Blocks A (mass 6.50kg ) and B (mass 12.00kg ) move on a frictionless, horizontal

Question

Blocks A (mass 6.50kg ) and B (mass 12.00kg ) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 3.00m/s . The blocks are equipped with ideal spring bumpers. The collision is head-on, so all motion before and after the collision is along a straight line. Let +x be the direction of the initial motion of A.

Part A

Find the maximum energy stored in the spring bumpers and the velocity of each block at that time.
Find the maximum energy.

Part B

Find the velocity of A

Part C

Find the velocity of B

Part D

Find the velocity of each block after they have moved apart.
Find the velocity of A.

Part E

Find the velocity of B

Explanation / Answer

Answer for PArt A)

When the blocks are at their closest, they must both be moving with the same velocity - makes sense when you think about it.And at closest approach the springs are most compressed and so have their maximum stored energy.

Since they both have the same velocity and since momentum is conserved.

Momentum before = 6.5 * 3 = Momentum at closest = (6.5 + 12) V

V = 19.5 / 18.5 = 1.054 m/s

answer to the first question - both blocks have the same velocity of 1.054 m/s

The energy stored in the bumpers is the initial energy

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