gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (11/03/85)
The monkey, rope, pulley, weight system is inherently UNSTABLE, so that whether the monkey or the weight rises fastest is critically dependent on initial conditions. It is funny to watch so many people try to defend one of the many possible outcomes as being the one true answer.
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (11/10/85)
Having allowed sufficient time for readers to ponder system instability, now I wish to observe that there is a finite characteristic time for the evolution of the instability (on the order of sqrt(2*h/g), where h is the distance to the pulley and g is as usual the gravitational acceleration; more if the angular momentum of the pulley is substantial), so if the monkey climbs sufficiently fast he can be assured of reaching the top before the counterweight does. For sufficiently fast climbing rate, the position of the counterweight at the end of the monkey's climb is dependent on variables such as rope density and moment of inertia of the pulley. If these are appreciable, the counterweight will remain at its initial position (except to the extent that the system instability has procgressed). If the monkey climbs much more slowly than the characteristic time for system collapse, then the experimental outcome is ill-determined. The in-between behavior could be interesting..
mcewan@uiucdcs.CS.UIUC.EDU (11/13/85)
> Having allowed sufficient time for readers to > ponder system instability, now I wish to observe > that there is a finite characteristic time for > the evolution of the instability (on the order > of sqrt(2*h/g), where h is the distance to the > pulley and g is as usual the gravitational > acceleration; more if the angular momentum of > the pulley is substantial), so if the monkey > climbs sufficiently fast he can be assured of > reaching the top before the counterweight does. > > For sufficiently fast climbing rate, the > position of the counterweight at the end of > the monkey's climb is dependent on variables > such as rope density and moment of inertia of > the pulley. If these are appreciable, the > counterweight will remain at its initial > position (except to the extent that the system > instability has procgressed). > > If the monkey climbs much more slowly than the > characteristic time for system collapse, then > the experimental outcome is ill-determined. > > The in-between behavior could be interesting.. Well, I pondered, and came to the conclusion that you can't read very well. Re-read the statement of the problem - the system is NOT unstable, the angular momentum of the pulley, the density of the rope, and the moment of intertia of the pulley are all ZERO. The key words are: MASSLESS rope, MASSLESS, FRICTIONLESS pulley. Scott McEwan {ihnp4,pur-ee}!uiucdcs!mcewan "A flash in front of my eyes ... I blink ... open my eyes to ... discover I am a dog in a pickup truck full of garbage ... no one but me sees the lid blow off the can ... it's 14 miles to the dump ... this is ... at last ... heaven."
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (11/15/85)
> Well, I pondered, and came to the conclusion that you can't read very well. > Re-read the statement of the problem - the system is NOT unstable, the > angular momentum of the pulley, the density of the rope, and the moment of > intertia of the pulley are all ZERO. The key words are: MASSLESS rope, > MASSLESS, FRICTIONLESS pulley. I read just fine; my first (of two) postings acknowledged the original statement of the problem. THAT IS EXACTLY THE SYSTEM THAT IS UNSTABLE. My consideration of actual physics instead of unrealizable idealizations is an attempt at "symmetry breaking", to make the problem attain a well-determined solution. After all, this is net.physics, not net.puzzle.
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (11/15/85)
In case it is still not clear what I mean by unstable, in the idealized monkey experiment, assuming the monkey is a very slow climber, if you were to perform the experiment 10,000 times, the monkey would reach the top before the counterweight 5,000 (plus or minus 100) times, the counterweight would get there first in all the other cases, and the two would never reach the top simultaneously. Does that help? (That's what you get for postulating such silly conditions in such delicate balance.)