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

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

`v = (m + M)/(m)√(2gh)`

Step-by-step explanation:

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

So we have

`(m + M)gh = (1)/(2)(m + M)v_1^2`

so we have

`v_1 = √(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 = (m + M)/(m)√(2gh)`