Why is momentum conserved but kinetic energy lost in inelastic collisions?

[Crumbles]

I am having a bit of a conceptual problem with the conservation laws.

Consider a system of two bodies of mass m each. One moving at speed V1 towards the second body which is at rest.

For the case of an inelastic collision, I understand that the total kinetic energy of the system is not conserved but the total momentum of the system is.

What is bugging me is how can this be if both KE and the momentum, P depend on the mass and velocity of the body.

If the KE before and after the collision is different, how can the momentum which also depends on m and v be the same?

In the case of an inelastic collision, energy is lost to the surroundings: if momentum conservation stems from the conservation of energy, how can the momentum be conserved?

 

[dextercioby]

Nope,conservation of momentum is a direct consequence of Newton's principles applied to isolated systems.However,the conservation on energy is true only for a restrained class of systems,namely conservative systems,for which the interaction forces are derived from a potential field...Dissipative forces are not derived from a potential field.

Daniel.

 

[Doc Al]

For the case of an inelastic collision, I understand that the total kinetic energy of the system is not conserved but the total momentum of the system is.

Right.

What is bugging me is how can this be if both KE and the momentum, P depend on the mass and velocity of the body.

Two comments: (1) It's the momentum of the system that's conserved, not the momenta of each body. (2) KE and momentum depend on the velocites in very different ways: momentum is a vector while KE is a scalar. To find the momentum of a system of two bodies you need to add the individual momentum vectors of each; if they point in opposite directions, they can cancel each other. But to find the KE of a system of two bodies, just add the KE of each; they always add, never cancel.

If the KE before and after the collision is different, how can the momentum which also depends on m and v be the same?

See above.

In the case of an inelastic collision, energy is lost to the surroundings: if momentum conservation stems from the conservation of energy, how can the momentum be conserved?

Two more comments: (1) In an inelastic collision between two bodies, mechanical energy is "lost" to thermal energy, deformation, sound, etc. (2) Conservation of momentum does not stem from conservation of energy! They are independent.

 

[Crumbles]

Thanks for explaining this. I always thought that the law of conservation of momentum was from the law of conservation of energy.

 

[dextercioby]

At fundamental level (elementary particles) these laws go hand in hand,though...But classically,there are certain conditions which must be fulfilled.

Daniel.