Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!linus!decvax!decwrl!Glacier!oliveb!hplabs!sri-unix!MJackson.Wbst@Xerox.ARPA From: MJackson.Wbst@Xerox.ARPA Newsgroups: net.physics Subject: Re: Monkey Query Message-ID: <711@sri-arpa.ARPA> Date: Wed, 30-Oct-85 13:31:01 EST Article-I.D.: sri-arpa.711 Posted: Wed Oct 30 13:31:01 1985 Date-Received: Sun, 3-Nov-85 11:52:26 EST Lines: 40 Simple answers to these questions quickly get confounded in the ambiguity of "The Monkey. . .starts climbing the Rope." It is simplest if we take this to mean that the Monkey exerts a force Fm on the Rope which exceeds MG (where M is n Kg and G is the acceleration of gravity). Then by considering tension in the Rope it is clear that: If the Rope is massless and the Pulley is frictionless and massless then the Monkey and the Weight both accelerate upward at the same rate A = Fm/M - G. If the Pulley has friction (let us assume speed-independent friction Fp) then the Monkey accelerates upward faster than the Weight, which may not move at all. The Monkey's acceleration is as before and the Weight's acceleration is (Fm - Fp)/M - G [if Fm > MG + Fp], or zero [if Fm<= MG + Fp]. If the Rope has mass (let us assume mass per unit length R and total length L [Monkey and Weight are at opposite ends]) then the Monkey's acceleration is as before and the Weight's acceleration Aw is initially (Fm - MG)/(M + RL). However, as rope passes over the Pulley this increases the weight on the left (Monkey) side, which raises the rate of acceleration of Rope and Weight. If we denote the length of Rope on the left by X we have: (Fm - MG - LRG) + 2XRG = (M + RL)Aw and since Aw is also d(dX/dt)/dt the Rope acceleration increases exponentially until the Weight hits the Pulley. Note well the first paragraph. If one takes "The Monkey. . .starts climbing the Rope" to mean the Monkey begins moving with a fixed upward velocity with respect to the Rope then the answers may look somewhat different, and further specification of the "start-up conditions" (how did he accelerate to this velocity?) may be required. In particular, if the Rope has mass and is long enough the Monkey will eventually find himself *descending* under this interpretation. Loved your diagram, by the way. Mark