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 . 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 75.0 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 3 goes into doing mechanical work (here, climbing stairs). The remainder goes into extra internal energy. Assume that the student's mass is 68.0 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? hp (c) Is this activity in itself a practical way to lose weight?

Explanation / Answer

a)

M = mass of fat = 1 kg

we know that 1 g fat = 9000 cal

so E = energy released by 1 kg fat = 1000 x 9000 = 9 x 106 cal

W = mechanical work done = 20% of E = 0.20 x 9 x 106

h = height gained each time = 95 x 0.15 m

m = mass of student = 68 kg

n = number of times student run the flight of stairs = ?

W = n mgh

0.20 x 9 x 106 = n (68) (9.8) (95 x 0.15)

n = 190

b)

t = total time taken = n (75) = 190 x 75 = 14250 sec

power is given as

P = W/t

P = (0.20 x 9 x 106)/14250

P = 126.31 Watt

in hp

P = 0.17 hp

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.