# Momentum must be conserved, so this is true, right?

#### StephenDoty

True or False:
In a collision between a light hydrogen molecule and a heavy water molecule, the momentum lost by one molecule is exactly the same as the momentum gained by the other molecule.

Momentum must be conserved, so this is true, right???

#### Nabeshin

In physics, momentum is always conserved. You just have to think about two things. A) Is the system being considered closed? and B) What happens as a result of momentum conservation.

#### StephenDoty

It seems to be a closed system to me

so isnt the momentum conserved making this true

so i can make sure I have this concept:
as a stone slides down a frictionless hill its mechanical energy is conserved but its momentum is not. true or false

well since we are not given any info on the velocity at the beginning or end and since the velocity is constantly changing we cannot make any assumptions about momentum thus this statement is true.

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#### Nabeshin

Well we know velocity is increasing, and p=mv, so momentum is increasing. Like I said, momentum is always conserved, so an equal amount has to come from somewhere else.

#### StephenDoty

so the first one is true and the second one is false?????

#### D H

Staff Emeritus
Like I said, momentum is always conserved, so an equal amount has to come from somewhere else.
Momentum is not always conserved. Momentum is conserved in a closed system, but not in an open system (i.e., one with external forces acting on it).

#### alphysicist

Homework Helper
Hi StephenDoty,

Both of your true/false statements are true. As the stone slides down the hill, its momentum increases, so its momentum is not conserved.

Deciding on whether momentum is conserved or not depends critically on what your system is. If there are no forces on the system from outside the system, then momentum is conserved. If there is a net force acting on the system from the outside, then the momentum will change with time.

So for the stone going down the hill, the wording of the question means that we want to consider the stone by itself as the system. There is a net outside force (the force from the earth), so momentum is not conserved for the stone.

Momentum is conserved if we had chosen (stone+earth) as a system. The change in the stone's momentum is equal in magnitude and opposite in direction to the change in the earth's momentum. (The earth pulls on the stone and the stone pulls on the earth, in addition to the action/reaction normal forces between stone and hill.) The momentum of (stone+earth) is conserved as the stone slides down the hill.

#### StephenDoty

good i have the concept then

thank you

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