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.

a) Find an expression for the bullet's speed in terms of k, d, M, m, and g.

b) What was the speed of a 13 g bullet if the block's mass is 2.5 kg and if the spring, with k = 50 N/m, was compressed by 48 cm?

Explanation / Answer

Given Mass of the bullet is m Mass of the block is M Spring constant is k a) Let the initial velocity of the bullet is v By using law of conservationof energy 1/2mv^2 = 1/2kd^2 + (M +m)gd v = (kd^2 + 2(M+m) gd) / M ---1 b) If m = 0.013 kg        M = 2.5 kg and k = 50 N/m        d = 0.48 m substitute the values in eq1 The speed of the bullet is     v = (50 N/m *(0.48m)^2 + 2(0.013 kg +2.5 kg) *9.8 m/s^2 *0.48 m / 2.5 kg     v =  3.75 m/s

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