Question

A ballistic pendulum can be used to measure the speed of a projectile, such as a bullet. The ballistic pendulum consists of a stationary 2.50- kg block of wood suspended by a wire of negligible mass. A 0.0100- kg bullet is fired into the block, and the block (with the bullet in it) swings to a maximum height of 0.650 m above the initial position (see class note for drawing). Find the speed with which the bullet is fired, assuming that air resistance is negligible.

Answer 1

`v_1 = 896.35 m/s`

Step-by-step explanation:

As we know that bullet + pendulum system will move to the height of 0.650 m above the initial position

so here we can use energy conservation to find the speed just after the bullet hit the block

`mgh = (1)/(2)mv^2`

`v = √(2gh)`

`v = √(2(9.81)(0.650))`

`v = 3.57 m/s`

Now we can use momentum conservation to find the initial speed of the bullet

`m_1v_1 = (m_1 + m_2)v`

`0.0100 v_1 = (2.50 + 0.01)(3.57)`

`v_1 = 896.35 m/s`