Three mountain climbers set out to climb a mountain from the same altitude and all arrive at the same location at the top. Mountain climber A took a long gradual slope to the top, B went a steeper but shorter path, and C tackled the sheer straight side to the top. Assume all three climbers weigh the same. Which did the most work?

A
B
C
all did the same amount of work

The work done by each mountain climber to climb the mountain is equal to how much gravitational potential energy they gained in the climb, and this is given by

[tex]W=\Delta U=mg\Delta h[/tex]

where m is the mass of the climber, g is the gravitational acceleration, and [tex]\Delta h[/tex] is the gap in altitude.

Since the three climbers have same weight, they also have same mass, so the term "m" in the formula is the same. Also, they started from the same altitude and arrive at the same altitude, so the gap [tex]\Delta h[/tex] is the same for all of them. Therefore, they gain the same gravitational potential energy, and so they did the same amount of work. So, the work does not depend on the path taken.