Does Gravitational Potential Energy Decrease on Collision?

[utkarshakash]

Homework Statement

Two small bodies initially at rest and free to move from a distance of 1m from each other are subjected to only their gravitational force of attraction. They approach each other and collide and do not separate. In respect to this collision which of the following statement is true?
a)The total gravitational potential energy(GPE) of 2 masses has increased on collision.
b)The total gravitational potential energy(GPE) of 2 masses has decreased on collision.

The Attempt at a Solution

I think option a) is correct as when the two bodies approach each other, the GPE increases as it is inversely proportional to distance. But option b) is the correct answer.

 

[rude man]

The GPE of one mass due to the other mass is always negative. It takes negative energy to move one mass from infinity to near the other mass. So the closer they get, the more negative the GPE.

 

[utkarshakash]

The GPE of one mass due to the other mass is always negative. It takes negative energy to move one mass from infinity to near the other mass. So the closer they get, the more negative the GPE.

OK. But what happens after they stick to each other? How does one define GPE of the system after that instant?

 

[rude man]

OK. But what happens after they stick to each other? How does one define GPE of the system after that instant?

GPE can't change after the collision. It's now a theoretical number based on the fact that they can't get any closer to each other.

For point masses the GPE approaches -infinity.

EDIT: I shouldn't have said the GPE can't change after the collision. If you then separate the masses the GPE will increase again.

 

[HalfLostAndSearching]

Your attempt at a solution is partially correct. It is true that the total gravitational potential energy (GPE) of the two masses increases as they approach each other due to the decrease in distance between them. However, when they collide and do not separate, the GPE is converted into kinetic energy, causing the masses to move and gain velocity. Therefore, the total GPE of the two masses decreases on collision. This is in accordance with the law of conservation of energy, which states that energy cannot be created or destroyed, but can only be converted from one form to another. In this case, the GPE is converted into kinetic energy.