A ballistic pendulum is a device used to measure the speed of a bullet. A bullet of mass m is fired at a block of wood (mass M) hanging from a string. The bullet embeds itself in the block, and causes the combined block plus bullet system to swing up a height h. What is v_o, the speed of the bullet before it hits the block?

Work backwards, starting with the swing of the pendulum just after the collision until it reaches its maximum height. Conservation of mechanical energy applies here, so:

½ (m+M)v_f² = (m+M)gh.

So, the speed of the system immediately after the collision is:

v_f = (2gh)^½

Apply conservation of momentum to determine the relationship between v_f and the bullet's speed before the collision. The wood block is stationary before the collision.

Momentum before the collision = momentum after the collision

mv_o = (m+M)v_f

Therefore

vo

=

M + m m

(2gh)½

Take the case where m = 30 g, M = 870 g, h = 0.74 m. This gives:

v_o = 114 m/s.