Question

General question: How do you relate power to time without knowing the mass of object being acted upon?

Specifics: This practice problem is really bugging me:
Given: Your max metabolic rate is 1500W (consumption of chemical energy) and your metabolic efficiency (chemical->mechanical energy) is 40%. Assume a flight of stairs is 3.5m high.
Find: How long it takes you to run up four flights of stairs (minimum).

The answer in the back of the book is 16s.

Thanks in advance.

Answer 1

Hmm.. that does seem interesting at first glance. I think it's possible though, and the m's will cancel.

Answer 2

Let me elaborate: Let m be the mass of the person running the flight of stairs. Let h be the final height you're at ( h = 14.0 m).

Answer 3

Now, first things first, what's the net mechanical energy loss to go up the stairs?

Answer 4

Taking he person to be the system the net loss would be mgh.

Answer 5

Okay. Now, you know that P = dE/dt = (in this case) = W/time, right?

Answer 6

Right. So, Pmech=mgh/t, yes?

Answer 7

Agreed. I see where you're going. Have you tried putting in m = 50 kg to see if it gives he same result?

Answer 8

I'm not sure I follow... Taking 16s as the given time and 600W (0.4*1500) as the mechanical power; solving for mass I get 70.0kg. Which I suppose is odd because the question implies that the relation should be mass independent.

I tried solving P=Fv and P=mgh/t as a system of equations but to no avail.

Answer 9

Firstly - of course it IS mass-dependent !
Raising up massive object requires more power than low-mass object.
Second POwer = Work/Time . ===> Shortest-time = Work/{Maximal POwer}

Answer 10

Ah, so I'm just supposed to approximate that the average person is ~70kg. It's the simple things that get you.

Thanks.