# Does a higher velocity make a collision more or less elastic? Does it have any impact on it at all?

Basically, if you increase the velocity before the collision, does the collision become more elastic? If you used conservation of energy as proof, (i.e the faster the velocity, and the less percent of energy lost), does that work?

• Collision of what? – GiorgioP Jan 24 at 6:31

One measure of the elasticity of a collision is the coefficient of restitution, which is given by

$$e=\sqrt \frac{KE_{after}}{KE_{before}}$$

Where e ranges from 0 to 1.

$$e$$=1 for a perfectly elastic collision and e=0 for a perfectly inelastic collision.

If e is a constant then increasing the initial velocity should not change the elasticity of the collision. However it is only a constant for a limited range of speeds.

In general, for a given object the greater the deformation the greater the loss in kinetic energy dissipated as heat. And the greater the impact velocity the greater the deformation. For small deformations behavior may approach Hooke's law (linear elastic), depending on the material, and the collision becomes more elastic.

Bottom line: Increasing the velocity before the collision generally makes the collision more inelastic.

Hope this helps.

• something is not right here, we know that under large stress the strain is not only non-linear but hysteretic; so if, say, two metals balls collide with large enough momenta there must be some inelastic yield, i.e., deformation and KE loss. – hyportnex Jan 24 at 10:32
• @hyportnex I felt that way too and did some more research. Found it’s constant only for a limited range of speeds. I’m going to delete this but want you to see my response first. Please acknowledge and thanks – Bob D Jan 24 at 11:01
• don't delete, just modify :) – hyportnex Jan 24 at 11:31
• @hyportnex Thanks for the advice – Bob D Jan 24 at 14:49

No, the elastic collision equations can be solved analytically for any starting speed. The collision becomes inelastic when you are also imposing conditions at the end of the collision, such as the two moving with the same speed, etc.

• when two cars collide at their fronts, say, with >10mph the inelasticity cannot just be imposed at the end (no pun intended), it takes many milliseconds to get to the final rather irreversible result. – hyportnex Jan 24 at 11:36
• @hyportnex You are right, but I interpreted the question in a different way. I interpreted if it was a matter of principle, rather than a characteristic of a specific material. – Wolphram jonny Jan 24 at 17:33
• Indeed the question was a bit vague and allows several interpretations. By the way, what is the atomic weight of "wophram"? – hyportnex Jan 24 at 17:48