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Blocks A (mass 6.50 kg ) and B (mass 10.00 kg ) move on a frictionless, horizont

ID: 1409186 • Letter: B

Question

Blocks A (mass 6.50 kg ) and B (mass 10.00 kg ) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 3.00 m/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.

Find the maximum energy stored in the spring bumpers.

Find the velocity of A when the maximum energy is stored in the spring bumpers.

Find the velocity of B when the maximum energy is stored in the spring bumpers.

Find the velocity of A after the blocks have moved apart.

Find the velocity of B after the blocks have moved apart.

Explanation / Answer

Here, Applying conservation of momentum

=>    6.50 * 3   + 0 = (6.50 + 10) * v

=>   v = 1.1818 m/sec

=>    maximum energy stored in the spring bumpers = - 1/2 * (6.50 + 10) * 1.18182   + 1/2 * (6.50) * 32

                                                                                  = 17.728 J

=>    velocity of A when the maximum energy is stored = 1.1818 m/sec

=>    velocity of B when the maximum energy is stored = 1.1818 m/sec

=>   velocity of A after the blocks have moved apart = [(mA-mB)/(mA+mB)]*VA1

                                                                                     = (3.5/16.5) * 3 = 0.636 m/sec

=> velocity of B after the blocks have moved apart = [(2*mA)/(mA+mB)]*VA1

                                                                                   = (13/16.5) * 3 = 2.363 m/sec