# Power involved in running upstairs

1. The problem statement, all variables and given/known data

A 65 kg student jogs upstairs from the first floor to the sixth, a vertical distance of 17.6 m, in 65 s. Find the power the student expends working against gravity (In kW.)

2. Relevant equations

F=m*A
W=F*d
P=W/t

3. The attempt at a solution

Tried solving here but didn't know how to incorporate gravity into this, got a crazy answer.

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#### davo789

So power is in Watts, which is Joules per Second. What does the student gain when (s)he runs upstairs?

The student would gain height as they climbed.

#### davo789

But why is it hard work going upstairs, but not down them?

Because gravity is weighing down on you as you ascend. I understand it physically, but I don't know where to incorporate g mathematically.

#### davo789

If you lift a weight up in to the air, what (other than height) are you giving it? If you drop it, it gains kinetic energy, but where does that energy come from?

Sorry that it appears I'm taking a really roundabout route with this; I'm trying to get you to come up with the answer!

It gains potential energy as it gains height, so can I use the law of conserved forces?

#### davo789

Excellent, yes it does. So you should be able to calculate how much energy the student has gained, and you know how long it took......

Got the right answer, thank you. That was a lot simpler than I thought it was... lol

#### davo789

These things often are!

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