Serway & Jewett — Conservation of Energy: Problem 22

Energy is conventionally measured in Calories as well as in joules. One Calorie in nutrition is one kilocalorie, defined as \(1 \text{ kcal} = 4\,186 \text{ J}\). Metabolizing \(1 \text{ g}\) of fat can release \(9.00 \text{ kcal}\). A student decides to try to lose weight by exercising. He plans to run up and down the stairs in a football stadium as fast as he can and as many times as necessary. To evaluate the program, suppose he runs up a flight of 80 steps, each \(0.150 \text{ m}\) high, in \(65.0 \text{ s}\). For simplicity, ignore the energy he uses in coming down (which is small). Assume a typical efficiency for human muscles is \(20.0\%\). This statement means that when your body converts \(100 \text{ J}\) from metabolizing fat, \(20 \text{ J}\) goes into doing mechanical work (here, climbing stairs). The remainder goes into extra internal energy. Assume the student’s mass is \(75.0 \text{ kg}\). (a) How many times must the student run the flight of stairs to lose \(1.00 \text{ kg}\) of fat? (b) What is his average power output, in watts and in horsepower, as he runs up the stairs? (c) Is this activity in itself a practical way to lose weight?