Blocks A (mass 8.00 kg ) and B (mass 15.00 kg , to the right of A) move on a fri
ID: 1445616 • Letter: B
Question
Blocks A (mass 8.00 kg ) and B (mass 15.00 kg , to the right of A) move on a frictionless, horizontal surface. Initially, block B is moving to the left at 0.500 m/s and block A is moving to the right at 2.00 m/s. The blocks are equipped with ideal spring bumpers. The collision is headon, so all motion before and after it is along a straight line. Let +x be the direction of the initial motion of A.
A) Find the maximum energy stored in the spring bumpers.
Express your answer with the appropriate units.
B)Find the velocity of block A when the energy stored in the spring bumpers is maximum.
Express your answer with the appropriate units.
C)Find the velocity of block B when the energy stored in the spring bumpers is maximum.
Express your answer with the appropriate units.
D)Find the velocity of block A after the blocks have moved apart.
Express your answer with the appropriate units.
E) Find the velocity of block B after the blocks have moved apart.
Express your answer with the appropriate units.
Explanation / Answer
a) Applying conservation of momentum
=> 8 * 2 - 15 * 0.5 = (8 + 15) * V
=> V = 0.369 m/sec
=> initial KE = 1/2 * 8 * 2 *2 + 1/2 * 15 * 0.5 * 0.5 = 17.875 J
=> Final KE = 1/2 * 23 * 0.369 * 0.369 = 1.5658 J
=> maximum energy stored in the spring bumpers = 17.875 - 1.5658
= 16.309 J
b) velocity of block A when the energy stored is maximum = 0.369 m/sec
c) velocity of block B when the energy stored is maximum = 0.369 m/sec
d) For an elastic collision
=> 8 * 2 - 15 * 0.5 = 8u + 15v
=> 8.5 = 8u + 15v
Also, (2 + 0.5 ) = v - u
=> v - u = 2.5
=> u = - 1.26 m/sec
=> v = 1.239 m/sec
=> velocity of block A after the blocks have moved apart = - 1.26 m/sec ( towards - ve X direction)
e) velocity of block B after the blocks have moved apart = 1.239 m/sec