Find the total gravitational potential energy of this system?

AI Thread Summary
To find the total gravitational potential energy of the system, the formula U = -G * (m1 * m2) / r is used, where G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them. The total energy is calculated by summing the potential energy for each pair of masses in the system. If all masses are doubled, the total gravitational potential energy also doubles. Conversely, if the sides of the rectangle are halved, the distances between the masses decrease, leading to an increase in the total gravitational potential energy. Understanding these relationships is crucial for solving the problem effectively.
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http://session.masteringphysics.com/problemAsset/1125570/2/Walker4e.ch12.Pr042.jpg
use this image for help

a. Consider the four masses shown in the figure . Find the total gravitational potential energy of this system.

b. How does your answer to part A change if all the masses in the system are doubled?

c. How does your answer to part A change if, instead, all the sides of the rectangle are halved in length?


I'm absolutely lost in this problem. I know that U=-GmMe/r
where Me is the mass of earth.
r= radius
However, I don't know how to apply that to so many different masses.
Please help and explain?!
 
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The total gravitational potential energy of the system is the total energy required to separate the constituent masses from each other ie the sum of the energy required to separate each pair of masses.
 

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