Question

A pendulum has a mass of 25 kg and is swinging on a rope that is 4 meters long How much gravitational potential energy does the pendulum have when the rope is completely horizontal? How much gravitational potential energy does the pendulum have when the rope is completely vertical?

Answer 1

The answer depends on the zero level of gravitational potential choice. Let's assume, we have chosen the zero level at the plane parallel to the ground and passing throug the pendulum suspension point.

Then when the rope is completely horizontal the pendulum has $U_1 = 0$ potential energy (because the pendulum is located at exactly zero potential plane).

When the rope is completely vertical the pendulum is located at the distance $h = 4m$ below the zero potential plane. Thus, its potential energy is:

$$U_2 = -mgh$$

where $m=25 kg$ is the mass of the pendulum, $h = 4m$ is the heinght below zero plane and $g = 9.8m$ is the gravitational acceleration. Sign "$-$" is due to location below zero plane. Thus, obtain:

$$U_2 = -25\cdot 9.8\cdot 4 = 980J$$

Answer. 0J, 980J.