Average Force and Momentum

1. May 31, 2004

e(ho0n3

Hi everyone,

I'm having a hard time understanding this problem: A molecule of mass m and speed v strikes a wall at right angles and rebounds with the same speed. If molecules, all of this type, strike the wall at intervals a time t apart (on the average) what is the average force on the wall averaged over a long time.

What do they mean averaged over a long time? I don't even know how long the collision is.

e(ho0n3

2. May 31, 2004

HallsofIvy

Staff Emeritus

That's WHY they ask for the force "averaged over a long time". A molecule of mass m and speed v has momentum mv. If it rebounds with the same speed (but opposite velocity) then it has momentum -mv: a total change in momentum of 2mv. That's the "impulse" the wall has imparted to it and the impulse the molecule imparts to the wall ("for every action there is an equal and opposite reaction").
v Since a molecule strikes the wall at "time t apart (on the average)", in a long time T, approximately T/t molecules will strike the wall and those molecules will impart a total impulse of (T/t)(2mv) to the wall. Now, what is the relationship between "impulse" and "force"?

3. May 31, 2004

e(ho0n3

I think I see what you're getting at. So,
$$\frac{T}{t}2mv = \int_{0}^{T}{F dt}$$
Then the average force is
$$\frac{1}{T}\int_{0}^{T}{F dt}=\frac{2mv}{t}$$

I guess I wasn't thinking in terms of the TOTAL impulse on the wall since the impulse occurs only during the strikes. The more of these physics problems I do, the dumber I seem to get.

Thanks,
e(ho0n3