Momentum conservation - falling object

jsmith613

If an object falls there are two ways to consider momentum conservation

Way 1:
The system involves just the object therefore the gravitational force is an EXTERNAL force so momentum is NOT conserved

Way 2:
The system involves object and earth. The increase in momentum of the object down = increase in momentum of earth up (therefore momentum is conserved)

Is this correct?

Doc Al

Perfectly correct.

jsmith613

ok so when we have a falling ball that reaches terminal velocity would I be correct in thinking momentum is NOT conserved because of the EXTERNAL force of air resistance?

Doc Al

Not sure what you mean. If something falling has reached terminal velocity, that means the net force on it is zero. It's moving at constant velocity. The momentum's not changing.

There are two external forces acting, which cancel each other: gravity and air resistance.

jsmith613

ok then before terminal velocity the momentum is falling because of air resistance...in this case as it APPROACHES terminal velocity, momentum is NOT conserved because of the external force AIR resistance..is that more correct?

Doc Al

Momentum is not conserved because there's a net force on the body, even without air resistance. Gravity is an external force also.

jsmith613

but i though we said that from "way 2" gravity is not an external force because we can consider the earth and ball as one system...that;s why momentum is conserved in way 2??

denjay

In your case of terminal velocity, there is an external force of the air on the falling object. In the 2nd scenario, there was no air resistance therefore no external force. IF you consider the object, earth (gravity), and air (resistance) as a single system, momentum is conserved as the object is impacting the molecules in the air which push back on the object.

Doc Al

I didn't realize you were talking about 'way 2'. In any case, why is the air not considered as part of the earth?

denjay

I believe he meant the earth as something that produces gravity. The atmosphere is usually not considered when thinking of gravity.

jsmith613

ok so your saying that using "Way 2" momentum is ALWAYS conserved (regardless of air-resistance / gravity) for falling objects

Doc Al

It depends on what you are consider as your system.

If your system is ball + earth (including air), then there are no external forces and total momentum is conserved.

But if your system is ball + earth (excluding air), then there are external forces and total momentum of that system is not necessarily conserved.

jsmith613

so I doubt I would be asked a question like this in an exam UNLESS it is clearly stated what is and what is not part of the system...right?

e.g: system is earth and ball ONLY means air is an external force...

Doc Al

Right. If they ask whether momentum is conserved they must specify the system they are considering, if there is any possibility of confusion.

jsmith613

thanks alot for you help :)

Khashishi

If you consider the momentum of the Earth and air and ball together, it will be conserved. If something if falling in air, then it's pushing some parcels of air down with it.

Ken G

A concise way to say this is that momentum is always conserved in a closed system, which just means including everything that is exerting forces on each other as part of the same system. It's all how you regard the system, and it should be clear in any question, but often there is value in breaking up the system into parts. When you do that, the concept of conservation of momentum means you are only "moving momentum around" from one part to another, just like with energy conservation (except bear in mind that momentum has a direction and energy doesn't).