A 5 g bullet is fired into a 2 kg wooden block attached to a spring with a force constant of 20 N/m. It lodges in the block, and the block and bullet compress the spring until they come to a rest. If the bullet was moving at 1000 m/s just before the collision, how far is the spring compressed when the bullet and block stop?

Question

A 5 g bullet is fired into a 2 kg wooden block attached to a spring with a force constant of 20 N/m.  It lodges in the block, and the block and bullet compress the spring until they come to a rest.  If the bullet was moving at 1000 m/s just before the collision, how far is the spring compressed when the bullet and block stop?

Elena · Answer

m1•v =(m1+m2)u, u=m1•v/(m1+m2). (m1+m2)u²/2=kx²/2, x=u•sqrt[(m1+m2)/k}= = m1•v•sqrt[(m1+m2)/k}/(m1+m2)= =m1•v/sqrt[k•(m1+m2)]= =0.005•1000/sqrt[20(2+0.005)]=3.53 m.