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

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 100 steps, each 0.150 m high, in 58.5 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 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 72.0 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?

Explanation / Answer

1 kg of fat=1000*9000=9000000 cal of energy=37674000 J

work done while climbing 100 steps of 0.15 m=72*9.8*(100*0.15)=10584 J

if 100 J from fat is burned ,used in exercising =20 J

if 37674000 J is burned from fat used in exercise=0.2*37674000 J=7534800 J

Let he run x times

x*10584=7534800

x=712 times(approx)

(b) power = work done/time=10584/58.5=180.92 W

1 hp=746 W

so in hp =0.243 hp

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