Blocks A (mass 2.50 kg) and B (mass 14.50 kg) move on a frictionless horizontal

Question

Blocks A (mass 2.50 kg) and B (mass 14.50 kg) move on a frictionless horizontal surface. Initially block B is at rest and block A is moving toward it at 8.00 m/s. The blocks are equipped with ideal spring bumpers. The collision is head on so all motion before and after collision is along a straight line. Let +x be the direction of the initial motion of A.

1. Find the maximum energy stored in the spring bumpers (Ub= ? J)

2.The velocity of each block at that time:

Va=? m/s

Vb=? m/s

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

Va=? m/s

Vb=? m/s

Explanation / Answer

Total momentum = (6.00 kg)(8.00 m/s) = 48 kg-m/s After collision (elastic): KE = 0.5 mv^2 = 3.00(64) = 192 J 192 J = 3v1^2 + 7.5v2^2 m1v1 + m2v2 = 48 kg-m/s ------------------ v1 = 48/m1 - m2v2/m1 v1 = 8 - 2.5v2 192 J = 3v1^2 + 7.5v2^2 192 J = 3(64 - 40v2 +6.25v2^2)+ 7.5v2^2

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