Why is momentum conserved in collisions but not for a rolling ball with friction?

[ShizukaSm]

Regarding momentum, and the "Law of conservation of linear momentum", my book states that it's more general than mechanical energy, since mechanical energy is only conserved for conservative forces, while linear momentum is conserved independent of the forces, as long as the sum of external forces is zero.

This really confuses me. Let's look at two situations:

Situation 1) Collision. When a collision between two balls occur, a vibration in the air is produced (the sound wave) which wastes a part of the energy, and thus mechanical energy isn't conserved. On the other hand, there are no external forces, so momentum is conserved.

Is this reasoning correct?

Situation 2) A ball is rolling on a table. There is friction. Ok, so, let's pick up our system as ball + table, in this case our momentum would be (Ball Momentum = x and Table momentum = 0), the friction force would be internal to the system, and yet we would lose momentum.
Now, for the mechanical energy part, friction would produce a certain heat, which would waste energy, and thus mechanical energy would also be reduced.

Is my second reasoning correct? And also, why isn't momentum conserved?

 

[voko]

In the second case, momentum is conserved. Friction transfers the ball's momentum to the table, it does not just disappear.

 

[ShizukaSm]

How come? The table won't move, it's velocity will remain as 0.

 

[Doc Al]

The table won't move, it's velocity will remain as 0.

The table is attached to the earth. External forces come into play.

 

[ShizukaSm]

The table is attached to the earth. External forces come into play.

Fair enough, this will maybe seen stupid, but I really want to understand that, so let's pick up the system (earth + ball), in this case Earth's forces on the table would be internal to the system.

 

[Doc Al]

Fair enough, this will maybe seen stupid, but I really want to understand that, so let's pick up the system (earth + ball), in this case Earth's forces on the table would be internal to the system.

Sure. If you include everything, then the total momentum will be conserved.

 

[voko]

How come? The table won't move, it's velocity will remain as 0.

Why would the table not move? It is much like the ball itself, it is just bigger, but still it is on some surface and there is friction in between. It will get some momentum, but because it so much heavier than the ball, its velocity will be very small, and its momentum will be transferred to the surface it is on very quickly.