# Potential Energy

1. Feb 24, 2014

### phymathlover

Can we say that positive potential energy means energy is given out by the system when it is brought to the present state of configuration and negative potential energy implies that energy needs to be provided to the system to achieve the present state?

2. Feb 24, 2014

### hilbert2

A value of potential energy doesn't really mean anything, only differences in potential energy matter.

For example, the pot. energy of a system of two planets with masses $M_{1}$ and $M_{2}$ is usually defined as

$V(r)=-G\frac{M_{1}M_{2}}{r}$ ,

where $G$ is the gravitational constant and $r$ is the separation between the planets. The definition makes the potential energy zero at infinite separation and negative at any finite separation. However, if we instead use the definition

$V(r)=-G\frac{M_{1}M_{2}}{r}+V_{0}$ ,

where $V_{0}$ is any constant with dimensions of energy, the model predicts exactly the same physics. Changing potential energies by an additive constant doesn't change anything.

3. Feb 24, 2014

### Staff: Mentor

Hilbert2 beat me to it, but here is my reply anyway.

The zero of energy is purely arbitrary. For example, you can put the zero of potential gravitational energy at the surface of the Earth, at the center of the Earth, or on the Moon. The same object in the same state can thus have positive, negative, or zero potential energy.

The sign of a change in potential energy tells you something about what happend. If the sign is positive, then energy was put into the system to bring it to its current state. If it is negative, energy was taken out. Using again the example of gravity, if I lift an object from the floor, it gains potential energy (positive sign for the change). If I let it drop, it will lose potential energy (negative sign for the change) as it gets converted to kinetic energy.