Find the total gravitational potential energy of this system?

In summary, the total gravitational potential energy for the given system can be calculated by summing the potential energies of each individual pair of masses using the formula U = -Gm1m2/r, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them. If all the masses in the system are doubled, the total gravitational potential energy will also be doubled since the masses are directly proportional to the potential energy.If the sides of the rectangle are halved in length, the distance between each pair of masses will also be halved, resulting in a decrease in the potential energy by a factor of four. In summary, halving the sides of the rectangle will result
  • #1
mattloverss
1
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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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  • #2
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.
 

FAQ: Find the total gravitational potential energy of this system?

What is gravitational potential energy?

Gravitational potential energy is the energy that an object possesses due to its position in a gravitational field. It is the energy that is required to move an object from one position to another within the gravitational field.

How is gravitational potential energy calculated?

The gravitational potential energy of a system is calculated by multiplying the mass of the object by the acceleration due to gravity (9.8 m/s^2) and the height of the object above a reference point. The formula is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

What units is gravitational potential energy measured in?

Gravitational potential energy is measured in joules (J) in the SI unit system. In the imperial unit system, it is measured in foot-pounds (ft-lb).

Can gravitational potential energy be negative?

Yes, gravitational potential energy can be negative. This typically occurs when the reference point used to calculate the potential energy is below the object's position. In this case, the potential energy is negative because the object would release energy if it were to fall to the reference point.

How does the total gravitational potential energy of a system change?

The total gravitational potential energy of a system can change when the mass, height, or reference point of the system changes. It can also change when there is a change in the gravitational field, such as a change in the distance between two objects or a change in the strength of the gravitational field.

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