Question

Blocks A (mass 2.00 kg ) and B (mass 12.00 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.

Find the maximum energy stored in the spring bumpers.

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

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

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

Answer 1

Given is:-

initial velocities  

Now,

part-a

Maximum energy will be stored in the spring bumpers when springs are compressed by maximum. This happens when the blocks are moving with same velocity.

This common velocity can be found by conserving the momentum.

or

by plugging all the values we get

which gives us

Applying conservation of energy, the maximum energy stored in the spring bumbers is given by

or

by plugging all the values we get

which gives us

Part-b

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

Part-c

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

Part-d

That is coefficient of restitution

Also momentum is conserved.

Solving the above equations,

(This is the velocity of B after the block have moved apart)

(This is the velocity of A after the block have moved apart)