A ballistic pendulum, as shown in the figure, was a device used in the past cent

Question

A ballistic pendulum, as shown in the figure, was a device used in the past century to measure the speed of bullets. The pendulum consists of a large block of wood suspended from long wires. Initially, the pendulum is at rest. The bullet strikes the block horizontally and remains stuck in it. The impact of the bullet puts the block in motion, causing it to swing upward to a height h. If the bullet has a mass of 11.5 g, and the block of mass 3.7 kg swings up to a height of h = 45.000 cm, what was the speed of the bullet before impact?

Explanation / Answer

Let v be the speed of the bullet before impact.

Use conservation of energy to find the speed of the block and bullet after impact:
KEi = PEf
(1/2)(M+m)v'^2 = (M+m)gh
v' = sqrt(2gh)

Use conservation of momentum to find the speed of the bullet and the block before impact:
pi = pf
mv = (M+m)v'
mv = (M+m)sqrt(2gh)
v = [(M+m)/m]sqrt(2gh)
v = [((3.7 kg)+(11.5x10^-3 kg))/(11.5x10^-3 kg)]sqrt[2(9.81 m/s^2)(0.45 m)]
v = 958.975 m/s

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