Calculate the *Acceleration* after a (mostly) elastic collision?

[Treva31]

How can I calculate the ACCELERATION of a stationary steel ball after being hit by a moving steel ball.

I know how to get the final velocity but how long does it take to accelerate to that velocity from zero?
Does it depend on the elasticity of the materials?
I guess we need to know long did the transfer of energy take??For example a 3kg stationary ball is hit by a 1kg ball moving at 15m/s, transferring all of its energy into the the stationary ball.
The 3kg ball will end up moving at 5m/s.
But how fast did it accelerate?

 

[cjl]

That depends, as you surmised, on the elasticity and stiffness of the materials. It's generally non-trivial to figure out.

 

[PeroK]

Moreover, the acceleration will not be constant. The acceleration may have approximately a simple harmonic profile.

 

[jrmichler]

As a first order approximation, an elastic collision can be modeled as a spring during the time that the two bodies are in contact. A steel ball peen hammer hitting a heavy steel plate will be in contact for about 1 millisecond, so the spring constant can be estimated from that.

When the contact time is short, it sets up vibrations in the parts. That's the CLANG that you hear in a steel on steel collision. Those vibrations take energy that would otherwise go into changing the velocity of the parts. Finding the contact time can be a challenge. High speed video at 10,000 or 20,000 frames per second is one way.