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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?
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?
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.
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