Energy is conventionally measured in Calories as well as in joules. One Calorie
ID: 1492659 • 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 95 steps, each 0.150 m high, in 53.0 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 fat, 20 J goes into doing mechanical work (here, climbing stairs). The remainder goes into extra internal energy. Assume that the student's mass is 73.0 kg.
(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?
(c) Is this activity in itself a practical way to lose weight?
Explanation / Answer
energy associated with 1 kg fat = 9 x1000 =9000 kcal
work done by the man in climbing stairs = mgh
m = 73 kg
g = 9.8 m/s2
h = 95 x 0.15 =14.25 m
W = 10194.45 J
=2.44 kcal
energy used by man
E = (2.44/20)x100 =12.18 kcal
so the number of tmes he has to climb the stairs is
n = 9000/12.18 =739.1
that is 740 times.
b) average power = W/t
P = 10194.45/53 =192.34 W
= 0.256 hp
c) this mght not be a practical way to loose weight
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