The ballistic pendulum is a device used to measure the speed of a fast-moving pr

Question

The ballistic pendulum is a device used to measure the speed of a fast-moving projectile such as a bullet. The bullet is fired into a large block of wood suspended from some light wires. The bullet is stopped by the block, and the entire system swings up to a height h. It is possible to obtain the initial speed of the bullet by measuring h and the two masses. As an example of the technique, assume that the mass of the bullet, m1, is 5.48 g, the mass of the pendulum, m2, is 1.022 kg, and h is 5.20 cm. Find the initial speed of the bullet, v1i.

Explanation / Answer

You solve this in two parts. First, you use conservation of momentum just before and just after the bullet impacts the block; m1v1 = (m1+m2)u "u" is the velocity of the block+bullet just after impact, while they are still essentially hanging straight down. Next, you use conservation of energy, taking the PE of block+bullet to be initially zero, but the KE is (1/2)(m1+m2)u^2. This equals the PE of block+bullet when it swings to maximum height "h" ; (1/2)(m1+m2)u^2 = (m1+m2)gh You now elliminate "u" from the two eqs and solve for v1; (1/2)[m1/(m1+m2)]^2v1^2 = gh v1 = [(m1+m2)/m1]SqRt(2gh) "v1" is now in terms of the known masses and height. Be sure to change height from cm to meters and bullet mass from grams to kg.

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