User talk:Laelele

Capstan
We do not need a separate artice: the proof of the capstan equation can be incorporated into capstan equation. &mdash; RHaworth (Talk | contribs) 15:44, 30 January 2009 (UTC)


 * Sorry about reverting you - I was trying to remove the example images and didn't mean to remove all your edits.-- Kubigula (talk) 03:35, 31 January 2009 (UTC)

The capstan equation derivation seem needlessly complex. Why not do it this way: Derivation of the Capstan Equation

The first step is to relate the radial or normal force F (Newtons/radian) of a rope wrapped around a capstan to the tension, T (Newtons), in the rope. This is classically done with a force balance method using vectors, trigonometry, and a little calculus. The answer can be found more simply with an energy argument as follows: Assume that the rope is inelastic (nonstretching) and the capstan is frictionless and compressible. Then the energy required to squeeze down the capstan radius R by an amount ∆R with one turn of rope equals the energy supplied by pulling the rope.

2 π ∆R F = 2 π ∆R T

Cancel 2 π ∆R on each side leaving F  =  T

Let the coefficient of friction between the rope and capstan be k = friction force/radial force. So the frictional force over a wrap angle d phi is

k F d phi = k T d phi

The increase in tension dT over an angle d phi is the frictional force over that angle so

dT = k T d phi

Divide both sides by T gives

dT / T = k d phi

Integrating both sides gives

Ln T = k phi + C

Exponentiate both sides to give

T = exp(k phi + C) = exp( C) exp( k phi)

For phi = 0   T = Tin so

Tout = Tin exp(k phi) 		QED EE483597 (talk) 00:08, 2 March 2015 (UTC)

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== Sa gaganapin na halalan bilang isang novel prize tittle holder, bimabati ko and nga mananalo sa gaganaping botohan kinabukasan umaasa ako na imaging tahimik at mapayapa ang aging halalan isang maagang pagbati para sa susunod na mga ihihirang. ==

Isang magandang pagbati para sa lahat at sa mga opisyal at sa mga residente ng nasasakupan, sikapin natin ang tahimik at mapayapang halalan isang parehas na kaganapan para sa kaayusan ng susunod na mga mamumuno Hindi lang sa Sweden at sa ibat ibang bansa na magaganap na halalan. Aking suporta at lubos niyo po maasahan ang aking suport sa abot ng aking kakayahan maraming salamt at god bless all. 112.203.26.193 (talk) 15:24, 30 April 2022 (UTC)

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