Question

George of the Jungle hangs from a 20 m long vine that makes a 39 degree with the vertical. If George has a mass of 85 kg, find his gravitational potential energy. ( Assume that the zero level is at the bottom of the swing ) include all units

Answer 1

The given problem can be exemplified in the following diagram:

We are asked to determine the gravitational potencial energy. To do that we will use the following formula:

`U=\text{mgh}`

Where "m" is the mass, "g" is the acceleration of gravity and "h" is the height. To determine the height we need to determine first the vertical component of the vine. We will use the function cosine:

`\cos 39=(H)/(20)`

Solving for H:_

`20m\cos 39=H`

Solving the operation:

`15.5m=H`

Now, the value of the height "h" is equivalent to the length of the vine minus the value of H, that is:

`\begin{gathered} h=20m-H \\ h=20m-15.5m \\ h=4.45m \end{gathered}`

Now we replace in the formula for the gravitational potential energy:

Solving the operation:

`U=3712.8J`

Therefore, the gravitational potential energy is 3712.8 Joules.