# An Alternate Solution Using Conservation of Energy

## Example 1: Finding the Velocity after an Inelastic Collision - One Object Initially At Rest

A 4.0-kg meatball is moving with a speed of 6.0 m/s directly toward a 2.0 kg meatball which is at rest. The two meatballs collide and stick together. What is their velocity immediately after the (inelastic) collision?

### Alternate Solution (Using Conservation of Momentum):

Since no external forces act on the two-meatball system, the system's momentum is conserved. The system's momentum before the collision is:

p_{before} = m_{1}v_{1} + m_{2}v_{2} = m_{1}v_{1}

and the system's momentum after the collision is:

p_{after} = (m_{1} + m_{2})v

If momentum is conserved, then:

p_{after} = p_{before}

(m_{1} + m_{2})v = m_{1}v_{1}

The velocity of the 6.0-kg meatball immediately after the collision is 4.0 m/s.

This is the "more traditional" solution to the problem.

*last update March 21, 2006 by JL Stanbrough*