# Conservation of Momentum

# The Exploding Meatball

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##

Problem:

A 10 kg meatball is sitting on a plate. Suddenly it explodes,
breaking up into two pieces. One piece has a mass of 4.0 kg and went
toward the right with a velocity of 21 m/s. What was the velocity of
the other piece?

## Solution:

If we consider the meatball from just before the explosion until
just after the explosion (before gravity and air resistance have time
to have much effect) we can consider the meatball to be an isolated
system. Therefore, the Law of Conservation of Momentum applies - so
how do you apply it?

- Make a diagram showing the "before explosion" and "after
explosion" situations.
- Write an expression for the total momentum in the system in
each situation.
- Invoke the Law of Conservation of Momentum by saying
p
_{after} = p_{before}".
- Solve the resulting equation.

This approach is used in the solution shown below:

So, the 6.0 kg piece of meatball left the scene with a speed of 14
m/s. The negative sign indicates direction - the 4.0 kg piece went to
the right (positive velocity) and the 6.0 kg piece went to the left
(negative velocity).

Once you "get the hang of it", applying the Law of Conservation of
Momentum to solve numerical problems is simple, straightforward, and
powerful. It is worth noting that you could not use Newton's
Laws to solve this problem, You do not know the forces acting
between the two chunks of meatball, so you can't use Newton's
Second Law to find the acceleration of the 6.0 kg chunk. Even if
you could somehow find its acceleration
(which you can't), you still can't use it to find the final velocity
of the chunk of meatball, since you don't know the time interval
during which the pieces accelerated. Part of the power of the Law of
Conservation of Momentum lies in the fact that you don't need to know
any of the details of the interactions within the system - as long as
the system is isolated (no outside forces and impulses) momentum will
be conserved.

BHS
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Physics -> Physics
1 -> Mechanics ->
Momentum -> this page

last update December 27, 2005 by JL
Stanbrough