Mechanical Energy Staircase Problem

• kimberlyphys

Homework Statement

Problem 1: A standard-sized and typically able college-age human walks
into a building for an appointment on the 10th story. The elevator is broken.
She walks up the 9 stories. Roughly speaking:

(a) How much mechanical energy does she need to expend to climb those
9 stories?

(b) How much time do you think it takes her to climb those stairs? As-
sume she is at least somewhat motivated to get to her appointment. If you
are having trouble estimating this, hire a friend to time themselves climbing stairs. Use that time and the total energy from part (a) to get a power, and express the power in horsepower. Are you surprised? Why is horsepower defi ned as it is?

(c) Now convert the energy you got in part (a) to what dieticians call "Calories", which are really SI kcal units. What fraction of a standard human 2000 kcal diet was this stair climbing exercise? Does this make sense given what you know about programs of "exercise"?

(d) How many flights of stairs could our subject climb in a day if all her body did was convert a 2000 kcal input of food into stair-climbing energy? Why is that not at all a realistic description of the body? On what bodily processes is energy spent in forms other than mechanical forms?

TME = PE + KE

The Attempt at a Solution

I'm pretty sure I can do all of the calculations in the final parts, I'm just extremely confused as to how to estimate the mechanical energy she needs to climb the staircase.

Work equates to energy. How is work defined (mathematically)? If she goes up 9 stories, has she changed her potential energy by doing work?

Well, I suppose her potential energy has increased, and the work would be the change in the total amount of energy? Thank you.

You've got it.

I'm still about confused as to how I would calculate this!

I'm still about confused as to how I would calculate this!

Well the work is force x distance right? Each step has a vertical distance associated with it, so each step you are expending energy to increase your potential energy. What specifically are you having trouble grasping?

at top when at rest i think PE=mgh and KE=0