Is there any possibility of a conflict between the conservation of momentum and the conservation of energy?

Question

Suppose that N sticky balls having masses m1, m2, m3, ... , mN are arranged about a point in space with various distances and in various directions.  The balls are all moving toward the point such that they will all arrive at the same moment. Since they are sticky balls, they will not rebound, but will adhere to each other in a lumpy cluster.

The amount of a particle's momentum is proportional to the speed to the first power, but the amount of a particle's kinetic energy is proportional to the speed squared.

Is it possible that the law of the conservation of momentum will require that the aggregate mass, after the collision of all the sticky balls, move in one direction, while the law of the conservation of energy will require it to move in a different direction?

stormfront105 · Accepted Answer

No. Momentum is always conserved in a closed system, while conservation of energy does not require kinetic energy to be conserved in an inelastic collision; it can be converted into other forms. There is no conflict between the two.

entropy · Answer

No. And, in fact, what you're referring to is an "inelastic collision." When object collide and stick together, Momentum MUST be conserved. However, there's no rule that says Kinetic Energy must be conserved.

This is just the case when objects collide and stick together. The Total Momentum before and after the collision is the same, but the Kinetic Energy is necessarily less, having been converted to another form of Energy.

Anonymous · Answer

I would say that there would most likely be a conflict if momentum and energy were both going out with the same mass.

rockEsquirrel · Answer

No, not a concern.

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Is there any possibility of a conflict between the conservation of momentum and the conservation of energy?

4 Answers