Solution: Work and Power in CyclingWhen you ride a bicycle

Problem 1CQ The brake shoes of your car are made of a material that can tolerate very high temperatures without being damaged. Why is this so?

Problem 1P During an etiquette class, you walk slowly and steadily at 0.20 m/s for 2.5 m with a 0.75 kg book balanced on top of your head. How much work does your head do on the book?

Problem 2CQ When you pound a nail with a hammer, the nail gets quite warm. Describe the energy transformations that lead to the addition of thermal energy in the nail.

Problem 2P A 2.0 kg book is lying on a 0.75-m-high table. You pick it up and place it on a bookshelf 2.3 m above the floor. During this process, a. How much work does gravity do on the book? b. How much work does your hand do on the book?

Problem 3CQ For Question, give a specific example of a system with the energy transformation shown. In these questions, W is the work done on the system, and are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero. W ? K

Problem 3P The two ropes seen in Figure P10.2 are used to lower a 255 kg piano exactly 5 m from a second-story window to the ground. How much work is done by each of the three forces?

Problem 4CQ For Question, give a specific example of a system with the energy transformation shown. In these questions, W is the work done on the system, and are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero. W ? U

Problem 4P The two ropes shown in the bird’s-eye view of Figure P10.3 are used to drag a crate exactly 3 m across the floor. How much work is done by each of the ropes on the crate?

Problem 5CQ For Question, give a specific example of a system with the energy transformation shown. In these questions, W is the work done on the system, and are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero. K ? U

Problem 5P a. At the airport, you ride a “moving sidewalk” that carries you horizontally for 25 m at 0.70 m/s. Assuming that you were moving at 0.70 m/s before stepping onto the moving sidewalk and continue at 0.70 m/s afterward, how much work does the moving sidewalk do on you? Your mass is 60 kg, ________________ b. An escalator carries you from one level to the next in the airport terminal. The upper level is 4.5 m above the lower level, and the length of the escalator is 7.0 m. How much work does the up escalator do on you when you ride it from the lower level to the upper level? ________________ c. How much work does the down escalator do on you when you ride it from the upper level to the lower level?

Problem 6CQ For Question, give a specific example of a system with the energy transformation shown. In these questions, W is the work done on the system, and are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero. K ? W

Problem 6P A boy flies a kite with the string at a 30° angle to the horizontal. The tension in the string is 4.5 N. How much work does the string do on the boy if the boy a. Stands still? b. Walks a horizontal distance of 11 m away from the kite? c. Walks a horizontal distance of 11 m toward the kite?

Problem 7CQ For Question, give a specific example of a system with the energy transformation shown. In these questions, W is the work done on the system, and are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero. U ? K

Problem 7P Which has the larger kinetic energy, a 10 g bullet fired at 500 m/s or a 10 kg bowling ball sliding at 10 m/s?

Problem 8CQ For Question, give a specific example of a system with the energy transformation shown. In these questions, W is the work done on the system, and are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero.

Problem 8P At what speed does a 1000 kg compact car have the same kinetic energy as a 20,000 kg truck going 25 km/h?

Problem 9CQ For Question, give a specific example of a system with the energy transformation shown. In these questions, W is the work done on the system, and are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero.

Problem 9P A car is traveling at 10 m/s. a. How fast would the car need to go to double its kinetic energy? b. By what factor does the car’s kinetic energy increase if its speed is doubled to 20 m/s?

Problem 10CQ For Question, give a specific example of a system with the energy transformation shown. In these questions, W is the work done on the system, and are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero.

Problem 10P Sam’s job at the amusement park is to slow down and bring to a stop the boats in the log ride. If a boat and its riders have a mass of 1200 kg and the boat drifts in at 1.2 m/s, how much work does Sam do to stop it?

Problem 11CQ A ball of putty is dropped from a height of 2 m onto a hard floor, where it sticks. What object or objects need to be included within the system if the system is to be isolated during this process?

Problem 11P A 20 g plastic ball is moving to the left at 30 m/s. How much work must be done on the ball to cause it to move to the right at 30 m/s?

Problem 12CQ A 0.5 kg mass on a 1-m-long string swings in a circle on a horizontal, frictionless table at a steady speed of 2 m/s. How much work does the tension in the string do on the mass during one revolution? Explain.

Problem 12P The turntable in a microwave oven has a moment of inertia of and rotates continuously, making a complete revolution every 4.0 s. What is its kinetic energy?

Problem 13CQ Particle A has less mass than particle B. Both are pushed forward across a frictionless surface by equal forces for 1 s. Both start from rest. a. Compare the amount of work done on each particle. That is, is the work done on A greater than, less than, or equal to the work done on B? Explain. b. Compare the impulses delivered to particles A and B. Explain. c. Compare the final speeds of particles A and B. Explain.

Problem 13P An energy storage system based on a flywheel (a rotating disk) can store a maximum of 4.0 MJ when the flywheel is rotating at 20,000 revolutions per minute. What is the moment of inertia of the flywheel?

Problem 14CQ The meaning of the word “work” is quite different in physics from its everyday usage. Give an example of an action a person could do that “feels like work” but that does not involve any work as we’ve defined it in this chapter.

Problem 14P The lowest point in Death Valley is 85.0 m below sea level. The summit of nearby Mt. Whitney has an elevation of 4420 m. What is the change in gravitational potential energy of an energetic 65.0 kg hiker who makes it from the floor of Death Valley to the top of Mt. Whitney?

Problem 15CQ To change a tire, you need to use a jack to raise one corner of your car. While doing so, you happen to notice that pushing the jack handle down 20 cm raises the car only 0.2 cm. Use energy concepts to explain why the handle must be moved so far to raise the car by such a small amount.

Problem 15P a. What is the kinetic energy of a 1500 kg car traveling at a speed of 30 m/s (?65 mph)? b. From what height should the car be dropped to have this same amount of kinetic energy just before impact? c. Does your answer to part b depend on the car’s mass?

Problem 16CQ You drop two balls from a tower, one of mass m and the other of mass 2 m . Just before they hit the ground, which ball, if either, has the larger kinetic energy? Explain.

Problem 16P The world’s fastest humans can reach speeds of about 11 m/s. In order to increase his gravitational potential energy by an amount equal to his kinetic energy at full speed, how high would such a sprinter need to climb?

Problem 17CQ A roller coaster car rolls down a frictionless track, reaching speed v at the bottom. a. If you want the car to go twice as fast at the bottom, by what factor must you increase the height of the track? b. Does your answer to part a depend on whether the track is straight or not? Explain.

Problem 17P A 72 kg bike racer climbs a 1200-m-long section of road that has a slope of 4.3°. By how much does his gravitational potential energy change during this climb?

Problem 18CQ A spring gun shoots out a plastic ball at speed v. The spring is then compressed twice the distance it was on the first shot. a. By what factor is the spring’s potential energy increased? b. By what factor is the ball’s speed increased? Explain.

Problem 18P A 1000 kg wrecking ball hangs from a 15-m-long cable. The ball is pulled back until the cable makes an angle of 25° with the vertical. By how much has the gravitational potential energy of the ball changed?

Problem 19CQ Sandy and Chris stand on the edge of a cliff and throw identical mass rocks at the same speed. Sandy throws her rock horizontally while Chris throws his upward at an angle of 45° to the horizontal. Are the rocks moving at the same speed when they hit the ground, or is one moving faster than the other? If one is moving faster, which one? Explain.

Problem 19P How far must you stretch a spring with k = 1000 N/m to store 200 J of energy?

Problem 20CQ A solid cylinder and a hollow cylinder have the same mass, same radius, and turn on frictionless, horizontal axles. (The hollow cylinder has lightweight spokes connecting it to the axle.) A rope is wrapped around each cylinder and tied to a block. The blocks have the same mass and are held the same height above the ground as shown in Figure Q10.20 . Both blocks are released simultaneously. The ropes do not slip. Which block hits the ground first? Or is it a tie? Explain.

Problem 20P How much energy can be stored in a spring with a spring constant of 500 N/m if its maximum possible stretch is 20 cm?

Problem 21CQ You are much more likely to be injured if you fall and your head strikes the ground than if your head strikes a gymnastics pad. Use energy and work concepts to explain why this is so.

Problem 22CQ If you walk up a flight of stairs at constant speed, gaining vertical height h, the work done on you (the system, of mass m) is A. +mgh, by the normal force of the stairs, ________________ B. ? mgh, by the normal force of the stairs, ________________ C. +mgh, by the gravitational force of the earth. ________________ D. ?mgh, by the gravitational force of the earth.

Problem 21P The elastic energy stored in your tendons can contribute up to 35% of your energy needs when running. Sports scientists have studied the change in length of the knee extensor tendon in sprinters and nonathletes. They find (on average) that the sprinters’ tendons stretch 41 mm, while nonathletes’ stretch only 33 mm. The spring constant for the tendon is the same for both groups, 33 N/mm. What is the difference in maximum stored energy between the sprinters and the nonathletes?

Problem 22P Marissa drags a 23 kg duffel bag 14 m across the gym floor. If the coefficient of kinetic friction between the floor and bag is 0.15, how much thermal energy does Marissa create?

Problem 23MCQ You and a friend each carry a 15 kg suitcase up two flights of stairs, walking at a constant speed. Take each suitcase to be the system. Suppose you carry your suitcase up the stairs in 30 s while your friend takes 60 s. Which of the following is true? A. You did more work, but both of you expended the same power. B. You did more work and expended more power. C. Both of you did equal work, but you expended more power. D. Both of you did equal work, but you expended less power.

Problem 23P Mark pushes his broken car 150 m down the block to his friend’s house. He has to exert a 110 N horizontal force to push the car at a constant speed. How much thermal energy is created in the tires and road during this short trip?

Problem 24MCQ A woman uses a pulley and a rope to raise a 20 kg weight to a height of 2 m. If it takes 4 s to do this, about how much power is she supplying? A. 100 W B. 200 W C. 300 W D. 400 W

Problem 24P A 900 N crate slides 12 m down a ramp that makes an angle of 35° with the horizontal. If the crate slides at a constant speed, how much thermal energy is created?

Problem 25MCQ A hockey puck sliding along frictionless ice with speed v to the right collides with a horizontal spring and compresses it by 2.0 cm before coming to a momentary stop. What will be the spring’s maximum compression if the same puck hits it at a speed of 2 v ? A. 2.0 cm B. 2.8 cm C. 4.0 cm D. 5.6 cm E. 8.0 cm P R

Problem 25P A 25 kg child slides down a playground slide at a constant speed. The slide has a height of 3.0 m and is 7.0 m long. Using the law of conservation of energy, find the magnitude of the kinetic friction force acting on the child.

Problem 26MCQ A block slides down a smooth ramp, starting from rest at a height h . When it reaches the bottom it’s moving at speed v. It then continues to slide up a second smooth ramp. At what height is its speed equal to v/2? A. h/4 B. h/2 C. 3h/4 D. 2h

Problem 26P A boy reaches out of a window and tosses a ball straight up with a speed of 10 m/s. The ball is 20 m above the ground as he releases it. Use conservation of energy to find a. The ball’s maximum height above the ground. b. The ball’s speed as it passes the window on its way down. c. The speed of impact on the ground.

Problem 27MCQ A wrecking ball is suspended from a 5.0-m-long cable that makes a 30° angle with the vertical. The ball is released and swings down. What is the ball’s speed at the lowest point? A. 7.7 m/s B. 4.4 m/s C. 3.6 m/s D. 3.1 m/s

Problem 27P a. With what minimum speed must you toss a 100 g ball straight up to just barely hit the 10-m-high ceiling of the gymnasium if you release the ball 1.5 m above the floor? Solve this problem using energy. b. With what speed does the ball hit the floor?

Problem 28P What minimum speed does a 100 g puck need to make it to the top of a frictionless ramp that is 3.0 m long and inclined at 20°?

Problem 29P A car is parked at the top of a 50-m-high hill. Its brakes fail and it rolls down the hill. How fast will it be going at the bottom? (Ignore friction.)

Problem 30P A 1500 kg car is approaching the hill shown in Figure at 10 m/s when it suddenly runs out of gas. a. Can the car make it to the top of the hill by coasting? ________________ b. If your answer to part a is yes, what is the car’s speed after coasting down the other side? FIGURE

Problem 31P 10 kg runaway grocery cart runs into a spring, attached to a wall, with spring constant 250 N/m and compresses it by 60 cm. What was the speed of the cart just before it hit the spring?

Problem 32P As a 15,000 kg jet lands on an aircraft carrier, its tail hook snags a cable to slow it down. The cable is attached to a spring with spring constant 60,000 N/m. If the spring stretches 30 m to stop the plane, what was the plane’s landing speed?

Problem 33P Your friend’s Frisbee has become stuck 16 m above the ground in a tree. You want to dislodge the Frisbee by throwing a rock at it. The Frisbee is stuck pretty tight, so you figure the rock needs to be traveling at least 5.0 m/s when it hits the Frisbee. If you release the rock 2.0 m above the ground, with what minimum speed must you throw it?

Problem 34P A fireman of mass 80 kg slides down a pole. When he reaches the bottom, 4.2 m below his starting point, his speed is 2.2 m/s. By how much has thermal energy increased during his slide?

Problem 35P A 20 kg child slides down a 3.0-m-high playground slide. She starts from rest, and her speed at the bottom is 2.0 m/s. a. What energy transfers and transformations occur during the slide? b. What is the total change in the thermal energy of the slide and the seat of her pants?

Problem 36P A hockey puck is given an initial speed of 5.0 m/s. If the coefficient of kinetic friction between the puck and the ice is 0.05, how far does the puck slide before coming to rest? Solve this problem using conservation of energy.

Problem 37P A 50 g marble moving at 2.0 m/s strikes a 20 g marble at rest. What is the speed of each marble immediately after the collision? Assume the collision is perfectly elastic and the marbles collide head-on.

Problem 38P Ball 1, with a mass of 100 g and traveling at 10 m/s, collides head-on with ball 2, which has a mass of 300 g and is initially at rest. What are the final velocities of each ball if the collision is (a) perfectly elastic? (b) perfectly inelastic?

Problem 39P An air-track glider undergoes a perfectly inelastic collision with an identical glider that is initially at rest. What fraction of the first glider’s initial kinetic energy is transformed into thermal energy in this collision?

Problem 40P Two balls undergo a perfectly elastic head-on collision, with one ball initially at rest. If the incoming ball has a speed of 200 m/s, what are the final speed and direction of each ball if a. The incoming ball is much more massive than the stationary ball? b. The stationary ball is much more massive than the incoming ball?

Problem 41P a. How much work must you do to push a 10 kg block of steel across a steel table at a steady speed of 1.0 m/s for 3.0 s? The coefficient of kinetic friction for steel on steel is 0.60. b. What is your power output while doing so?

Problem 42P a. How much work does an elevator motor do to lift a 1000 kg elevator a height of 100 m at a constant speed? b. How much power must the motor supply to do this in 50 s at constant speed?

Problem 43P A 1000 kg sports car accelerates from 0 to 30 m/s in 10 s. What is the average power of the engine?

Problem 44P In just 0.30 s, you compress a spring (spring constant 5000 N/m), which is initially at its equilibrium length, by 4.0 cm. What is your average power output?

Problem 45P In the winter sport of curling, players give a 20 kg stone a push across a sheet of ice. A curler accelerates a stone to a speed of 3.0 m/s over a time of 2.0 s. a. How much force does the curler exert on the stone? ________________ b. What average power does the curler use to bring the stone up to speed?

Problem 46P A 710 kg car drives at a constant speed of 23 m/s. It is subject to a drag force of 500 N. What power is required from the car’s engine to drive the car a. On level ground? b. Up a hill with a slope of 2.0°?

Problem 47P An elevator weighing 2500 N ascends at a constant speed of 8.0 m/s. How much power must the motor supply to do this?

Problem 48GP A 2.3 kg box, starting from rest, is pushed up a ramp by a 10 N force parallel to the ramp. The ramp is 2.0 m long and tilted at 17°. The speed of the box at the top of the ramp is 0.80 m/s. Consider the system to be the box + ramp + earth. a. How much work W does the force do on the system? b. What is the change ?K in the kinetic energy of the system? c. What is the change in the gravitational potential energy of the system? d. What is the change in the thermal energy of the system?

Problem 49GP A 55 kg skateboarder wants to just make it to the upper edge of a “half-pipe” with a radius of 3.0 m, as shown in Figure P10.55. What speed does he need at the bottom if he is to coast all the way up? a. First do the calculation treating the skateboarder and board as a point particle, with the entire mass nearly in contact with the half-pipe. b. More realistically, the mass of the skateboarder in a deep crouch might be thought of as concentrated 0.75 m from the half-pipe. Assuming he remains in that position all the way up, what is needed to reach the upper edge?

Problem 50GP Fleas have remarkable jumping ability. A 0.50 mg flea, jumping straight up, would reach a height of 40 cm if there were no air resistance. In reality, air resistance limits the height to 20 cm. a. What is the flea’s kinetic energy as it leaves the ground? b. At its highest point, what fraction of the initial kinetic energy has been converted to potential energy?

Problem 51GP A marble slides without friction in a vertical plane around the inside of a smooth, 20-cm-diameter horizontal pipe. The marble’s speed at the bottom is 3.0 m/s; this is fast enough so that the marble makes a complete loop, never losing contact with the pipe. What is its speed at the top?

Problem 53GP Suppose you lift a 20 kg box by a height of 1.0 m. a. How much work do you do in lifting the box? Instead of lifting the box straight up, suppose you push it up a 1.0-m-high ramp that makes a 30° degree angle with the horizontal, as shown in Figure P10.59. Being clever, you choose a ramp with no friction. b. How much force F is required to push the box straight up the slope at a constant speed? c. How long is the ramp? d. Use your force and distance results to calculate the work you do in pushing the box up the ramp. How does this compare to your answer to part a?

Problem 52GP A 20 kg child is on a swing that hangs from 3.0-m-long chains, as shown in Figure P10.58. What is her speed at the bottom of the arc if she swings out to a 45° angle before reversing direction?

Problem 54GP A cannon tilted up at a 30° angle fires a cannon ball at 80 m/s from atop a 10-m-high fortress wall. What is the ball’s impact speed on the ground below? Ignore air resistance.

Problem 55GP The sledder shown in Figure starts from the top of a frictionless hill and slides down into the valley. What initial speed vi does the sledder need to just make it over the next hill? FIGURE

Problem 56GP In a physics lab experiment, a spring clamped to the table shoots a 20 g ball horizontally. When the spring is compressed 20 cm, the ball travels horizontally 5.0 m and lands on the floor 1.5 m below the point at which it left the spring. What is the spring constant?

Problem 57GP A 50 g ice cube can slide without friction up and down a 30° slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 10 cm. The spring constant is 25 N/m. When the ice cube is released, what distance will it travel up the slope before reversing direction?

Problem 58GP The maximum energy a bone can absorb without breaking is surprisingly small. For a healthy human of mass 60 kg, experimental data show that the leg bones of both legs can absorb about 200 J. a. From what maximum height could a person jump and land rigidly upright on both feet without breaking his legs? Assume that all the energy is absorbed in the leg bones in a rigid landing. b. People jump from much greater heights than this; explain how this is possible. Hint: Think about how people land when they jump from greater heights.

Problem 59GP In an amusement park water slide, people slide down an essentially frictionless tube. The top of the slide is 3.0 m above the bottom where they exit the slide, moving horizontally, 1.2 m above a swimming pool. What horizontal distance do they travel from the exit point before hitting the water? Does the mass of the person make any difference?

Problem 60GP The 5.0-m-long rope in Figure P10.66 hangs vertically from a tree right at the edge of a ravine. A woman wants to use the rope to swing to the other side of the ravine. She runs as fast as she can, grabs the rope, and swings out over the ravine. a. As she swings, what energy conversion is taking place? b. When she’s directly over the far edge of the ravine, how much higher is she than when she started? c. Given your answers to parts a and b, how fast must she be running when she grabs the rope in order to swing all the way across the ravine?

Problem 61GP You have been asked to design a “ballistic spring system” to measure the speed of bullets. A bullet of mass m is fired into a block of mass M. The block, with the embedded bullet, then slides across a frictionless table and collides with a horizontal spring whose spring constant is k. The opposite end of the spring is anchored to a wall. The spring’s maximum compression d is measured. a. Find an expression for the bullet’s initial speed in terms of m, M, k, and d. Hint: This is a two-part problem. The bullet’s collision with the block is an inelastic collision. What quantity is conserved in an inelastic collision? Subsequently the block hits a spring on a frictionless surface. What quantity is conserved in this collision? b. What was the speed of a 5.0 g bullet if the block’s mass is 2.0 kg and if the spring, with k = 50 N/m, was compressed by 10 cm? c. What fraction of the bullet’s initial kinetic energy is “lost”? Where did it go?

Problem 62GP A new event, shown in Figure P10.68, has been proposed for the Winter Olympics. An athlete will sprint 100 m, starting from rest, then leap onto a 20 kg bobsled. The person and bobsled will then slide down a 50-m-long ice-covered ramp, sloped at 20°, and into a spring with a carefully calibrated spring constant of 2000 N/m. The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 40 kg, has been training for this event. She can reach a maximum speed of 12 m/s in the 100 m dash. a. How far will Lisa compress the spring? b. The Olympic committee has very exact specifications about the shape and angle of the ramp. Is this necessary? If the committee asks your opinion, what factors about the ramp will you tell them are important?

Problem 63GP Boxes A and B in Figure P10.69 have masses of 12.0 kg and 4.0 kg, respectively. The two boxes are released from rest. Use conservation of energy to find the boxes’ speed when box B has fallen a distance of 0.50 m. Assume a frictionless upper surface.

Problem 64GP What would be the speed of the boxes in Problem 69 if the coefficient of kinetic friction between box A and the surface it slides on were 0.20? Use conservation of energy. Reference: Problem 69: Boxes A and B in Figure P10.69 have masses of 12.0 kg and 4.0 kg, respectively. The two boxes are released from rest. Use conservation of energy to find the boxes’ speed when box B has fallen a distance of 0.50 m. Assume a frictionless upper surface.

Problem 65GP A 20 g ball is fired horizontally with initial speed vi toward a 100 g ball that is hanging motionless from a 1.0-m-long string. The balls undergo a head-on, perfectly elastic collision, after which the 100 g ball swings out to a maximum angle . What was vi?

Problem 66GP Two coupled boxcars are rolling along at 2.5 m/s when they collide with and couple to a third, stationary boxcar. a. What is the final speed of the three coupled boxcars? b. What fraction of the cars’ initial kinetic energy is transformed into thermal energy?

Problem 67GP A fish scale, consisting of a spring with spring constant k = 200 N/m, is hung vertically from the ceiling. A 5.0 kg fish is attached to the end of the unstretched spring and then released. The fish moves downward until the spring is fully stretched, then starts to move back up as the spring begins to contract. What is the maximum distance through which the fish falls?

Problem 68GP A 70 kg human sprinter can accelerate from rest to 10 m/s in 3.0 s. During the same time interval, a 30 kg greyhound can accelerate from rest to 20 m/s. Compute (a) the change in kinetic energy and (b) the average power output for each.

Problem 69GP A 50 g ball of clay traveling at speed vi hits and sticks to a 1.0 kg block sitting at rest on a frictionless surface. a. What is the speed of the block after the collision? ________________ b. Show that the mechanical energy is not conserved in this collision. What percentage of the ball’s initial kinetic energy is “lost”? Where did this kinetic energy go?

Problem 70GP A package of mass m is released from rest at a warehouse loading dock and slides down a 3.0-m-high frictionless chute to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass 2m, from the bottom of the chute as shown in Figure P10.76. a. Suppose the packages stick together. What is their common speed after the collision? b. Suppose the collision between the packages is perfectly elastic. To what height does the package of mass m rebound?

Problem 71GP A 50 kg sprinter, starting from rest, runs 50 m in 7.0 s at constant acceleration. a. What is the magnitude of the horizontal force acting on the sprinter? b. What is the sprinter’s average power output during the first 2.0 s of his run? c. What is the sprinter’s average power output during the final 2.0 s?

Problem 72GP A 50 kg sprinter, starting from rest, runs 50 m in 7.0 s at constant acceleration. a. What is the magnitude of the horizontal force acting on the sprinter? b. What is the sprinter’s average power output during the first 2.0 s of his run? c. What is the sprinter’s average power output during the final 2.0 s?

Problem 73GP A 2.0 hp electric motor on a water well pumps water from 10m below the surface. The density of water is 1.0 kg per L. How many liters of water can the motor pump in 1 h?

Problem 74GP The human heart has to pump the average adult’s 6.0 L of blood through the body every minute. The heart must do work to overcome frictional forces that resist the blood flow. The average blood pressure is . a. Compute the work done moving the 6.0 L of blood completely through the body, assuming the blood pressure always takes its average value. b. What power output must the heart have to do this task once a minute? Hint: When the heart contracts, it applies force to the blood. Pressure is just force/area, so we can write work = pressure × area × distance. But area × distance is just the blood volume passing through the heart.

Problem 75PP Tennis Ball Testing A tennis ball bouncing on a hard surface compresses and then rebounds. The details of the rebound are specified in tennis regulations. Tennis balls, to be acceptable for tournament play, must have a mass of 57.5 g. When dropped from a height of 2.5 m onto a concrete surface, a ball must rebound to a height of 1.4 m. During impact, the ball compresses by approximately 6 mm. How fast is the ball moving when it hits the concrete surface? (Ignore air resistance.) A. 5 m/s B. 7 m/s C. 25 m/s D. 50 m/s

Problem 76PP A tennis ball bouncing on a hard surface compresses and then rebounds. The details of the rebound are specified in tennis regulations. Tennis balls, to be acceptable for tournament play, must have a mass of 57.5 g. When dropped from a height of 2.5 m onto a concrete surface, a ball must rebound to a height of 1.4 m. During impact, the ball compresses by approximately 6 mm. If the ball accelerates uniformly when it hits the floor, what is its approximate acceleration as it comes to rest before rebounding?

Problem 77PP Tennis Ball Testing A tennis ball bouncing on a hard surface compresses and then rebounds. The details of the rebound are specified in tennis regulations. Tennis balls, to be acceptable for tournament play, must have a mass of 57.5 g. When dropped from a height of 2.5 m onto a concrete surface, a ball must rebound to a height of 1.4 m. During impact, the ball compresses by approximately 6 mm. The ball’s kinetic energy just after the bounce is less than just before the bounce. In what form does this lost energy end up? A. Elastic potential energy B. Gravitational potential energy C. Thermal energy D. Rotational kinetic energy

Problem 78PP Tennis Ball Testing A tennis ball bouncing on a hard surface compresses and then rebounds. The details of the rebound are specified in tennis regulations. Tennis balls, to be acceptable for tournament play, must have a mass of 57.5 g. When dropped from a height of 2.5 m onto a concrete surface, a ball must rebound to a height of 1.4 m. During impact, the ball compresses by approximately 6 mm. By approximately what percent does the kinetic energy decrease? A. 35% B. 45% C. 55% D. 65%

Problem 79PP Tennis Ball Testing A tennis ball bouncing on a hard surface compresses and then rebounds. The details of the rebound are specified in tennis regulations. Tennis balls, to be acceptable for tournament play, must have a mass of 57.5 g. When dropped from a height of 2.5 m onto a concrete surface, a ball must rebound to a height of 1.4 m. During impact, the ball compresses by approximately 6 mm. When a tennis ball bounces from a racket, the ball loses approximately 30% of its kinetic energy to thermal energy. A ball that hits a racket at a speed of 10 m/s will rebound with approximately what speed? A. 8.5 m/s B. 7.0 m/s C. 4.5 m/s D. 3.0 m/s

Problem 80PP Work and Power in Cycling When you ride a bicycle at constant speed, almost all of the energy you expend goes into the work you do against the drag force of the air. In this problem, assume that all of the energy expended goes into working against drag. As we saw in Section 5.6, the drag force on an object is approximately proportional to the square of its speed with respect to the air. For this problem, assume that exactly and that the air is motionless with respect to the ground unless noted otherwise. Suppose a cyclist and her bicycle have a combined mass of 60 kg and she is cycling along at a speed of 5 m/s. If the drag force on the cyclist is 10 N, how much energy does she use in cycling 1 km? A. 6 kJ B. 10 kJ C. 50 Kj D. 100 kJ

Problem 81PP Work and Power in Cycling When you ride a bicycle at constant speed, almost all of the energy you expend goes into the work you do against the drag force of the air. In this problem, assume that all of the energy expended goes into working against drag. As we saw in Section 5.6, the drag force on an object is approximately proportional to the square of its speed with respect to the air. For this problem, assume that exactly and that the air is motionless with respect to the ground unless noted otherwise. Suppose a cyclist and her bicycle have a combined mass of 60 kg and she is cycling along at a speed of 5 m/s. Under these conditions, how much power does she expend as she cycles? A. 10 W B. 50 W C. 100 W D. 200 W

Problem 82PP Work and Power in Cycling When you ride a bicycle at constant speed, almost all of the energy you expend goes into the work you do against the drag force of the air. In this problem, assume that all of the energy expended goes into working against drag. As we saw in Section 5.6, the drag force on an object is approximately proportional to the square of its speed with respect to the air. For this problem, assume that exactly and that the air is motionless with respect to the ground unless noted otherwise. Suppose a cyclist and her bicycle have a combined mass of 60 kg and she is cycling along at a speed of 5 m/s. If she doubles her speed to 10 m/s, how much energy does she use in cycling 1 km? A. 20 kJ B. 40 kJ C. 200 kJ D. 400 kJ

Problem 83PP Work and Power in Cycling When you ride a bicycle at constant speed, almost all of the energy you expend goes into the work you do against the drag force of the air. In this problem, assume that all of the energy expended goes into working against drag. As we saw in Section 5.6, the drag force on an object is approximately proportional to the square of its speed with respect to the air. For this problem, assume that exactly and that the air is motionless with respect to the ground unless noted otherwise. Suppose a cyclist and her bicycle have a combined mass of 60 kg and she is cycling along at a speed of 5 m/s. How much power does she expend when cycling at that speed? A. 100 W B. 200 W C. 400 W D. 1000 W

Problem 84PP Work and Power in Cycling When you ride a bicycle at constant speed, almost all of the energy you expend goes into the work you do against the drag force of the air. In this problem, assume that all of the energy expended goes into working against drag. As we saw in Section 5.6, the drag force on an object is approximately proportional to the square of its speed with respect to the air. For this problem, assume that exactly and that the air is motionless with respect to the ground unless noted otherwise. Suppose a cyclist and her bicycle have a combined mass of 60 kg and she is cycling along at a speed of 5 m/s. Upon reducing her speed back down to 5 m/s, she hits a headwind of 5 m/s. How much power is she expending now? A. 100 W B. 200 W C. 500 W D. 1000 W