Question

The ballistic pendulum is a device used to measure the speed of a projectile such as a bullet. The projectile of mass m is fired into a large block of wood or other material of mass M which is suspended like a pendulum. As a result of the collision, the pendulum and projectile together swing up to a maximum height ℎ. Determine the relationship between the initial horizontal speed v of the projectile and the maximum height ℎ.

Answer 1

Answer:

Relation between initial speed of bullet and height h is given as

$v = \frac{m + M}{m}\sqrt{2gh}$

Explanation:

As we know that system of block and bullet swings up to height h after collision

So we have

$(m + M)gh = \frac{1}{2}(m + M)v_1^2$

so we have

$v_1 = \sqrt{2gh}$

so speed of the block + bullet just after the impact is given by above equation

Now we also know that there is no force on the system of bullet + block in the direction of motion

So we can use momentum conservation

$mv = (m + M)v_1$

now we have

$v = \frac{m + M}{m}\sqrt{2gh}$