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Collisions

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Question

A 50 g bullet moving with velocity 10 m/s strikes a block of mass 950 g at rest and gets embedded in it. The loss in kinetic energy will be (in %)

Moderate
Solution

Initial K.E. of system = K.E. of the bullet = 12mBvB2
By the law of conservation of linear momentum 
mBvB+0=msys.×vsys.
vsys.=mBvBmsys.=50×1050+950=0.5m/s
Fractional loss in K.E.  =  12mBvB212msys.vsys.212mBvB2
By substituting  mB=50×103kg,vB=10m/s
                      msys.=1kg,vs=0.5m/s we get 
Fractional loss =  95100    Percentage loss = 95%


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