# Potential Energy Problem

We know that, the potential energy of a particle is $U= mgh$ where $h$ is the height from the zero potential point.

But what I have found in Resnick's Fundamental of physics book is that they wrote the potential energy for the sphere at height h is equal$= Mgh$ .

Will not it be $= Mg(h+R)$? I have added the $R$ to the height $h$ because, from the ground the height of the center of mass of the sphere is $(h+R)$.

• The diagram is a bit confusing; at the top point, the center point of the ball is not $h+R$ above the top of the ramp, but instead $h+Rcos(\theta)$. That might work if the ramp were floating so the ball could roll to touching the bottom of the ramp, so that the center point ended up at $Rcos(\theta)$... – Daniel Griscom Sep 9 '15 at 22:16

## 1 Answer

Well, it depends on what you call zero potential energy. If you say "ball sitting on the floor" is zero potential energy, then $Mgh$ is the correct formula for the potential energy of the ball on the ramp. If you say "ball material flattened onto the floor" is zero, then $Mg(h+R)$ is indeed the correct formula. If you say "ball sitting at the bottom of a 30 meter pit" is zero, then the formula would be $Mg(h+30)$.

None of these zero points is "wrong"; potential energy is always determined relative to some arbitrary zero point. As the problem is written, though, it implies that zero is "ball sitting on the floor", hence $Mgh$ is indeed the expected answer.