# Final velocities of a two point-masses in inelastic collision [duplicate]

Two particles of same mass in a 2D frame collide with known initial (i) velocities. I would like to know the final (f) velocities of them after the collision.

As in any other collision, momentum is conserved after the collision. Writing in components:

$$v_{x,1}^{i} + v_{x,2}^{i} = v_{x,1}^{f} + v_{x,2}^{f}$$ $$v_{y,1}^{i} + v_{y,2}^{i} = v_{y,1}^{f} + v_{y,2}^{f}$$

The total energy (not the mechanical) is also conserved. K accounts for the thermal energy. $$v_{x,1}^{2,i} + v_{y,1}^{2,i} + v_{x,2}^{2,i} + v_{y,2}^{2,i}= v_{x,1}^{2,f} + v_{y,1}^{2,f} + v_{x,2}^{2,f} + v_{y,2}^{2,f} + 2 \cdot K/m$$ I obtain with this 3 equations for 4 unknown quantities, the x and y components of the velocities of particle 1 and particle 2. How could this be solved?. What information should I add? I can only think of modelling the collision with a potential of some kind.

• You need more information. You have to know how inelastic the collision is. You have the extremes of perfectly elastic and perfectly inelastic, and a continuum of possibilities in between. For example, you have to know the fraction of energy lost, or how much heat was generated in the collision. – garyp Sep 26 '16 at 19:06
• Write the equations in the center of mass frame. – Floris Sep 26 '16 at 19:11
• My question was made by assuming that the thermal coefficient is known in advance. I know it is not realistic but I wanted to focus on the obtainton of the final velocities provided the rest is known. – Fisiquin Sep 26 '16 at 19:16
• point masses are ideal objects, there can be no other collision between them except absolutely perpendicular ones; at any other angle, the collision will fail; point masses cannot collide in plastic manner (e.g., there can't take any sort of deformation). they can't take friction; their internal temperature is absolute zero and it's a constant. Meaning, it can't change! Meaning, there is no possibility for "inelastic collision" to occur between two point masses. – Bekim Bacaj Jul 13 '17 at 13:27