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how can linear momentum be conserved in an inelastic collision?

Hey all I'm struggling to get my head round how linear momentum can be conserved in an inelastic collision, if kinetic energy is converted into other types of energy :confused:

Thanks for your help! :smile:

Reply 1

langlitz

Original post by ilovetuna

Hey all I'm struggling to get my head round how linear momentum can be conserved in an inelastic collision, if kinetic energy is converted into other types of energy :confused:

Thanks for your help! :smile:

Momentum is always conserved!
Inelastic or elastic only refers to how energy is converted not momentum

Reply 2

Stonebridge

Well both momentum and energy are conserved. They are two things that, for some reason, in the universe are always conserved.

With energy, kinetic energy is only part of the story, there are other forms, as you say yourself. So energy gets converted into other forms but the total energy is conserved. It's just difficult to track where it all went. (Heat, sound, potential energy of deformation etc)

In the case of momentum there is no "other form" for it to turn into so it just all stays as momentum.

Another thing to bear in mind is that momentum is a vector and energy is a scalar.
Two objects moving towards each other, for example, have kinetic energy and momentum.
Lets say the energy is 10J each. So the total is 20J
Let's say the momentum of the one is 10kgm/s so the other must be -10kgm/s because it's moving in the other direction.
The total is zero.

If the two objects crash, stick together and both stop, the total momentum at the end is still zero.
The kinetic energy goes from 20J to zero and gets converted into other forms. But the total afterwards is still 20J.
There is nothing mysterious about this. The numbers make sense.
You just have to remember that it's total energy that is conserved (that's the physical principle) and that kinetic energy isn't the whole story. There is no reason why it should be conserved.

The other thing to think about is that when two objects interact/collide they apply an equal and opposite force on each other. (Newton's 3rd Law) Let's say the force is F.

If they are in contact with each other for a time t then the objects each get an impulse Ft.
One gets Ft and the other -Ft as the forces are in the opposite direction. (Newton 3)

Force x time is change in momentum. (Impulse formula)
So the change in momentum of the one object is Ft and of the other is -Ft
The total change in momentum is Ft + (-Ft) which is zero.
Conclusion.
When the two interact, the total change in momentum is zero.
That is, momentum is conserved.

Hope this helps.

(edited 9 years ago)

Reply 3

Protoxylic

Ke is proportional to the square of the velocity whereas momentum is proportional to the velocity. Here you can see why momentum can be conserved in cases where Ke is not; specifically in those cases where objects coalesce.