Blocks A (mass 6.50kg ) and B (mass 13.00kg ) move on a frictionless, horizontal

Question

Blocks A (mass 6.50kg ) and B (mass 13.00kg ) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 10.0m/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.

Ub =

Part B

Find the velocity of A.

vA =

Part C

Find the velocity of B.

vB =

Part D

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

vA =

Part E

Find the velocity of B.

vB =

Explanation / Answer

Total momentum = (6.50 kg)(10.00 m/s) = 65kg-m/s

After collision (elastic):

KE = 0.5 mv^2 = 3.25(100) = 325 J

325J = 3.25v1^2 + 7.5v2^2

m1v1 + m2v2 = 65 kg-m/s
------------------
v1 = 65/m1 - m2v2/m1

v1 = 10- 2.3v2

325J = 3.25 v1^2 + 7.5v2^2

325 J = 3.25(100 - 46v2 +5.3 v2^2)+ 7.5v2^2
325=325-149.5v2+24.725v2^2
24.725v2^2+149.5v2=0
v2=0
v2=-6.04 m/s

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