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

In summary, the acceleration of a stationary steel ball after being hit by a moving steel ball depends on the elasticity and stiffness of the materials, as well as the contact time between the two balls. The acceleration may have a simple harmonic profile and can be estimated by modeling the collision as a spring. However, the contact time can be difficult to determine and may require high-speed video analysis.
  • #1
Treva31
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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?
 
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  • #2
That depends, as you surmised, on the elasticity and stiffness of the materials. It's generally non-trivial to figure out.
 
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  • #3
Moreover, the acceleration will not be constant. The acceleration may have approximately a simple harmonic profile.
 
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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.
 
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1. What is an elastic collision?

An elastic collision is a type of collision between two objects where both kinetic energy and momentum are conserved. This means that the total energy and momentum before and after the collision are the same.

2. How do you calculate the acceleration after an elastic collision?

The acceleration after an elastic collision can be calculated using the formula a = (v2 - v1) / t, where v2 is the final velocity of the object after the collision, v1 is the initial velocity, and t is the time taken for the collision to occur.

3. What factors affect the acceleration after an elastic collision?

The acceleration after an elastic collision can be affected by factors such as the masses and velocities of the objects involved, as well as the angle and direction of the collision.

4. Can the acceleration after an elastic collision ever be negative?

Yes, the acceleration after an elastic collision can be negative if the objects involved are moving in opposite directions before the collision and the final velocity of one object is less than its initial velocity.

5. How is an elastic collision different from an inelastic collision?

An inelastic collision is a type of collision where kinetic energy is not conserved, meaning that some of the energy is lost in the form of heat or sound. In contrast, an elastic collision involves no loss of energy and both kinetic energy and momentum are conserved.

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