# Gravitational potential energy of a system

1. Nov 30, 2013

### roshan2004

1. The problem statement, all variables and given/known data
What is the gravitational potential energy of a system of 8 masses of 10 kg each placed at the corners of a cube of length 0.25 meter apart.

2. Relevant equations
U=-G*m1*m2/r

3. The attempt at a solution
I have actually taken one particle pair at a time and sum all of their potential energy, but the answer is not quite right.

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2. Nov 30, 2013

### Simon Bridge

You just want to find the work needed to remove all the masses to infinity.
So pick one ... remove it: how much work would that take?

OK so now you have 5 masses - pick one, remove it: how much work did that take?

Rinse and repeat.

3. Nov 30, 2013

### roshan2004

I think there are 8 masses in here.

4. Nov 30, 2013

### Simon Bridge

Good - you are paying attention ;)
How would you have to change the suggestion to account for the different number of masses?

5. Nov 30, 2013

### roshan2004

I think it will be very tiresome to pick each and every particle and work out their work done in bringing them from infinity to that position. There must be some quick method.......

6. Nov 30, 2013

### Simon Bridge

Yes and no - there is no getting around having to do this for every particle.
But you only have 8 steps to do, and, once you get started, you should notice a pattern that makes things easier.

Finding this out is a big part of why the exercize is set in the first place.
There is no Royal road to knowledge.