ballistic pendulum

The ballistic pendulum is a device that determines the bullet velocity of a revolver.

The velocity of a revolver bullet can be determined using a device called a ballistic pendulum.

This device is composed of a block of mass M that is suspended by two strings of negligible mass.

The bullet of mass m and speed v, coming from a horizontal shot, will lodge in the block causing the assembly to be raised to a certain maximum height h.

By the law of conservation of motion, we have that: the moment before the collision is equal to the moment after the collision.
mv = (M+m).V where V is the speed of the assembly (block-bullet).
V = mv/M + m – equation I

After the bullet-block collision, the set gains speed and loses it as it gains height. At the maximum height (h), all the kinetic energy of the set is converted into gravitational potential energy. Therefore, we have that:
Ec = Epg
(M + m).V²/2 = (M + m).gh
Then: V =√(2.gh) – equation II

Equating equations I and II, we have:
mv/ M + m = √(2.gh)

v = [(M + m).√(2.gh)]/m

Schematic of a ballistic pendulum

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