Elastic Collisions, with limited data.?

Question

Hi,
I am building a simulation. I need to figure out how to get V Final for two objects, given V initial and Mass for each. They are all circles.
How do you solve for this situation? I know that they are circular so the impulse vector will be along the line through their centers.
I'm not sure how to use this. There are 4 unknowns , but only 3 equations (conservation of energy, momentum for each direction)

Answer 1

You say the collisions are elastic. You say they are circles. I think you mean spheres. Right? And I think you mean the collisions are in one dimension.

You have the initial velocities , u1 and u2. You ahve the masses, m1 and m2. And you need final velocities v1 and v2? That's only 2 unknowns I think.

v1 = ((m1-m2)/(m1+m2))*u1 + (2m2/(m1+m2)*u2
v2 = (2m1/(m1+m2))*u1 + ((m2-m1)/(m1+m2))*u2

Answer 2

It's not clear what is given in the situation. V? Do the objects stick together? Do you know the masses?

It may be that you are overcounting your unknowns. On the other hand, it may be that you are correctly counting, in which case the fact that you have fewer equations than unknowns says that there is an infinite number of possible initial situations that lead to the same outcome.

Answer 3

The kinetic energies in a perfectly elastic collision is maintained, i.e., KE before collision is the same as KE after collision. However, if the collision is not perfectly elastic, then some of the KE will mostly be converted to heat. Hope this helps.