Blocks A (mass 3.00kg ) and B (mass 14.00kg ) move on a frictionless, horizontal

Question

Blocks A (mass 3.00kg ) and B (mass 14.00kg ) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 9.00m/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.

Part A

Find the maximum energy stored in the spring bumpers and the velocity of each block at that time.
Find the maximum energy.

Part B

Find the velocity of A.

Part C

Find the velocity of B.

Part D

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

Part E

Find the velocity of B.

Explanation / Answer

A)the collision will be perfectly elastic and the maximum compression will be at a point when they both have the same velcoity.so,

conserving momentum,

3*9=(3+14)*v

or v=1.588 m/s

so energy stored in the springs = 0.5*3*9^2 - 0.5*(3+14)*1.588^2

=100.065 Joules

B) velocity of A=1.588 m/s

C)velocty of B=1.588 m/s

D)now let the velcotiy of A be x and that of B be y.so, conserving momentum and energy,

3*9 = 3*x + 14*y

conserving energy,

0.5*3*9^2 = 0.5*3*x^2 + 0.5*14*y^2

solving ,we get x= -5.82 m/s

y=3.17 m/s

so velocity of A = -5.82 m/s

E)velocity of B = 3.17 m/s

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