# Potential energy of a system (gravity)

1. Apr 18, 2012

### jjr

1. The problem statement, all variables and given/known data
Show that the potential energy of a system which consists of four equal particles, each with mass M, that are placed in different corners of a square with sides of length d, is given by
ep = - $\frac{G M^2}{d}$*(4 + √(2))

2. Relevant equations

The gravitational force F(r) = - $\frac{G M m}{r^2}$ * ur
Potential gravitational energy Ep(r) = - $\frac{G M m}{r}$

3. The attempt at a solution

I'm having a hard time achieveing an intuitive comprehension of how one might solve this problem. As far as I can understand, they're asking how much work would be done if all the particles moved in to the center? I'm not sure if I should figure out the work it would take to bring each individual particle in to the center one at a time, all at once, or if I need to approach this in some other way.. Any hints would be greatly appreciated

J

2. Apr 18, 2012

### ehild

The gravitational potential is zero at infinity. You need to calculate the work needed to take the system apart, to move the particles one by one to infinity. The negative of that work is equal to the potential energy of the system.

ehild

3. Apr 18, 2012

### jjr

Of course! Thanks:)