Question

A mountain climber starts at the base of a mountain, climbs all the way to the peak, and then climbs back down to the base. At which point is the climber's potential energy the greatest?

Answer 1

Given:

A climber climbs the mountain to the peak and climbs back down.

To Find:

The point where climbers potential energy is maximum.

Solution:

Let,

Mass of the climber = m

Height of the mountain = h

From the definition of gravitational potential energy, we know that it is the energy stored in an object due to its position above earth's surface. Mathematically it can be expressed as,

Potential energy (U) = mgh       ......(1)

∴At the ground positions h = 0, hence from the equation (1), U = 0

Now, let x be the height of a random point between ground and peak of the mountain. Here, x < h (∵ h is maximum height)

∴ U = mgx, which is less than U=mgh the potential energy at height h (∵ g = acceleration due to gravity = constant, and mass of the climber is also constant)

∴From the above discussion we can conclude that, climber's potential energy is maximum in the peak of the mountain.