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Energy is conventionally measured in Calories as well as in joules. One Calorie

ID: 2029454 • Letter: E

Question

Energy is conventionally measured in Calories as well as in joules. One Calorie in nutrition is one kilocalorie, defined as 1 kcal 4 186 J. Metabolizing 1 g of fat can release 9.00 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 85 steps, each 0.150 m high, in 53.5 s For simplicity, ignore the energy he uses in coming down which is small Assume that a typical efficiency for human muscles is 20.0% Therefore when your body converts 100 J from metabolizing at, 20 J goes into doing mechanical work (here, climbing stairs). The remainder goes into extra internal energy. Assume that the student's mass is 79.0 k. (a) How many times must the student run the flight of stairs to lose 1.00 kg of fat? times (b) What is his average power output, in watts and horsepower, as he runs up the stairs? hp (c) Is this activity in itself a practical way to lose weight? This answer has not been graded yet.

Explanation / Answer

(a) for 1 kg fat, energy released is given as

E = 1000 g * 9 kcal/g = 9000 kcal.

mechanical energy generated by 1 kg (1000g) fat = 20% of 9000 = 1800 kcal

Height gained during exercise = 85*0.15 = 12.75 m

P.E = mgh = 79*9.8*12.75 = 9871.05 joules

in kcal, P.E = 2.358 kcal (after dividing by 4186 joules)

Therefore, no. of times = 1800 / 2.358 = 763 trips

(b) P = E/t = 9871.05 / 53.5 = 184.5 watt

In hp , P = 0.247 hp