Gravitational potential energy of a system

[roshan2004]

Homework Statement

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.

Homework Equations

U=-G*m1*m2/r

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.

 

[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.

 

[roshan2004]

I think there are 8 masses in here.

 

[Simon Bridge]

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

 

[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...

 

[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.