IIT JEE , AIEEE Forum - Physics , Mechanics

sreejith.m.s

Aball of mass m is projected with a speed u in to a barrel of spring gun of mass M,initially at on frictinless surface. the mass m sticks in the barrel at the point of maximum compressin of the spring. what fraction of the KE of the ball is stored in the spring? neglect friction.

vikalp

The problem involves two concepts -

1. the conservation of linear momentum.

2. the conservation of energy .

But first we say that the system is our ball + barrel ....now as there is no external force acting on the system ( no friction) so we can conserve the linear momentum :

mu = (m+ M)v ..............................................................(1)

( letting the final velocity of the system be v)

1/2 mu²= 1/2 (m+M) v² + Z .........................................(2)

(letting the energy store in spring be denoted by Z)

so putting the values from eqn 1 to eqn 2 we can get ...

Z = 1/2 mu² [ M /m+M ]

or Z / (K.E)_i = M/M+m

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