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Chapter 7: Q17 CQ (page 259)
List the energy conversions that occur when riding a bicycle.
When a rider is riding the bicycle, he uses his muscular energy to push the pedals of the bicycle. While pedaling muscular energy is converted into kinetic energy.
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Suppose a 350-g kookaburra (a large kingfisher bird) picks up a 75-g snake and raises it 2.5 m from the ground to a branch.
(a) How much work did the bird do on the snake?
(b) How much work did it do to raise its own center of mass to the branch?
(a) What is the efficiency of an out-of-condition professor who does \(2.10 \times {10^5}{\rm{ J}}\) of useful work while metabolizing \(500{\rm{ kcal}}\) of food energy?
(b) How many food calories would a well-conditioned athlete metabolize in doing the same work with an efficiency of \(20\% \)?
Very large forces are produced in joints when a person jumps from some height to the ground.
(a) Calculate the magnitude of the force produced if an 80.0-kg person jumps from a 0.600–m-high ledge and lands stiffly, compressing joint material 1.50 cm as a result. (Be certain to include the weight of the person.)
(b) In practice the knees bend almost involuntarily to help extend the distance over which you stop. Calculate the magnitude of the force produced if the stopping distance is 0.300 m.
(c) Compare both forces with the weight of the person.
The awe-inspiring Great Pyramid of Cheops was built more than 4500 years ago. Its square base, originally 230 m on a side, covered 13.1 acres, and it was 146 m high, with a mass of about 7×109 kg. (The pyramid’s dimensions are slightly different today due to quarrying and some sagging.) Historians estimate that 20,000 workers spent 20 years to construct it, working 12-hour days, 330 days per year.
(a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth its height.
(b) Only a fraction of the workers lifted blocks; most were involved in support services such as building ramps (see Figure 7.45), bringing food and water, and hauling blocks to the site. Calculate the efficiency of the workers who did the lifting, assuming there were 1000 of them and they consumed food energy at the rate of 300 kcal/h. What does your answer imply about how much of their work went into block-lifting, versus how much work went into friction and lifting and lowering their own bodies?
(c) Calculate the mass of food that had to be supplied each day, assuming that the average worker required 3600 kcal per day and that their diet was 5% protein, 60% carbohydrate, and 35% fat. (These proportions neglect the mass of bulk and nondigestible materials consumed.)
Figure 7.45 Ancient pyramids were probably constructed using ramps as simple machines. (credit: Franck Monnier, Wikimedia Commons)
The person in the figure does work on the lawn mower. Under what conditions would the mower gain energy? Under what conditions would it
lose energy?
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