What Does Negative Potential Energy Indicate in Colliding Iron Balls in Space?

[SpaceThoughts]

Hi Everyone.

I am hoping to get a little help with this:
Two equal balls of iron each with a mass of 1000 kg are placed in rest in space 10 meters from each other.
Because of gravity they start to accelerate towards each other, and collide in the end.
I would like to know how to calculate the energy that turns into heat, when the masses collide.
Using the below formula gives me the potential energy between the two masses before the eksperiment starts.

U = -G (m1 m2)/r

I calculated the potential energy to be: -0,00000667428 Joule when G is 6,67428.
But what does that negative figure really mean?

It can’t mean that this same amount in Joule (positive) +0,00000667428 is turned into heat when the balls collide, because another calculation with a distance of 20 meter gives me: -0,00000333714.
This amount in Joule (positive) is +0,00000333714, a lower amount of energy in the collision, which is inconsistent and can’t be true. More initial distance means more power when they collide.

So what does this calculation mean, and how will I be able to retrieve the actual final positive kinetic energy the balls have the exact minute they hit each other, and right before the kinetic energy turns into heat?

PS: I know I can subtract two calculations of different distances, and get the difference in potential energy with this formula, but that doesn’t help me much.

Best regards.

 

[Nugatory]

PS: I know I can subtract two calculations of different distances, and get the difference in potential energy with this formula, but that doesn’t help me much.

Why is not helping you? It’s exactly the calculation you need: the difference between the potential energy at the start and at the end is the energy that is released (and if you are careful with the signs it will come out positive). This is just conservation of energy at work.

 

[SpaceThoughts]

Why is not helping you? It’s exactly the calculation you need: the difference between the potential energy at the start and at the end is the energy that is released (and if you are careful with the signs it will come out positive). This is just conservation of energy at work.

Thanks a lot.
I understand I get the right positive figures when calculating two distances, and then subtract, for my example above.
But I am still confused and I still need to know:

From my first calculation above with a distance of 10 meters I get: -0,00000667428.
I assume this figure is the number in Joule that will turn into heat (positive) when the two balls collide (and if they could move through each other, so their masscenters united), right?

If not, what does that figure reflect? A potential energy, but which one?

If yes, how come that if I make another (independant and single) calculation with a distance of 20 meter I will get a larger number: -0,00000333714 which it should be. But if this figure also is the number in Joule I will get when the two centers of masses meet from their new position, there is something wrong, because this number positive is a smaller number. More distance (20m) means more energy converted in the collision.
I am sure I am missing something important here, but what?

 

[jbriggs444]

If not, what does that figure reflect?

The potential energy deficit they have relative to what they would have with infinite separation.

 

[PeroK]

Hi Everyone.

I am hoping to get a little help with this:
Two equal balls of iron each with a mass of 1000 kg are placed in rest in space 10 meters from each other.
Because of gravity they start to accelerate towards each other, and collide in the end.
I would like to know how to calculate the energy that turns into heat, when the masses collide.
Using the below formula gives me the potential energy between the two masses before the eksperiment starts.

U = -G (m1 m2)/r

I calculated the potential energy to be: -0,00000667428 Joule when G is 6,67428.
But what does that negative figure really mean?

It can’t mean that this same amount in Joule (positive) +0,00000667428 is turned into heat when the balls collide, because another calculation with a distance of 20 meter gives me: -0,00000333714.
This amount in Joule (positive) is +0,00000333714, a lower amount of energy in the collision, which is inconsistent and can’t be true. More initial distance means more power when they collide.

So what does this calculation mean, and how will I be able to retrieve the actual final positive kinetic energy the balls have the exact minute they hit each other, and right before the kinetic energy turns into heat?

PS: I know I can subtract two calculations of different distances, and get the difference in potential energy with this formula, but that doesn’t help me much.

Best regards.

What's the radius of the balls? And, what's the final configuration of the masses after the collision?

 

[Mister T]

Two equal balls of iron each with a mass of 1000 kg are placed in rest in space 10 meters from each other.
Because of gravity they start to accelerate towards each other, and collide in the end.
I would like to know how to calculate the energy that turns into heat, when the masses collide.

You would need more information about the collision. For example is it an elastic collision?

Using the below formula gives me the potential energy between the two masses before the eksperiment starts.

U = -G (m1 m2)/r

I calculated the potential energy to be: -0,00000667428 Joule when G is 6,67428.
But what does that negative figure really mean?

It's negative because the potential energy is lower when they are 10 meters apart than when they are an infinite distance apart.

 

[Nugatory]

From my first calculation above with a distance of 10 meters I get: -0,00000667428.
I assume this figure is the number in Joule that will turn into heat (positive) when the two balls collide (and if they could move through each other, so their masscenters united), right?

That assumption may be your problem. You can’t do much of anything with the value of a potential calculated at a single point because only the difference between potentials is meaningful. For an analogy, think about elevations: I can say that the roof of my house is 305 meters from sea level and the basement floor is 297 meters from sea level; or I can say that the roof is 5 meters from ground level and the basement floor is -3 meters from ground level; or I could say that the center of the Earth is at elevation zero and the roof and basement would both be at enormous elevations. But whether these numbers are big and small, positive or negative doesn’t tell us anything. What matters is the difference between them: eight meters is the height of the house from lowest floor to top of roof.

Potential are the same way. The value of the potential at any given point doesn’t tell us anything because we can make it be anything we want just by choosing which point we call “zero potential”. However, the difference between the potentials at point A and point B is meaningful: it’s the energy to move from point A to point B.

Do remember that in your problem the center of masses of the two cannonballs will never touch; they can’t get closer than the size of the balls allows. Thus, $r$ will never be zero.

 

[SpaceThoughts]

Thanks for your kind and clear answer. I fully understand now, and yes I am aware of radius of the balls etc.