34. Place a small rubber ball on top of a basketball or soccer ball and then drop them together. If vertical alignment nicely remains as they fall to the floor, you’ll see that the small ball bounces unusually high. Can you reconcile this with energy conservation?
The only logical reasoning I can come up with for it to bounce unusually high is that when you place the rubber ball on top of the basketball and then it hits the floor and the basketball bounces upward and hits the rubber ball making it bounce higher. This happens because it’s already higher in the air than usual and it uses the energy from the basketball which is an object that is already going in motion upward instead of hitting just the floor that doesn’t have movement at all.
42. Calculate the work done in lifting a 100-N block of ice a vertical distance of 5 m.
Gravitational potential energy = mass X acceleration
Due to gravity X height; PE = mgh
Potential energy = mgh = (100N) (5m) = 500 Nm = 500 joules
48. Show that 90 J of work is needed to increase the speed of a 20-kg cart by 3 m/s.
Power = work done w
Time interval t
64. Show that 480 W of power is expended by a weightlifter when lifting a 60-kg barbell a vertical distance of 1.2 m in a time interval of 1.5 s.
76. In grandpa’s time automobiles were previously manufactured to be as rigid as possible, whereas autos are now designed to crumple upon impact. Why?
82. If you throw a ball horizontally while standing on a skateboard, you roll backward with a momentum that matches that of the ball. Will you roll backward if you hold onto the ball while going through the motions of throwing it? Explain in terms of momentum conservation.
94. When a cannon with a longer barrel is fired, the force of expanding gases acts on the cannonball for a longer distance. What effect does this have on the velocity of the emerging cannonball? (Do you see why long-range cannons have such long barrels?)
116. Suppose that three astronauts outside a spaceship decide to play catch. All three astronauts have the same mass and are equally strong. The first astronaut throws the second astronaut toward the third one and the game begins. Describe the motion of the astronauts as the game proceeds. How long will the game last?
120. Why bother using a machine if it cannot multiply work input to achieve greater work output?
124. To combat wasteful habits, we often speak of “conserving energy,” by which we mean turning off lights, heating or cooling systems, and hot water when not being used. In this chapter, we also speak of “energy conservation.” Distinguish between these two usages.
126. If an automobile had a 100%-efficient engine, transferring all of the fuel’s energy to work, would the engine be warm to your touch? Would its exhaust heat the surrounding air? Would it make any noise? Would it vibrate? Would any of its fuel go unused? Discuss.
62. What would be the path of the Moon if somehow all gravitational forces on it vanished to zero?
68. Why do the passengers in high-altitude jet planes feel the sensation of weight while passengers in the International Space Station do not?
72. If you were in a freely falling elevator and you dropped a pencil, it would hover in front of you. Is there a force of gravity acting on the pencil? Defend your answer.
74. A heavy crate accidentally falls from a high-flying airplane just as it flies directly above a shiny red Porsche smartly parked in a car lot. Relative to the Porsche, where does the crate crash?
78. When you jump upward, your hang time is the time your feet are off the ground. Does hang time depend on your vertical component of velocity when you jump, your horizontal component of velocity, or both? Defend your answer.
94. Newton tells us that gravitational force acts on all bodies in proportion to their masses. Why, then, doesn’t a heavy body fall faster than a light body?
96. Two facts: A freely falling object at Earth’s surface drops vertically 5 m in 1 s. Earth’s curvature “drops” 5 m for each 8-km tangent. Discuss how these two facts relate to the 8-km/s speed necessary to orbit Earth.
98. A friend says that astronauts inside the International Space Station are weightless because they’re beyond the pull of Earth’s gravity. Correct your friend’s ignorance.
110. A park ranger wants to shoot a monkey hanging from a branch of a tree with a tranquilizing dart. The ranger aims directly at the monkey, not realizing that the dart will follow a parabolic path and thus will fall below the monkey. The monkey, however, sees the dart leave the gun and lets go of the branch to avoid being hit. Will the monkey be hit anyway? Does the velocity of the dart affect your answer, assuming that it is great enough to travel the horizontal distance to the tree before hitting the ground? Defend your answer.