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. What was the speed of a 10 g bullet if the block's mass is 2.1 kg and if the spring, with k = 54 N/m , was compressed by 44 cm ?

Answer 1

conservation of momentum

m*vi = (M+m)vf

vf = mvi/(M+m)

conservation of energy

1/2*(M+m)vf^2 = 1/2*kd^2

put the value of vf from above

1/2*(M+m)[mvi/(M+m)]^2 = 1/2*kd^2

vi = d*sqrt[(M+m)*k/m^2)

given = M = 2.1

m = 10g = 10x10^-3 kg

k = 54

d = 44 cm = 44 x 10^-2

vi = 469.67 m/s