BIOLOGICAL APPLICATION In one model of a person jogging,

Chapter , Problem 104

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BIOLOGICAL APPLICATION In one model of a person jogging, the energy expended is assumed to go into accelerating and decelerating the feet and the lower portions of the legs. If the jogging speed is v, then the maximum speed of the foot and lower leg is about 2v. (From the moment a foot leaves the ground, to the moment it next contacts the ground, the foot travels nearly twice as far as the torso, so it must be going, on average, nearly twice as fast as the torso.) If the mass of the foot and lower portion of a leg is m, the energy needed to accelerate the foot and lower portion of a leg from rest to speed 2v is and the same energy is needed to decelerate this mass back to rest for the next stride. Assume that the mass of the foot and lower portion of a mans leg is and that he jogs at a speed of with between one footfall and the next. The energy he must provide to each leg in each of travel is so the energy he must provide to both legs during each second of jogging is Calculate the rate of the mans energy expenditure using this model, assuming that his muscles have an efficiency of 20 percent.