Question

A box is at rest at the top of a frictionless inclined plane. As the box slides down the ramp where along the ramp would the box have half of its original potential energy?

Answer 1

The potential energy of a mass is given by the formula:

`E_p=m\cdot g\cdot h`

Where m is the mass, g is the gravity acceleration and h is the height.

Since the mass and gravity will be constant, for half the potential energy, we have:

`\begin{gathered} E^(\prime)_p=m\cdot g\cdot h^(\prime) \\ E^(\prime)_p=(E_p)/(2) \\ \\ m\cdot g\cdot h^(\prime)=(m\cdot g\cdot h)/(2) \\ h^(\prime)=(h)/(2) \end{gathered}`

So the box will have half the potential energy at half the height of the ramp.