Blocks A (mass 2.00 kg) and B (mass 10.00 kg) move on a frictionless, horizontal

Question

Blocks A (mass 2.00 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 2.00 m/s. The blocks are equipped with ideal spring bumpers, as in Example 8.10 (Section 8.4). The collision is head-on, so all motion before and after the collision is along a straight line. (a) Find the maximum energy stored in the spring bumpers and the velocity of each block ad that time. (b) Find the velocity of each block after they have moved apart.

Explanation / Answer

Given,

Mass od block A = m1 = 2 kg and that of B = m2 = 10 Kg

Speed of block A = v1 = 2.00 m/s

The intial P of the system is due to the block 1 only as B is in rest, so we have as per the law of conservation of linear momentum,

P(intial) = P(final)

m1v1 = (m1+m2)V

2 x 2 = (2+10) V

so we get V = 4/12 = 0.33 m/s

both the blocks will have same velocity of 0.33 m/s

Energy stored will be the KEof block 1 - KE afterwards

E = 1/2m1v12 - 1/2(m1+m2)V2 =.5 x 2 x 4 - .5 x 12 x .1089

E = 3.35 Joules

Part(b)

The velocity with whcih each block is moving apart be va2 and vb2 will be given by :

va2 = (m1-m2)v1/(m1+m2)

va2 = 16/12 = 1.33 m/s

vb2 = 2m1v1 / (m1+m2) = 2x2x2 / 12 = 0.67m/s

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