Calculating Energy Expenditure for Weight Loss Through Stair Climbing

[xX1SHOt]

Homework Statement

Energy is conventionally measured in Calories as well as in joules. One Calorie in nutrition is one kilocalorie, defined as 1 kcal = 4186 J. Metabolizing 1 g of fat can release 9.00 kcal. A student decides to try to lose weight by exercising. She plans to run up and down the stairs in a football stadium as fast as she can and as many times as necessary. Is this in itself a practical way to lose weight? To evaluate the program, suppose she runs up a flight of 100 steps, each 0.150 m high, in 59.5 s. For simplicity, ignore the energy she 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 54.0 kg.
(a) How many times must she run the flight of stairs to lose 1 lb of fat?

Homework Equations

work = F*d which equals the same as total potential energy PE = mgh

The Attempt at a Solution

ok i interpreted it as only 20% of work burns fat, if that's wrong that'd be nice to know.

(54 kg)(9.8 m/s^2)(15) = 7938 J

1lb = .4536 kg

.2 * 9kcal/g * 1000g/kg * 1kg/2.2046lbs * 4186J/kcal * 1walk/7938J = 430.56 walks/lb

i messed up a calculation and entered 2152.78 walks/lb the first time and it said that i was between 10% and 100% of the correct answer. Does what i just showed make sense and if it at least the calculations are correct is it wrong where i thought 20% of energy used burns fat? or maybe its 80% ? or maybe its 120%?

any thoughts would be helpful as i only have one more chance to answer before its permanently wrong

 

[diazona]

ok i interpreted it as only 20% of work burns fat, if that's wrong that'd be nice to know.

Yep, it's wrong. Did you see this sentence:

Therefore when your body converts 100 J from metabolizing fat, 20 J goes into doing mechanical work (here, climbing stairs).

Also, in

(54 kg)(9.8 m/s^2)(15) = 7938 J

Where did 15 come from?

 

[xX1SHOt]

15 is the total height being walked up .15m per step * 100 steps = 15
her mass is 54kg and acceleration is 9.8m/s^2.
the total energy or work it takes to get to the top is Fd.
do you have a different way to determine the total distance?