13 A weight lifter raises a 100-kg barbell to a height of 2.2 m. What isthe barbells

What is a conservation law? What is the basic approach taken when using a conservation law?

Why is the alternate form of Newtons second law of motion given in this chapter the more general form?

Could the linear momentum of a turtle be greater than the linear momentum of a horse? Explain why or why not.

An astronaut working with many tools some distance away from a spacecraft is stranded when the maneuvering unit malfunctions. How can the astronaut return to the spacecraft by sacrificing some of the tools?

For what type of interaction between bodies is the law of conser- vation of linear momentum most useful?

For what type of interaction between bodies is the law of conser- vation of linear momentum most useful?

If we know that a force of 5 N acts on an object while it moves 2 meters, can we calculate how much work was done with no other information? Explain.

During a head-on collision between two automobiles, the occupants are decelerated rapidly. Use the idea of work to explain why an air bag that quickly inflates in front of an occupant reduces the likeli- hood of injury.

When climbing a flight of stairs, do you do work on the stairs? Do the stairs do work on you?

People and machines around us do work all the time. But is it possible for things such as magnets and Earth to do work? Explain.

Identify as many different ways as you can for giving energy to a basketball.

Identify as many different forms of energy as you can that are around you at this moment.

When you throw a ball, the work you do to accelerate it equals the kinetic energy the ball gains. If you do twice as much work when throwing the ball, does it go twice as fast? Explain.

Describe the motion of an object that possesses kinetic energy yet undergoes no net displacement

How can the gravitational potential energy of something be neg- ative?

What is elastic potential energy? Identify as many things that currently surround you that possesses elastic potential energy.

Identify the energy conversions taking place in each of the following situations. Name all of the relevant forms of energy that are involved. (a) A camper rubbing two sticks together to start a fire. (b) An arrow shot straight upward, from the moment the bowstring is released by the archer to the moment when the arrow reaches its highest point. (c) A nail being pounded into a board, from the moment a carpen- ter starts to swing a hammer to the moment when the nail has been driven some distance into the wood by the blow. (d) A meteoroid entering Earths atmosphere.

Solar-powered spotlights have batteries that are charged by solar cells during the day and then operate lights at night. Describe the energy conversions in this entire process, starting with the Suns nuclear energy and ending with the light from the spotlight being absorbed by the surroundings. Name all of the forms of energy that are involved.

Truck drivers approaching a steep hill that they must climb often increase their speed. What good does this do, if any?

If you hold a ball at eye level and drop it, it will bounce back, but not to its original height. Identify the energy conversions that take place during the process, and explain why the ball does not reach its original release level.

A ball is thrown straight upward from the surface of the Moon. Is the maximum height it reaches less than, equal to, or greater than the maximum height reached by a ball thrown upward on Earth with the same initial speed? (Ignore air resistance in both cases.) Explain.

Many sports involve collisions between thingssuch as balls and racketsand between peopleas in football or hockey. Character- ize the various sports collisions as elastic or inelastic.

Carts A and B stick together whenever they collide. The mass of A is twice the mass of B. How could you roll the carts toward each other in such a way that they would be stopped after the collision? (Assume there is no friction.)

Is it possible for one object to gain mechanical energy from another without touching it? Explain.

How are the physical concepts power and speed similar?

Two cranes are lifting identical steel beams at the same time. One crane is putting out twice as much power as the other. Assuming friction is negligible, what can you conclude is happening to explain this difference?

A person runs up several flights of stairs and is exhausted at the top. Later, the same person walks up the same stairs and does not feel as tired. Why is this? Ignoring air resistance, does it take more work or energy to run up the stairs than to walk up?

How can a satellites speed decrease without its angular momen- tum changing?

Why do divers executing midair somersaults pull their legs in against their bodies?

It is possible for a body to be both spinning and moving in a circle in such a way that its total angular momentum is zero. Describe how this can be.

A sprinter with a mass of 65 kg reaches a speed of 10 m/s during a race. Find the sprinters linear momentum.

2. Which has the larger linear momentum: a 2,000-kg houseboat going 5 m/s or a 600-kg speedboat going 20 m/s?

3. In Section 2.4, we computed the force needed to accelerate a 1,000-kg car from 0 to 27 m/s in 10 s. Compute the force using the alternate form of Newtons second law. The change in momentum is the cars momentum when going 27 m/s minus its momentum when going 0 m/s.

.4. A runner with a mass of 80 kg accelerates from 0 to 9 m/s in 3 s. Find the net force on the runner using the alternate form of New- tons second law. hat is their speed? 8. Two persons on ice skates stand face to face and then push each other away ( Figure 3.46). Their masses are 60 and 90 kg. Find the ratio of their speeds immediately afterward. Which person has the higher speed?

5. A pitcher throws a 0.5-kg ball of clay at a 6-kg block of wood. The clay sticks to the wood on impact, and their joint velocity afterward is 3 m/s. What was the original speed of the clay?

6. A 3,000-kg truck runs into the rear of a 1,000-kg car that was sta- tionary. The truck and car are locked together after the collision and

A sprinter with a mass of 65 kg reaches a speed of 10 m/s during a race. Find the sprinters linear momentum. 2. Which has the larger linear momentum: a 2,000-kg houseboat going 5 m/s or a 600-kg speedboat going 20 m/s? 3. In Section 2.4, we computed the force needed to accelerate a 1,000-kg car from 0 to 27 m/s in 10 s. Compute the force using the alternate form of Newtons second law. The change in momentum is the cars momentum when going 27 m/s minus its momentum when going 0 m/s. 4. A runner with a mass of 80 kg accelerates from 0 to 9 m/s in 3 s. Find the net force on the runner using the alternate form of New- tons second law. 5. A pitcher throws a 0.5-kg ball of clay at a 6-kg block of wood. The clay sticks to the wood on impact, and their joint velocity afterward is 3 m/s. What was the original speed of the clay? 6. A 3,000-kg truck runs into the rear of a 1,000-kg car that was sta- tionary. The truck and car are locked together after the collision and move with speed 9 m/s. What was the speed of the truck before the collision? 7. A 50-kg boy on roller skates moves with a speed of 5 m/s. He runs into a 40-kg girl on skates. Assuming they cling together after the collision, what is their speed? 8. Two persons on ice skates stand face to face and then push each other away ( Figure 3.46). Their masses are 60 and 90 kg. Find the ratio of their speeds immediately afterward. Which person has the higher speed?

8. Two persons on ice skates stand face to face and then push each other away ( Figure 3.46). Their masses are 60 and 90 kg. Find the ratio of their speeds immediately afterward. Which person has the higher speed?

A loaded gun is dropped on a frozen lake. The gun fires, with the bullet going horizontally in one direction and the gun sliding on the ice in the other direction. The bullets mass is 0.02 kg, and its speed is 300 m/s. If the guns mass is 1.2 kg, what is its speed?

10. A running back with a mass of 80 kg and a speed of 8 m/s collides with, and is held by, a 120-kg defensive tackle going in the opposite direction. How fast must the tackle be going before the collision for their speed afterward to be zero?

11. A motorist runs out of gas on a level road 200 m from a gas station. The driver pushes the 1,200-kg car to the gas station. If a 150-N force is required to keep the car moving, how much work does the driver do?

12. In Figure 3.10, the rock weighs 100 lb and is lifted 1 ft by the lever. (a) How much work is done? (b) The other end of the lever is pushed down 3 ft while lifting the rock. What force had to act on that end?

13 A weight lifter raises a 100-kg barbell to a height of 2.2 m. What is the barbells potential energy?

14. A microwave antenna with a mass of 80 kg sits atop a tower that is 50 m tall. What is the antennas potential energy?

15. A personal watercraft and rider have a combined mass of 400 kg. f 26.7 m above the ocean. Ignoring air resistance, how fast are the divers going when they hit the water?

16. As it orbits Earth, the 11,000-kg Hubble Space Telescope travels at a speed of 7,900 m/s and is 560,000 m above Earths surface. (a) What is its kinetic energy? (b) What is its potential energy?

17. The kinetic energy of a motorcycle and rider is 60,000 J. If their total mass is 300 kg, what is their speed?

18. In compressing the spring in a toy dart gun, 0.5 J of work is done. When the gun is fired, the spring gives its potential energy to a dart with a mass of 0.02 kg. (a) What is the darts kinetic energy as it leaves the gun? (b) What is the darts speed? (b) How fast will the payload be traveling when it reaches the bot- tom of the shaft? Convert your answer to mph for a compari- son to highway speeds.

19. A worker at the top of a 629-m-tall television transmitting tower in North Dakota accidentally drops a heavy tool. If air resistance is negligible, how fast is the tool going just before it hits the ground?

20. A student drops a water balloon out of a dorm window 12 m above the ground. What is its speed when it hits the ground?

21. A child on a swing has a speed of 7.7 m/s at the low point of the arc ( Figure 3.47). How high will the swing be at the high point? of the shaft? Convert your answer to mph for a compari-

22. The cliff divers at Acapulco, Mexico, jump off a cliff 26.7 m above the ocean. Ignoring air resistance, how fast are the divers going when they hit the water?

23. At NASAs Zero Gravity Research Facility in Cleveland, Ohio, experi- mental payloads fall freely from rest in an evacuated vertical shaft through a distance of 132 m. (a) If a particular payload has a mass of 45 kg, what is its potential energy relative to the bottom of the shaft? (b) How fast will the payload be traveling when it reaches the bot- tom of the shaft? Convert your answer to mph for a compari- son to highway speeds.

24. The fastest that a human has run is about 12 m/s. (a) If a pole vaulter could run this fast and convert all of her kinetic energy into gravitational potential energy, how high would she go? (b) Compare this height with the world record in the pole vault.

25. A bicycle and rider going 10 m/s approach a hill. Their total mass is 80 kg. (a) What is their kinetic energy? (b) If the rider coasts up the hill without pedaling, how high above its starting level will the bicycle be when it finally rolls to a stop?

26. In January 2003, an 18-year-old student gained a bit of fame for survivingwith only minor injuriesa remarkable traffic accident. The vehicle he was driving was clipped by another one, left the road, and rolled several times. He was thrown upward from the vehicle (he wasnt wearing a seat belt) and ended up dangling from an overhead telephone cable and a ground wire about 8 meters above the ground. Rescuers got him down after 20 minutes. It is estimated that he reached a maximum height of about 10 meters. (a) Estimate the drivers vertical speed when he was thrown from the vehicle. (b) If he had not landed in the wires, how fast would he have been going when he hit the ground?

27. The ceiling of an arena is 20 m above the floor. What is the mini- mum speed that a thrown ball would need to just reach the ceiling?

28. Compute how much kinetic energy was lost in the inelastic colli- sion in Problem 6.

29. Compute how much kinetic energy was lost in the inelastic colli- sion in Problem 7.

30. A 1,000-W motor powers a hoist used to lift cars at a service station. (a) How much time would it take to raise a 1,500-kg car 2 m? (b) If the original motor is replaced with one rated at 2,000 W, how long would it take to complete this task?

31. How long does it take a worker producing 200 W of power to do 10,000 J of work?

32. An elevator is able to raise 1,000 kg to a height of 40 m in 15 s. (a) How much work does the elevator do? (b) What is the elevators power output?

33. A particular hydraulic pile driver uses a ram with a mass of 1040 kg. If the maximum pile energy is 11,780 J, how high must the ram be raised to achieve this value? Assuming it takes 0.62 s for the pile dri- vers winch motor to raise the ram at a constant speed to this height, what is the power output by the motor in completing this task? Express your answer in both watts and horsepower.

34. A compact car can climb a hill in 10 s. The top of the hill is 30 m higher than the bottom, and the cars mass is 1,000 kg. What is the power output of the car?

35. In the annual Empire State Building race, contestants run up 1,575 steps to a height of 1,050 ft. In 2003, Australian Paul Crake completed the race in a record time of 9 min and 33 s. Mr. Crake weighed 143 lb (65 kg). (a) How much work did Mr. Crake do in reaching the top of the building? (b) What was his average power output (in ft-lb/s and in hp)?

36. It takes 100 minutes for a middle-aged physics professor to ride his bicycle up the road to Alpe dHuez in France. The vertical height of the climb is 1,120 m, and the combined mass of the rider and bicy- cle is 85 kg. What is the bicyclists average power output?

37. Two small 0.25-kg masses are attached to opposite ends of a very lightweight rigid rod 0.5 m long. The system is spinning in a hori- zontal plane around a vertical axis perpendicular to the rod located halfway between the masses. Each mass is moving in a circle of radius 0.25 m at a speed of 0.75 m/s. What is the total angular momentum of this system?

Rank the following three collisions in terms of the extent of damage that the car would experience. Explain your reasons for ranking the collisions as you did. (a) A car going 10 m/s striking an identical car that was stationary on level ground. (b) A car going 10 m/s running into an immovable concrete wall. (c) A head-on collision between identical cars, both going 10 m/s.

A bullet with a mass of 0.01 kg is fired horizontally into a block of wood hanging on a string. The bullet sticks in the wood and causes it to swing upward to a height of 0.1 m. If the mass of the wood block is 2 kg, what was the initial speed of the bullet?

3. In a head-on, inelastic collision, a 4,000-kg truck going 10 m/s east strikes a 1,000-kg car going 20 m/s west. (a) What is the speed and direction of the wreckage? (b) How much kinetic energy was lost in the collision?

A person on a swing moves so that the chain is horizontal at the turning points ( Figure 3.48). Show that the centripetal accelera- tion of the person at the low point of the arc is exactly 2 g, regard- less of the length of the chain. This means that the force on the chains at the low point is equal to three times the persons weight. (Hint: The vertical distance between the turning point and the low point equals the length of the chain.)

5. Assume that as a car brakes to a stop it undergoes a constant accel- eration (deceleration). Explain why the stopping distance becomes four times as large if the initial speed is doubled.

The shot used in the shot-put event is a metal ball with a mass of 7.3 kg. When thrown in Olympic competition, it is accelerated to a speed of about 14 m/s. As an approximation, lets say that the athlete exerts a constant force on the shot while throwing it and that it moves a distance of 3 m while accelerating. (a) What is the shots kinetic energy? (b) Compute the force that acts on the shot. (c) It takes about 0.5 s to accelerate the shot. Compute the power required. Convert your answer to horsepower.

At the point in its orbit when it is closest to the Sun, Halleys Comet moves with a speed of 54,500 m/s ( Figure 3.49). When it is at its most distant point, the separation between it and the Sun is about 60 times larger than when it is at its closest point. What is the speed of the comet at the distant point?