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Chapter 7: Q6 CQ (page 258)
When solving for speed in Example 7.4, we kept only the positive root. Why?
We keep only the positive root of the speed because speed cannot be negative.
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In a downhill ski race, surprisingly, little advantage is gained by getting a running start. (This is because the initial kinetic energy is small compared with the gain in gravitational potential energy on even small hills.) To demonstrate this, find the final speed and the time taken for a skier who skies 70.0 m along a 30掳 slope neglecting friction:
(a) Starting from rest.
(b) Starting with an initial speed of 2.50 m/s.
(c) Does the answer surprise you? Discuss why it is still advantageous to get a running start in very competitive events.
Give an example of a situation in which there is a force and a displacement, but the force does no work. Explain why it does no work.
(a) Calculate the force the woman in Figure 7.46 exerts to do a push-up at constant speed, taking all data to be known to three digits.
(b) How much work does she do if her center of mass rises 0.240 m?
(c) What is her useful power output if she does 25 push-ups in 1 min? (Should work done lowering her body be included? See the discussion of useful work in Work, Energy, and Power in Humans.
Figure 7.46 Forces involved in doing push-ups. The woman鈥檚 weight acts as a force exerted downward on her center of gravity (CG).
Boxing gloves are padded to lessen the force of a blow.
(a) Calculate the force exerted by a boxing glove on an opponent鈥檚 face, if the glove and face compress 7.50 cm during a blow in which the 7.00-kg arm and glove are brought to rest from an initial speed of 10.0 m/s.
(b) Calculate the force exerted by an identical blow in the gory old days when no gloves were used and the knuckles and face would compress only 2.00 cm.
(c) Discuss the magnitude of the force with glove on. Does it seem high enough to cause damage even though it is lower than the force with no glove?
(a) How long will it take an 850-kg car with a useful power output of 40.0 hp (1 hp = 746 W) to reach a speed of 15.0 m/s, neglecting friction?
(b) How long will this acceleration take if the car also climbs a 3.00-m high hill in the process?
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