# Law of conservation of energy and law of conservation of momentum cannot both be true?

For example, lets assume there is an elastic collision between two balls. The first ball has a mass of 2 kg and an initial velocity of 4 m/s. The second ball has a mass of 4 kg and is at rest so it has an initial velocity of 0. Let's assume that after the collision, the first ball stops, and the second ball starts moving.

Then according to the law of conservation of momentum, the second ball should have a velocity of 2 m/s. But in order for the collision to be elastic, the second ball should have a velocity of √8 m/s.

How can both laws be true if they give different values for an elastic collision?

• " Let's assume that after the collision, the first ball stops, and the second ball starts moving." ...why did you assume that ? Dec 6, 2020 at 12:49
• Hence your assumption is wrong. Dec 6, 2020 at 12:50
• how do you know the assumption is wrong? And if so what would be the correct assumption? This happens when playing pool, and also in newton's cradle Dec 6, 2020 at 13:09
• Welcome to this community! Your assumption cannot be said to be wrong or right, it's underdetermined since you haven't told what your frame of reference is. Dec 6, 2020 at 13:16
• Does this answer your question? When to use Conservation of Energy vs Conservation of Momentum Dec 6, 2020 at 13:56

lets assume there is an elastic collision ... Let's assume that after the collision, the first ball stops

These two assumptions are incompatible. The fact that you are not finding a solution where both momentum and energy are conserved is a clear indication of the inconsistency of your assumption.

If you drop the first assumption then the physically correct solution is the one that conserved momentum and not energy. The change in energy is due to the fact that the collision is inelastic and represents a change in energy between kinetic energy and some other form of energy.

If you drop the second assumption then you use the conservation of energy to get one equation and the conservation of momentum to get another equation. Then you solve those two equations for the two unknown velocities.

• I'd like to add: the situation described in the question is actually possible – if the observer uses a non-inertial frame of reference. But in such a frame there there are additional inertial forces, and both balances of momentum and energy turn out to be satisfied anyway, taking these forces into account. Dec 6, 2020 at 13:14
• these two assumptions are not incompatible. Let's say for example the two balls had identical mass. The first ball stops and the second ball starts moving at the initial speed of the first ball. This is an elastic collision where momentum is also conserved Dec 6, 2020 at 13:16
• @Neelim but they don’t have the same mass in your problem. I guess you could have listed the mass as an assumption, but you didn’t.
– Dale
Dec 6, 2020 at 13:22
• I think any mass can be assumed here, there can be no wrong assumption. the result will change according to the mass Dec 6, 2020 at 13:23
• @Neelim The bottom line is that balance of momentum and energy are experimentally found to be true, from microphysics to macrophysics, from Newtonian mechanics to general relativity. Your example and reasoning have many unclear points. When everything is clarified you'll find that either your thought experiment is physically impossible, or else it satisfies the two balances. Dec 6, 2020 at 13:30