Question

a ball mass m=60g is shot with speed vi=22m/s into the barrel of a spring gum of mass M=240g initially a rest on a frictionless surface. the ball sticks in the barrel at the point of maximum compression of the spring. assum 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 friction of the initial kinetic energy of the ball is stored in the spring?

Answer 1

a)

Vf =(m/m+M)Vi =(0.06/0.06+0.24)*22

Vf=4.4 m/s

b)

KEi =(1/2)mVi^2= (1/2)*0.06*22^2 =14.52 J

KEf =(1/2)(m+M)Vf^2 =(1/2)*0.3*4.4^2 =2.904 J

dKE =KEf-KEi =-11.6 J

fractional change =|dKE/KEi| =|11.62/14.52| =0.8