Gravitational Potential Energy of a particle

[peaceandlove]

Homework Statement

Four particles, each of mass 60.0 g, form a square with an edge length of d = 0.700 m. If d is reduced to 0.100 m, what is the change in the gravitational potential energy of the four-particle system?

Homework Equations

U = -GMm/r

The Attempt at a Solution

I found the U of the system when d = 0.700 m and then I found the U when d = 0.100 m. Using those two values, I found what I believe to be the change in the U of the system. However, I keep getting the wrong answer.

U_1=-6.45898846e-12
U_2=-2.60012192e-11
(delta)U=1.95422308e-11

 

[peaceandlove]

Nevermind, I figured it out.

 

[nlightner]

I would like to add that the gravitational potential energy of a particle is the energy that is associated with its position in a gravitational field. It is a form of potential energy that is dependent on the mass and separation of the particles. In this case, the gravitational potential energy of the four-particle system is given by the equation U = -GMm/r, where G is the gravitational constant, M is the mass of one particle, m is the mass of the other particle, and r is the distance between them.

To find the change in potential energy when the distance between the particles is changed from 0.700 m to 0.100 m, we can use the equation (delta)U = U_2 - U_1. Plugging in the values given in the problem, we get (delta)U = -2.60012192e-11 - (-6.45898846e-12) = 1.95422308e-11. This means that the change in the gravitational potential energy of the four-particle system is 1.95422308e-11 Joules.

It is important to note that this value is negative, which indicates that the potential energy of the system has decreased when the distance between the particles was reduced. This makes sense as the particles are now closer together and therefore have a stronger gravitational attraction, resulting in a decrease in potential energy.