How high can a hike climb with the energy from a candy bar?

Question

A candy bar label says it has 240 Calories (240,000 calories). Typical efficiency of energy conversion for a human is 25%.

If a 68kg person were to use the energy in the candy bar to climb a mountain how high could he go?

For this I know Ki+Ui=Kf+Uf. Then I think Ui and Kf will be 0. So Ki=Uf or 1/2mv^2=mgy? I’m not sure where to go from there.

If he climbs that distance in an hour what would be the average power exerted?

p=w/t? how do I get work?

Answer 1

In this example, the candy bar itself provides a kind of chemical potential energy, call it Ui. You are using that energy to climb to a certain height - you'll be converting the candy bar's potential energy into gravitational potential energy, Uf =mgh. However, you only get to use 25% of the candy bar's energy. Remember to convert the calories to Joules. Each cal = 4.184 J

So.

0.25*Ui = mgh, solve for h

0.25 * (240,000 * 4.184) = 68(9.8) h

h = about 380m