Originally Posted By: paul
why dont you simply tell me what you think the answers are
then see if I agree to them.

I have told you and you don't agree. There really is no point going anywhere beyond this point until you understand how much momentum is transferred from an object that does a U-turn.

The answer to Q3 is -2000
We can verify this with:
Initial momentum + change in momentum = final momentum
1000 + -2000 = -1000


we can keep dilly dallying around with examples but using the pipe example would be best.

I agree.

Acceleration of one mass:
500N for 7.8s = impulse of 3900 Ns -> gives the mass a momentum of 3900 kgm/s and the pipe -3900 kgm/s.


Turnaround of one mass:
a velocity of 39.0385 m/s
3903.85 N = 100 kg * 39.0385 m/s

This is the magnitude of the force that would deccelerate 100kg from 39.0m/s to 0 in 1 second. The mass then has to speed up again from 0 to 39m/s in the other direction, so this force is applied for 2 seconds.

Impulse applied to the mass = -3903.85N * 2s = -7808 Ns
This reduces the mass's momentum by 7808 kgm/s and increases the pipe's by 7808 kgm/s


at any time durring acceleration the 20 masses being pushed by the 500 kg-m/s/s or 500N are pushing back on the pipe with the same force with a combined force of 500N * 20 = 10000N

So over 7.8s there's:
10000N pushing one way, impulse = 78000 Ns
and 20 masses doing U-turns, which is 20 * 7808 Ns = 156200Ns in the opposite direction.

The overall force on the pipe is continuously in the opposite direction to what the accelerations should cause. So the pipe's moving backwards.

What about the other U-bend bringing it back to the proper direction? I'm starting to get confused about where all the masses are. While that acceleration was occuring, there were 20 floaters, entering the 2nd u-bend one-by-one? These would go back into the accelerator at some speed - but that's impossible because we specified 20 masses accelerating from 0, not from 39m/s. I'm losing the ability to visualize it. Could you possibly draw a time-sequence of events?

Edited by kallog (06/21/10 10:55 PM)