A 60.5-kg hiker starts at an elevation of 1280 m and climbs to the top of a peak 2570 m high. (a) What is the hiker's change in potential energy?
(b) What is the minimum work required of the hiker?
(c) Can the actual work done be greater than this? Explain.

A) Change in potential energy is approximately 766 KJ

B) The minimum work required by the hiker is 765 KJ

C). Yes, the actual work can be greater than this

Explanation:

A) The hiker's potential energy can be calculated at the two different elevations, and then subtracted.

P.E at 1280 m = m X g X h = 60.5kg X 9.81 m/s2 X 1280 = 759, 686 J

P.E at 2570 m = m X g X h = 60.5kg X 9.81 m/s2 X 2570 = 1, 525, 307.85 J

Change in P.E = 1, 525, 307.85 J -759, 686 J = 765, 621.85 J = 766 KJ

B) Work which was done = Force X distance moved.

The force can be got from the effect of gravity on the hiker's mass = 60.5 kg X 9.81 = 593.5 Newton.

The distance moved can be obtained by subtracting the two elevations = 2570 -1280 = 1290 m

Work done = 593 X 1290 = 765, 615 J

The minimum work required by the hiker is 765 KJ

C) Yes, the actual work can be greater than this. This is because we can now put into consideration the fact that the hiker is climbing up the elevation against the force of gravity. This will mean that the hiker is actually doing more work than if he covered the distance on flat terrain,

in physics zero. in muscle fatigue could be high