A ball of mass 0.25 kg is fired with velocity 160 m/s into the barrel of a sprin

Question

A ball of mass 0.25 kg is fired with velocity 160 m/s into the barrel of a spring gun of mass 2.1 kg initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. No energy is lost to friction. What fraction of the ball's initial kinetic energy is stored in the spring?

A ball of mass 0.25 kg is fired with velocity 160 m/s into the barrel of a spring gun of mass 2.1 kg initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. No energy is lost to friction. What fraction of the ball's initial kinetic energy is stored in the spring?

Explanation / Answer

let the maximum compression be x.so,

and the final velocity of the system be v.so,

m1v1=(m1+m2)*v2

so,

0.25*160=(0.25+2.1)*v

or v=17.02 m/s

now conserving energy,

0,5mv^2=0.5(m1+m2)v2^2+PE

or PE=0.5*0.25*160^2-0.5*(0.25+2.1)*17.02^2

=2859.63 J

so PE/KE=2859.63/(0.5*0.25*160*160)

=0.8936

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