In the figure, a ball of mass m = 60 g is shot with speed v_1 = 19 m/s (in negat

Question

In the figure, a ball of mass m = 60 g is shot with speed v_1 = 19 m/s (in negative direction of an x axis) into the barrel of a spring gun of mass M = 226 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 increases in thermal energy due to friction between the ball and there 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) Conseving momentum

mu = Mv

60*19 = (226+60)*v

v = 3.99 m/s

b) Conserving energy

0.5mu^2 = 0.5(M+m)v^2 + SE

Let spring energy be SE

0.5*60*19^2 = 0.5*(226+60)*3.99^2 + SE

SE = 8558 units

SE/KE_i = 0.79

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