Horizontal elastic collision between a ball and a block attached to a spring?

  • #1

Homework Statement



The problem states: A 0.140 kg block on a frictionless table is firmly attached to one end of a spring with k = 25 N/m. The other end of the spring is anchored to the wall. A 0.023 kg ball is thrown horizontally toward the block with a speed of 5.2 m/s. What is the ball's speed immediately after the collision (if the collision is perfectly elastic)?

Homework Equations



F(spring) = -k(change in s)
K(f) + U(f) = K(i) + U(i) ...---> K = (1/2)mv^2 ...U = (1/2)k(change s)^2

The Attempt at a Solution



The one thing that prevents me from solving the problem is that I am unable to find the length of the compressed spring, and I also do not know how to use F = -k(change s) in this problem. I know that since this is perfectly ellastic, I should use conservation of momentum or conservation of energy, but I always come out with two unknown variables.... the final velocity of the ball and usually, change in s. Any pointers? Thanks so much.
 

Answers and Replies

  • #2
674
2
I could be wrong on this, but immediately after the collision the spring has barely moved at all. Therefore it is just an elastic collision between a ball and a block. Pretend the spring isn't there.

If there is a later question asking the amplitude of the oscillations, then you will know the initial velocity of the block from the previous elastic equation. And can solve for the amplitude.
 
  • #3
172
1
Use conservation of momentum and conservation of kinetic energy. Stop the experiment before the spring starts to compress. You get two variables, but you also have two equations.

It's just algebra from there.
 

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