# The Conservation of Momentum in a Completely Inelastic Collision.

## Homework Statement

A bullet with mass mA and velocity vA makes a completely inelastic collision with a still pendulum of mass B. After the collision, the pendulum swings to a height of y from its equilibrium with the bullet in it. In terms of y, mB and mA, what is the initial velocity?

My textbook says that momentum is not conserved because of the external forces of tension and gravity acting on the system; this makes sense to me. But, in my book's work, it gets the answer by using Pinitial = Pfinal, where the initial is the bullet's mass multiplied by its velocity, and the final momentum is both masses multiplied by their velocity in the +x direction. How can they say that momentum is not conserved and then use the conservative equation?

## The Attempt at a Solution

Doc Al
Mentor
My textbook says that momentum is not conserved because of the external forces of tension and gravity acting on the system; this makes sense to me.
In general, that's true.

But, in my book's work, it gets the answer by using Pinitial = Pfinal, where the initial is the bullet's mass multiplied by its velocity, and the final momentum is both masses multiplied by their velocity in the +x direction. How can they say that momentum is not conserved and then use the conservative equation?
During the collision one usually assumes that the forces of impact are so great, and act for so short a time, that other forces can be neglected. This is called the impulse approximation.

I think that the point being made is that DURING THE COLLISION (as Doc Al says) momentum is conserved.
After the collision you cannot use conservation of momentum to find the heigh 'y'.
You should use conservation of energy to find 'y' (KE = PE)

Oh I see.

Thanks for the replies