# B Conservation of Momentum with Friction?

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1. Oct 18, 2016

### Robzoid

When reading lessons on the conservation of momentum, you usually see examples with colliding balls or something to that effect. These examples always seem to fail to mention friction. These balls will always come to a stop due to friction. How is momentum conserved when it is lost to friction? In a system of with an initial net momentum, where does the momentum go once the momentum of all the macro-cosmic objects is reduced, by friction, to 0?

I know momentum is conserved for closed systems. Many people might simply say that the friction is an external force. However, you should be able to choose your system so that it includes the source of friction.

Part of me wants to say that the momentum dissipates into the microscopic movement of the atoms in the surface which caused the friction. However, I've also heard that the momentum vector of atoms cancel out as a result of friction.

Any help will be greatly appreciated it. I've been racking my brain about this one for the past few days.

2. Oct 18, 2016

### PhanthomJay

If you don't consider friction as an external force, then the earth must be considered as part of your system. Momentum of the object that is lost is gained by the earth, speeding it up by a wee bit. Otherwise, if you don't consider the earth as part of the system, momentum is not conserved when friction or any external force is acting, rather, momentum is changed , per newtons 2nd law.

3. Oct 18, 2016

### Staff: Mentor

Consider two blocks, one on top of the other. Initially the lower block is at rest and the upper block is sliding along the top surface of the lower block. Three is a force from friction acting to slow the upper block. But by Newton's third law there is an equal and opposite force on the lower block so it accelerates. Thus when the upper block comes to rest relative to the lower block neither block is at rest; both are moving at the same speed and their combined momentum is equal to the initial momentum of the upper block.

That's a closed-system analysis. If the mass of the lower block is very much larger than that of the upper block (for example, the lower block is the planet earth and the upper block is some object that I've been carrying around) it's easier to consider the lower block as immobile and treat the upper block as an open system.