In the figure, a ball of mass m = 60 g is shot with speed vi = 24 m/s (in the ne

Question

In the figure, a ball of mass m = 60 g is shot with speed vi = 24 m/s (in the negative direction of an x axis) into the barrel of a spring gun of mass M = 237 g initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. Assume that the increase in thermal energy due to friction between the ball and the barrel is negligible. (a) What is the speed of the spring gun after the ball stops in the barrel? (b) What fraction of the initial kinetic energy of the ball is stored in the spring?

Explanation / Answer

(a) the speed of the spring gun after the ball stops in the barrel is

Vf = mVi + MVf/m+M

= (60*24)/(60+237)

= 4.8 m/s

(b)

initial KE = 1/2 mVi^2 = 1/2*(0.06)(24)^2 = 17.28 J

final KE = 1/2 (m+M)Vf^2 = 1/2*(0.06+0.237)(4.8)^2 = 3.421 J

dKE =KEf-KEi = 3.421-17.28 = -13.8 J

fractional change =|dKE/KEi| = |13.8/17.28| = 0.798 or 79.8%

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