 1.0 m/s. (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?

Problem 51GP Ethan, whose mass is 80 kg, stands at one end of a very 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 m/s, measured relative to the cart. What is the speed of the cart when Ethan has reached his top speed?

Problem 52GP The cars of a long coal train are filled by pulling them under a hopper, from which coal falls into the cars at a rate of 10,000 kg/s. Ignoring friction due to the rails, what is the average force that the engine must exert on the coal train to keep it moving under the hopper at a speed of 0.50 m/s?

Problem 53GP Three identical train cars, coupled together, are rolling east at 2.0 m/s. A fourth car traveling east at 4.0 m/s 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?

Problem 54GP A 110 kg linebacker running at 2.0 m/s and an 82 kg quarterback running at 3.0 m/s have a head-on collision in midair. The linebacker grabs and holds onto the quarterback. Who ends up moving forward after they hit?

Problem 55GP Most geologists believe that the dinosaurs became extinct 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 hits the earth with an impact speed of . 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.)

Problem 56GP At the center of a 50-m-diarneter circular ice rink, a 75 kg skater traveling north at 2.5 m/s collides with and holds onto a 60 kg skater who had been heading west at 3.5 m/s. a. How long will it take them to glide to the edge of the rink? b. Where will they reach it? Give your answer as an angle north of west.

Problem 57GP 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?

Problem 58GP One billiard ball is shot east at 2.00 m/s. A second, identical billiard ball is shot west at 1.00 m/s. The balls have a glancing collision, not a head-on collision, deflecting the second ball by 90° and sending it north at 1.41 m/s. What are the speed and direction of the first ball after the collision?

Problem 59GP 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. What was the speed of the bullet?

Problem 60GP You are part of a search-and-rescue mission that has imtbeen called out to look for a lost explorer. You’ve found the missing explorer, but you’re separated from him by a 200-m-high cliff and a 30-m-wide raging river, as shown in Figure 60. To save his life, you need to get a 5.0 kg package of emergency supplies across the river. Unfortunately, you can’t throw the package hard enough to make it across. Fortunately, you happen to have a 1.0 kg rocket intended for launching flares. Improvising quickly, you attach a sharpened stick to the front of the rocket, so that it will impale itself into the package of supplies, then fire the rocket at ground level toward the supplies. What minimum speed must the rocket have iust before impact in order to save the explorer’s life? FIGURE 60

Problem 61GP A 1500 kg weather rocket accelerates upward at . 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?

Problem 62GP Two 500 g blocks of wood are 2.0 m apart on a frictionless table. A 10 g bullet is fired at 400 m/s 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 m/s. What is the speed of the second block after the bullet stops?

Problem 63GP A 500 kg cannon fires a 10 kg cannonball with a speed of 200 m/s 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 earth?

Problem 64GP Laura, whose mass is 35 kg, jumps horizontally off a 55 kg canoe at 1.5 m/s relative to the canoe. What is the canoe’s speed just after she jumps?

Problem 65GP

Problem 66GP A proton is shot at 5.0 × 107 m/s toward a gold target. The nucleus of a gold atom, with a mass 197 times that of the proton, repels the proton and deflects it straight back with 90% of its initial speed. What is the recoil speed of the gold nucleus?

Problem 68GP

Problem 67GP 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?

Problem 69GP 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. Initially, 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 final angular speed? Give your answer in rpm.

Problem 70GP 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 # m2/s. What is the tension in the string?

Problem 71GP Figure 71 shows a 100 g puck revolving in a 20-cm-radius circle on a frictionless table. The string passes through a hole in the center of the table and is tied to two 200 g weights. a. What speed does the puck need to support the two weights? b. The lower weight is a light bag filled with sand. Suppose a pin pokes a hole in the bag and the sand slowly leaks out while the puck is revolving. What will be the puck’s speed and the radius of its trajectory after all of the sand is gone? FIGURE 71

Problem 72GP A 2.0 kg, 20-cm-diameter turntable rotates at 100 rpm on frictionless 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 this event?

Problem 73GP 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 m/s. What is the final angular speed of the merry-go-round?

Problem 74GP A 3.0-m-diameter merry-go-round with a mass of 250 kg is spinning at 20 rpm. John runs around the merry-go-round at 5.0 m/s, 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?

Problem 75GP Disk A, with a mass of 2.0 kg and a radius of 40 cm, rotates clockwise about a frictionless vertical 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, after which they rotate together. After the collision, what is their common angular speed (in rev/s) and in which direction do they rotate?

Problem 76PP Hitting a Golf Ball Consider a golf club hitting a golf ball. To a good approximation, we can model this as a collision between the rapidly moving head of the golf club and the stationary golf ball, ignoring the shaft of the club and the golfer. A golf ball has a mass of 46 g. Suppose a 200 g club head is moving at a speed of 40 m/s just before striking the golf ball. After the collision, the golf ball’s speed is 60 m/s. What is the momentum of the club + ball system right before the collision? A. 1.8 kg . m/s B. 8.0 kg . m/s C. 3220 kg . m/s D. 8000 kg . m/s

Problem 77PP Hitting a Golf Ball Consider a golf club hitting a golf ball. To a good approximation, we can model this as a collision between the rapidly moving head of the golf club and the stationary golf ball, ignoring the shaft of the club and the golfer. A golf ball has a mass of 46 g. Suppose a 200 g club head is moving at a speed of 40 m/s just before striking the golf ball. After the collision, the golf ball’s speed is 60 m/s. Immediately after the collision, the momentum of the club + ball system will be A. Less than before the collision. B. The same as before the collision. C. Greater than before the collision.

Problem 78PP Hitting a Golf Ball Consider a golf club hitting a golf ball. To a good approximation, we can model this as a collision between the rapidly moving head of the golf club and the stationary golf ball, ignoring the shaft of the club and the golfer. A golf ball has a mass of 46 g. Suppose a 200 g club head is moving at a speed of 40 m/s just before striking the golf ball. After the collision, the golf ball’s speed is 60 m/s. 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.

Problem 79PP Hitting a Golf Ball Consider a golf club hitting a golf ball. To a good approximation, we can model this as a collision between the rapidly moving head of the golf club and the stationary golf ball, ignoring the shaft of the club and the golfer. A golf ball has a mass of 46 g. Suppose a 200 g club head is moving at a speed of 40 m/s just before striking the golf ball. After the collision, the golf ball’s speed is 60 m/s. By approximately how much does the club head slow down as a result of hitting the ball? A. 4 m/s B. 6 m/s C. 14 m/s D. 26 m/s