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## Homework Statement

A small block m=4kg and a large block m=12kg have a head on collision on a frictionless table. Before the collision, the small block is traveling 8m/s to the right and the large block is traveling 4m/s to the left.

A. If the small block bounces back at 3m/s to the left, find the final velocity of the large block.

B. Suppose instead the two blocks stick together after they collide. How many Joules of energy would be lost?

## Homework Equations

[tex]p=mv[/tex]

[tex]KE=\frac{1}{2}mv^{2}[/tex]

## The Attempt at a Solution

I will define to the right to be the positive x direction.

First I will calculate initial momentum for both blocks.

[tex]p_{i a}=mv[/tex]

[tex]p_{i a}=(4kg)(8m/s)[/tex]

[tex]p_{i a}=32kg m/s[/tex]

[tex]p_{i b}=mv[/tex]

[tex]p_{i b}=(12kg)(-4m/s)[/tex]

[tex]p_{i b}=-48kg m/s[/tex]

[tex]p_{i}=-16kg m/s[/tex]

Now final momentum:

[tex]p_{f a}=mv[/tex]

[tex]p_{f a}=(4kg)(-3m/s)[/tex]

[tex]p_{f a}=-12kg m/s[/tex]

[tex]p_{f b}=mv[/tex]

[tex]p_{f b}=(12kg)v[/tex]

[tex]p_{f b}=12v[/tex]

[tex]p_{f}=-12kg m/s + 12v[/tex]

If momentum is conserved, then

[tex]p_{i}=p_{f}[/tex]

[tex]-16kg m/s=-12kg m/s + 12v[/tex]

[tex]v=\frac{-1}{3}[/tex]