You have been asked to design a \"ballistic spring system\" to measure the speed

Question

You have been asked to design a "ballistic spring system" to measure the speed of bullets. A spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass m is fired vertically upward into the bottom of the block. The spring's maximum compression d is measured. Find an expression for the bullet's speed v_{ m{B}}. What was the speed of a 12g bullet if the block's mass is 2.5kg and if the spring, with k = 57N/m , was compressed by 44cm ?

Explanation / Answer

mv = (M + m) v' 1/2(M+m)v'^2 = 1/2 kd^2 v' = d sqrt(k/(M+ m)) v = d*sqrt[k*(m+M)]/m v_B = 204.77 m/s

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