A 64g ball is shot into the barrel of a spring-gun with a speed of 24m/s. The sp

Question

A 64g ball is shot into the barrel of a spring-gun with a speed of 24m/s. The spring-gun has a mass of 280g and is initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. Assume that friction between the ball and the barrel is negligible. Note that momentum is conserved as the ball becomes stuck in the spring gun because the net-force on the system containing both the ball and the spring gun is zero. What is the change in the kinetic energy of the ball and the spring gun ?

Explanation / Answer

Speed of the ball and spring gun after sticking

using law of conservation of momentum

m1*u1 + 0 = (m1+m2)*v

64*24 = (64+280)*v

v = 0.255 m/s

then change in kinetic energy is dK = (0.5)(0.064+0.280)*(0.255^2) = 0.0111843 J

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