Ball 1, with a mass of 100 g and traveling at 10 mis, coll ideshead-on with ball 2

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

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.

For Questions 3 through I 0, give a specific example of a system with the energy transformation shown. ln these questions, W is the work done on the system, and K, U, and ,h 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

For Questions 3 through I 0, give a specific example of a system with the energy transformation shown. ln these questions, W is the work done on the system, and K, U, and ,h 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

For Questions 3 through I 0, give a specific example of a system with the energy transformation shown. ln these questions, W is the work done on the system, and K, U, and ,h 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

For Questions 3 through I 0, give a specific example of a system with the energy transformation shown. ln these questions, W is the work done on the system, and K, U, and ,h 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

For Questions 3 through I 0, give a specific example of a system with the energy transformation shown. ln these questions, W is the work done on the system, and K, U, and ,h 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

For Questions 3 through I 0, give a specific example of a system with the energy transformation shown. ln these questions, W is the work done on the system, and K, U, and ,h 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 -6~

For Questions 3 through I 0, give a specific example of a system with the energy transformation shown. ln these questions, W is the work done on the system, and K, U, and ,h 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 - 6~

For Questions 3 through I 0, give a specific example of a system with the energy transformation shown. ln these questions, W is the work done on the system, and K, U, and ,h 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-6~

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?

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 duri ng one revolution? Explain.

Particle A has less mass than particle B. Both are pushed forward across a frictionless surface by equal forces for I 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.

Puck B has twice the mass of puck A. Starting from rest, both pucks are pulled the same distance across fri ctionless ice by strings with the same tension. a. Compare the final kinetic energies of pucks A and B. b. Compare the final speeds of pucks A and B.

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.

You drop two balls from a tower, one of mass m and the other of mass 2111. Just before they hit the ground, which ball, if either, has the larger kinetic energy? Explain.

A roller coaster car rolls down a frictionless track, reaching speed v at the bottom. a. lf 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 strai ght or not? Explain.

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.

Sandy and Chris stand on the edge of a cl iff 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.

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 Q I0.20. Both blocks are released simultaneously. The ropes do not slip. Which block hits the ground first? Or is it a tie? Explain.

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

Jason slides a large crate down a ramp from a truck to the ground. To control the crate and keep it sl iding at constant speed, Jason backs down the ramp in front of the crate whi le pushing upward on it. During its trip to the bottom, is the thermal energy c reated in the ramp and the crate greater than, less than, or equal to the crate's loss of gravitational pote ntial energy? Explain.

A roller coaster starts from rest at its highest point and then descends on its (fri ctionless) track. Its speed is 30 m/s when it reaches ground leve l. What was its speed when its height was half that of its starting point? A. 11 mis B. 15 mis C. 21 mis D. 25 mis

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 can-y 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.

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. IOOW B. 200W C. 300W D. 400W

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 2v? A. 2.0 cm J3. 2.8 cm C. 4.0 cm D. 5.6 cm E. 8.0 cm

A block slides down a smooth ramp, starting from re st 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 vl2? A. hl4 B. hl2 C. 3hl4 D. 2h

A wrecking ba ll is suspended from a 5.0 -m-long cable that ma kes a 30 angle with the vertical. T he ba ll is released and swi ngs down. What is the ba ll's speed at the lowest point? A. 7.7 mis B. 4.4 mis C. 3.6 mis D. 3.1 mis

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?

What minimum speed does a 100 g puck need to make it to the top of a fri ctionless ramp that is 3.0 m long and inclined at 20?

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.)

A 1500 kg car is approaching the hill shown in Figure P l 0.32 at 10 mis 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?

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

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 Nim. If the spring stretches 30 m to stop the plane, what was the plane's landing speed?

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 mis when it hits the Frisbee. If you release the rock 2.0 m above the ground, with what minimum speed must you throw it?

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 mis. By how much has thermal energy increased during his slide?

A 20 kg chi ld sl ides down a 3.0-m-high playground slide. She starts from rest, and her speed at the bottom is 2.0 mis. 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?

A hockey puck is given an initial speed of 5.0 mis. 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.

In the winter activity of tubing, riders slide down snowcovered slopes while sitting on large inflated rubber tubes. To get to the top of the slope, a tider and his tube, with a total mass of 80 kg, are pulled at a constant speed by a tow rope that maintains a constant tension of 340 N. How much thermal energy is created in the slope and the tube during the ascent of a 30-m-high, 120-m-long slope?

A cycli st is coasting at 12 mis when she starts down a 450-m-long slope that is 30 m high. The cyclist and her bicycle have a combined mass of70 kg. A steady 12 N drag force due to air resistance acts on her as she coasts all the way to the bottom. What is her speed at the bottom of the slope?

A 50 g marble moving at 2.0 mis 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.

Ball 1, with a mass of 100 g and traveling at 10 mis, coll ides 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?

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?

Two balls undergo a perfectly elastic head-on collision, with one ball initially at rest. If the incoming ball has a speed of 200 mis, 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?

a. How much work must you do to push a I 0 kg block of steel across a steel table at a steady speed of 1.0 mis for 3.0 s? The coefficient of kinetic frict.ion for steel on steel is 0.60. b. What is your power output while doing so?

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?

A 1000 kg sports-car accelerates from 0 to 30 mis in 10 s. What is the average power of the engine?

In just 0.30 s, you compress a spring (spring constant 5000 Nim), which is initially at its equil ibrium length, by 4.0 cm. What is your average power output?

An elite Tour de France cyclist can maintain an output power of 450 W during a sustained climb. At this output power, how long would it take an 85 kg cyclist (including the mass of his bike) to climb the famed 11 00-m-high Alpe d'Huez mountain stage?

A 7 10 kg car drives at a constant speed of 23 mis. 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?

. Ill An e levator weighing 2500 N ascends at a constant speed of 8.0 mis. How much power must the motor supply to do this?

How much work does Scott do to push a 80 kg sofa 2.0 m across the floor at a constant speed? The coeffi cient of kinetic friction between the sofa and the floor is 0.23.

A 550 kg elevator accelerates upward at 1.2 mls2 for the first 15 m of its motion. How much work is done during this part of its motion by the cable that lifts the elevator?

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 mis. 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!:;. Ug in the gravitational potent.ial energy of the system? d. What is the change t:;.E,h in the thermal energy of the system?

A 55 kg skateboarder wants to just make it to the upper edge of a "half-pipe" with a v; 3.0 m radius of 3.0 m, as shown in Figure Pl0.55. What speed v; 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 v; is needed to reach the upper edge?

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 iinitial kinetic energy has been converted to potential energy?

You are driving your 1500 kg car at 20 mis down a hill with a 5.0 slope when a deer suddenly jumps out onto the roadway. You slam on your brakes, skidding to a stop. How far do you skid before stopping ifthe kinetic friction force between your tires and the road is 1.2 X 104 N? Solve this problem using conservation of energy.

A 20 kg child is on a swing that hangs from 3.0-m-long chains, as shown in Figure Pl0.58. What is her speed v; at the bottom of the arc if she swings out to a 45 angle before reversing direction?

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 P I0.59. Being clever, you choose a ramp with no friction. b. How much force Fis 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?

A cannon ti lted up at a 30 angle fires a cannon ball at 80 mis from atop a 10-m-high fortress wall. What is the ball 's impact speed on the ground below? Ignore air resistance.

The sledder shown in Figure PI0.61 starts from the top of a fri ctionless hill and slides down into the valley. What in itial speed v; does the sledder need to j ust make it over the next hill?

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?

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 Nim. When the ice cube is released, what distance will it travel up the slope before reversing direction?

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.

In an amusement pai:k water slide, people slide down an INT 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?

The 5.0-m-long rope in Figure P I 0.66 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. Gi ven 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?

You have been asked to design a "ballistic spring system" to measure the speed of bullets. A bullet of mass mis fired into a block of mass M. The block, with the embedded bullet, then slides across a fri ctionless 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 dis measured. a. Find an expression for the bullet's initial speed v8 in terms of 111 , 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 fri ctionless surface. What quantity is conserved in this coll ision? b. What was the speed of a 5.0 g bullet ifthe block's mass is 2.0 kg and ifthe 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?

A new event, shown in Figure P I0.68, has been proposed for the Winter Olympics. An athlete will sprint I 00 m, sta1ting from rest, then leap onto a 20 kg bobsled. The person and bobsled will then slide down a 50-m-long ice-{;overed ramp, sloped at 20, and into a spring with a carefully calibrated spring constant of2000 N/m. The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is40 kg, has been training for this event. She can reach a maximum speed of 12 mis in the I 00 m dash. a. How far will Li sa compress the spring? b. The Olympic committee has very exact specifications about the shape and angle of the ramp. ls this necessary? lf the committee asks your opinion, what factors about the ramp wi ll you tell them are important?

Boxes A and Bin Figure PI0.69 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.

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.

20 g ball is fired horizontally with initial speed v, toward a I 00 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 I 00 g ball swings out to a maximum angle Omax = 50. What was v,?

Two coupled boxcars are rolling along at 2.5 mis 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?

A fi sh scale, consjsting of a spring with spring constant k = 200 Nim, is hung vertically from the ceiling. A 5.0 kg fish is attached to the end of the unstretched spring and then released. The fi sh 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?

A 70 kg human sprinter can accelerate from rest to I 0 m/s in 3.0 s. During the same time interval, a 30 kg greyhound can accelerate from rest to 20 mis. Compute (a) the change in kinetic energy and (b) the average power output for each.

A 50 g ball of clay traveling at 6.5 m/s 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?

A package of mass m is released from rest at a warehouse INT loading dock and slides down a 3.0-m-high fri c tionless c hute to a waiting truck. Unfortunate ly, the truck driver went on a break without having removed the previous package, of mass 2111, from the bottom of the chute as shown in Figure PI0.76. a. Suppose the package s stick together. What is the ir common speed after the collision? b. Suppose the collision between the packages is perfectly e lastic. To what height does the package of mass m rebound?

A 50 kg sprinter, sta1ting from rest, runs 50 m in 7.0 sat conINT stant 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 js the sprinter's average power output during the final 2.0 s?

Bob can throw a 500 g rock with a speed of 30 mis. During the time the rock is in his hand, his hand moves forward by 1.0 m. a. How much force, assumed to be constant, does Bob apply to the rock? b. How much work does Bob do ou the rock?

The mass of an elevator and its occupants is 1200 kg. The electric motor that li fts the elevator can provide a maximum power of 15 kW. What is the maximum constant speed at which th is motor can li ft the elevator?

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 1.3 x I 04 N/m2 . 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 appl ies force to the blood. Pressure is just force/area, so we can write work = pressure X area x distance. But area x distance is just the blood volume passing through the heart.

How fast is the ball moving when it hits the concrete surface? (Ignore air resistance.} A. 5 mis B. 7 mis C. 25 m/s D. 50 mis

If the ball accelerates uniformly when it hits the floor, what is its approximate acceleration as it comes to rest before rebounding? A. I 000 m/s2 B. 2000 m/s2 C. 3000 mls2 D. 4000 mls2

The ball's kinetic energy just afterthe 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

By approximately what percent does the kjnetic energy decrease? A. 35% B. 45% C. 55% D. 65%

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 mis will rebound with approximately what speed? A. 8.5 mis B. 7.0 mis C. 4.5 mis D. 3.0 mis

If the drag force on the cyclist is I 0 N, how much energy does she use in cycling I km? A. 6kJ B. IOkJ c. 50 kJ D. 100 kJ

Under these conditions, how much power does she expend as she cycles? A. IOW B. SOW C. IOOW D. 200W

If she doubles her speed to IO mis, how much energy does she use in cycling I km? A. 20 kJ B. 40 kJ c. 200 kJ D. 400 kJ

How much power does she expend when cycling at that speed? A. IOOW B. 200W C. 400W D. IOOOW

Upon reducing her speed back down to 5 mis, she hi ts a headwind of 5 mis. How much power is she expending now? A. JOO W B. 200 W C. 500 W D. 1000 W