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March 29, 2017

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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?

  • physics - ,

    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.

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