A ball of mass 0.40 kg is fired with velocity 140 m/s into the barrel of a sprin

Question

A ball of mass 0.40 kg is fired with velocity 140 m/s into the barrel of a spring gun of mass 2.4 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 0.40 kg is fired with velocity 140 m/s into the barrel of a spring gun of mass 2.4 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

Momentum is conserved.

0.40 * 140 = 56 = (0.40 + 2.4 ) V

V(velocity of gun after ) = 56/ 2.8 = 20 m/s

Original KE = 0.5 . 0.40 . 140^2 = 3920 J

Final KE = 0.5 . 2.8 . 20^2 = 560J

"Lost " energy stored in spring = 3360 J

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