Originally Posted By: paul

you have never added a direction to velocity , normaly
when you see velocity written down you do not also see
a direction.


All the time I've been treating it as a 1-dimensional system, so there are only 2 directions. I used +/- to indicate these - a 1-dimensional vector is just a number which can be either positive or negative so that's how I wrote them. If you consider it as 3D then it's the same except all the vector quantities are just the x-components of the 3D vectors. You can ignore the y and z components because any forces in those directions do nothing to the motion of the pipe along its length. The geometry can be set up so they cancel out anyway.


Quote:

accelerated from 0 m/s to 50 m/s/North
50 m/s/Left
50 m/s/South
50 m/s/Right


That hides important accelerations:
accelerated from 0 m/s to 50 m/s/North
accelerated from 50m/s/North to 50 m/s/Left
accelerated from 50m/s/Left to 50 m/s/South
accelerated from 50m/s/South to 50 m/s/Right

But it's sufficient to consider only 1 component of velocity for our purposes. That makes it much much simpler.

If you don't like the 1D simplification, then just replace the u-bends with springs. I've been treating them the same as springs all the way through.

Quote:

please explain this fantasy of yours , how does the turnaround provide even more force?


The force at the turnaround is determined by the mass's speed. Each time round it gets faster so applies more force. Even if you switch off the accelerator the mass will keep going round applying high forces at each turnaround, despite the accelerator's force being zero.

I've written out all the equations ages ago. You can go back and find them if you want.


Edited by kallog (06/24/10 01:02 PM)