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"Answer This" Questions

Chapter 10

10-A. When is work being done?

In which of the following situations is work being done according to the physics definition of work?
a) A parachutist is in free fall after jumping out of an airplane. Does the gravitational force of the Earth do work on the parachutist?
b) You lift a heavy box from the floor until
your arms are extended and the box is above your head. Did you do work on the box?
c) You now hold the same heavy box over your head with your hands and walk horizontally for 10 meters. Did you do work on the box during your walk?

 

Answer:

a) The parachutist ultimately falls at constant terminal velocity after an initial acceleration. Earth is exerting the force of gravity on the parachutist over the distance he moves, so that gravity is definitely doing work. After the parachutist reaches terminal velocity the air resistance matches the force of gravity (but in the opposite direction) and his potential energy is being converted via the air resistance into thermal energy of the air rather than additional kinetic energy.

b) Your lifting exerted a force that opposed the force of gravity. The force acted through a distance and so you did work on the box.

c) Because the force exerted by your arms was in the vertical direction, but your motion was horizontal, the force did not act through any distance (it was not in the direction of your motion), so that no work was done.

 

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10-A. Energy of a diver.

A diver comes off a diving board. What type of energy does she have at the highest point in her dive?
a) kinetic energy only.
b) potential energy only, even if she is spinning at the top of her dive.
c) potential energy only, but only if she is not spinning at the top of her dive.
d) both kinetic and potential energy; it doesn’t matter whether she is spinning at the top
or not.
e) None of the above.

Answer:

Either c) or d) depending on how you perceived the diver's flight. See the two possible trajectories in the figure below. In the A trajectory the diver goes almost straight up before she starts down. If we assume she is not spinning at the top, then she has no velocity—she has stopped momentarily and she would have only potential energy. If she were spinning, she would have both kinetic energy (of spin motion) and potential energy at the top of trajectory A; the answer for A must be c). Of course at the top of A, she is accelerating and gravity will soon convert her potential energy into kinetic energy.

In trajectory B, she is still going forward at the highest point of her dive because she initially jumped forward as well as up. At that point she has both kinetic energy and potential energy. If she were spinning at that point, she would have even more kinetic energy. In this case the answer would be d).

 

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10-A. Types of energy.

Which of the two objects in the following comparisons has more energy, and what type of energy is it?
a) a large truck parked on a level street or a fluttering butterfly
b) a hot air balloon with three passengers on board descending at 5 feet per second, or a baseball thrown at 50 miles per hour
c) a 2-pound flower vase on top of a table, or a 50-pound box resting on the floor

Answer:

a) The butterfly. The fluttering butterfly has kinetic energy, as well as potential energy due to its height off the ground. The parked truck has neither kinetic nor potential enery. (If the truck were parked on a hill it would have potential energy.)

b) The balloon and passengers. Both objects have kinetic energy. One can compare the kinetic energy. A baseball weighs about 1/3 pound and has mass we will denote as m; the balloon and passengers have a mass Nm, where N is likely more than 2000. (A person weighing 150 lbs would have mass about 150/(1/3)m = 450m.) The kinetic energy of the balloon and crew is (1/2) Nm (5ft/s)2 and that of the baseball is (1/2) m(50ft/s)2. The ratio of the first to the second is N(5/50)2 = N/100. We see that this is much larger than 1 so that the balloon et al has more kinetic energy because of it large mass. The balloon and crew also have potential energy in an amount that depends on height above the ground. The baseball presumably also has some potential energy, which is likely much less than that of the balloon.

c) The vase. The vase on the table has some potential energy. The box on the floor, while more massive, has no height and so no potential energy.

 

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10-G. Intensity and amplitude

A musician playing a bass drum hits the drum softly, generating a pressure wave of amplitude A. A little later, the musician hits the drum very hard, generating a pressure wave having amplitude 2.5A. How much louder would the second sound be compared to the first?


Answer:

c) 6.25. Loudness depends on amplitude squared. Thus the second sound is (2.5)2 = 6.25 louder than the first.

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