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