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Conservation of momentum but not kinetic energy

I was wondering how this is possible by considering the equation for momentum being mv. Surely if kinetic energy was decreased, the velocity would have to also be decreased, and thus so momentum? Maybe I'm using this equation in the wrong way, or the kinetic energy comes from the internal energy or something....
Original post by Rehabilax
I was wondering how this is possible by considering the equation for momentum being mv. Surely if kinetic energy was decreased, the velocity would have to also be decreased, and thus so momentum? Maybe I'm using this equation in the wrong way, or the kinetic energy comes from the internal energy or something....



Conservation of kinetic energy or momentum doesn't mean that the ke or momentum of a particular object doesn't change.
It applies to a system of two or more interacting objects.
It's the total ke or momentum, of all the interacting objects, that is being considered.

Kinetic energy is not always conserved in a collision. The ke of both objects will change. The total ke of the objects will only be conserved if the collision is perfectly elastic. ke is normally lost as heat in collisions.

On the other hand, momentum is always conserved for the whole system. The momentum of the individual bodies will change but the total remains constant.

So yes. If the ke of an object changes because v changes, so does its momentum. But that's not what conservation means.
(edited 9 years ago)
Reply 2
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Rehabilax
OP
Ok, so if we consider a situation where two objects collide in an inelastic collision they lose kinetic energy as a system (to heat, sound etc). If we then measure the mass and velocity of these two objects after the collision to calculate the total momentum of the system, surely it would be less than the total momentum of the system before the collision? I'm sorry if I'm missing something, but I don't understand the principle in this situation.
Original post by Rehabilax
Ok, so if we consider a situation where two objects collide in an inelastic collision they lose kinetic energy as a system (to heat, sound etc). If we then measure the mass and velocity of these two objects after the collision to calculate the total momentum of the system, surely it would be less than the total momentum of the system before the collision? I'm sorry if I'm missing something, but I don't understand the principle in this situation.


Two objects of equal mass collide head on and both stop.
Before the collision they both have ke.
After the collision they have none.
All ke is lost for the individual objects and the system.

Before the collision they both had momentum.
Object A had, say, mv
Object B, moving in the opposite direction, had -mv

Before collision total momentum was mv + (-mv) = 0
After collision momentum = 0

The point you are missing is that momentum is a vector.
ke is not.
Momentum is always conserved.
The only way this collision situation could have taken place as it did is for both objects to have had the same mass and equal and opposite velocities at the start. This ensures conservation of momentum.
Reply 4
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Rehabilax
OP
Ah ok, thanks a lot! :smile:

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