Potential Energy EX 1

The only conservative force acting in this system (Earth-block) is the gravitational force. The change in gravitational potential energy depends on the change in the height of the object (which means that the distance between the Earth and the block has changed.) Since the gravitational potential energy increased by 40 J we know that the object has moved up some distance $\Delta r$ along the incline or increased its height by some height $h$. We can compute the height $h$ from

$\Delta U=mgh$

because the increase in gravitational potential energy is small and will result in a change of height which is much smaller than the radius of the Earth. Substituting 40 J for $\Delta U$, we get

$40=(2)(10)h$

Solving for $h$, we get $h=2$ m. Since $h$ is related to $\Delta r$ (see the diagram below), we can find $\Delta r$.

${h \over \Delta r}=\sin(37^{\circ })$

Solving for $\Delta r$, we get

$\Delta r={2 \over \sin(37^{\circ })}={2 \over 0.6}=3.3m$