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:

$\begin{gathered} E^{\prime}_p=m\cdot g\cdot h^{\prime} \\ E^{\prime}_p=\frac{E_p}{2} \\ \\ m\cdot g\cdot h^{\prime}=\frac{m\cdot g\cdot h}{2} \\ h^{\prime}=\frac{h}{2} \end{gathered}$

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