We do not need a separate artice: the proof of the capstan equation can be incorporated into capstan equation. — RHaworth ( Talk | contribs) 15:44, 30 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)
Your upload of File:Capstan eqn2.png or contribution to its description is noted, and thanks (even if belatedly) for your contribution. In order to help make better use of the media, an attempt has been made by an automated process to identify and add certain information to the media's description page.
This notification is placed on your talk page because a bot has identified you either as the uploader of the file, or as a contributor to its metadata. It would be appreciated if you could carefully review the information the bot added. To opt out of these notifications, please follow the instructions here. Thanks! Message delivered by Theo's Little Bot ( opt-out) 15:04, 11 March 2014 (UTC)
Hi,
You appear to be eligible to vote in the current
Arbitration Committee election. The
Arbitration Committee is the panel of editors responsible for conducting the Wikipedia
arbitration process. It has the authority to enact binding solutions for disputes between editors, primarily related to serious behavioural issues that the community has been unable to resolve. This includes the ability to impose
site bans,
topic bans, editing restrictions, and other measures needed to maintain our editing environment. The
arbitration policy describes the Committee's roles and responsibilities in greater detail. If you wish to participate, you are welcome to
review the candidates' statements and submit your choices on
the voting page. For the Election committee,
MediaWiki message delivery (
talk)
14:00, 24 November 2015 (UTC)
Hi,
You appear to be eligible to vote in the current
Arbitration Committee election. The
Arbitration Committee is the panel of editors responsible for conducting the Wikipedia
arbitration process. It has the authority to enact binding solutions for disputes between editors, primarily related to serious behavioural issues that the community has been unable to resolve. This includes the ability to impose
site bans,
topic bans, editing restrictions, and other measures needed to maintain our editing environment. The
arbitration policy describes the Committee's roles and responsibilities in greater detail. If you wish to participate, you are welcome to
review the candidates' statements and submit your choices on
the voting page. For the Election committee,
MediaWiki message delivery (
talk)
14:06, 24 November 2015 (UTC)
The file File:Capstan eqn2.png has been proposed for deletion because of the following concern:
unused, low-res, no obvious use
While all constructive contributions to Wikipedia are appreciated, pages may be deleted for any of several reasons.
You may prevent the proposed deletion by removing the {{proposed deletion/dated files}}
notice, but please explain why in your
edit summary or on
the file's talk page.
Please consider addressing the issues raised. Removing {{proposed deletion/dated files}}
will stop the
proposed deletion process, but other
deletion processes exist. In particular, the
speedy deletion process can result in deletion without discussion, and
files for discussion allows discussion to reach
consensus for deletion.
This bot DID NOT nominate any file(s) for deletion; please refer to the page history of each individual file for details. Thanks, FastilyBot ( talk) 01:01, 2 April 2020 (UTC)
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)
The file File:Laelelenr1 2009.png has been proposed for deletion because of the following concern:
Unused. Superseded by File:Capstan-derivation-diagram.svg.
While all constructive contributions to Wikipedia are appreciated, pages may be deleted for any of several reasons.
You may prevent the proposed deletion by removing the {{proposed deletion/dated files}}
notice, but please explain why in your
edit summary or on
the file's talk page.
Please consider addressing the issues raised. Removing {{proposed deletion/dated files}}
will stop the
proposed deletion process, but other
deletion processes exist. In particular, the
speedy deletion process can result in deletion without discussion, and
files for discussion allows discussion to reach
consensus for deletion. --
Minorax«¦
talk¦»
23:54, 5 August 2022 (UTC)
We do not need a separate artice: the proof of the capstan equation can be incorporated into capstan equation. — RHaworth ( Talk | contribs) 15:44, 30 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)
Your upload of File:Capstan eqn2.png or contribution to its description is noted, and thanks (even if belatedly) for your contribution. In order to help make better use of the media, an attempt has been made by an automated process to identify and add certain information to the media's description page.
This notification is placed on your talk page because a bot has identified you either as the uploader of the file, or as a contributor to its metadata. It would be appreciated if you could carefully review the information the bot added. To opt out of these notifications, please follow the instructions here. Thanks! Message delivered by Theo's Little Bot ( opt-out) 15:04, 11 March 2014 (UTC)
Hi,
You appear to be eligible to vote in the current
Arbitration Committee election. The
Arbitration Committee is the panel of editors responsible for conducting the Wikipedia
arbitration process. It has the authority to enact binding solutions for disputes between editors, primarily related to serious behavioural issues that the community has been unable to resolve. This includes the ability to impose
site bans,
topic bans, editing restrictions, and other measures needed to maintain our editing environment. The
arbitration policy describes the Committee's roles and responsibilities in greater detail. If you wish to participate, you are welcome to
review the candidates' statements and submit your choices on
the voting page. For the Election committee,
MediaWiki message delivery (
talk)
14:00, 24 November 2015 (UTC)
Hi,
You appear to be eligible to vote in the current
Arbitration Committee election. The
Arbitration Committee is the panel of editors responsible for conducting the Wikipedia
arbitration process. It has the authority to enact binding solutions for disputes between editors, primarily related to serious behavioural issues that the community has been unable to resolve. This includes the ability to impose
site bans,
topic bans, editing restrictions, and other measures needed to maintain our editing environment. The
arbitration policy describes the Committee's roles and responsibilities in greater detail. If you wish to participate, you are welcome to
review the candidates' statements and submit your choices on
the voting page. For the Election committee,
MediaWiki message delivery (
talk)
14:06, 24 November 2015 (UTC)
The file File:Capstan eqn2.png has been proposed for deletion because of the following concern:
unused, low-res, no obvious use
While all constructive contributions to Wikipedia are appreciated, pages may be deleted for any of several reasons.
You may prevent the proposed deletion by removing the {{proposed deletion/dated files}}
notice, but please explain why in your
edit summary or on
the file's talk page.
Please consider addressing the issues raised. Removing {{proposed deletion/dated files}}
will stop the
proposed deletion process, but other
deletion processes exist. In particular, the
speedy deletion process can result in deletion without discussion, and
files for discussion allows discussion to reach
consensus for deletion.
This bot DID NOT nominate any file(s) for deletion; please refer to the page history of each individual file for details. Thanks, FastilyBot ( talk) 01:01, 2 April 2020 (UTC)
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)
The file File:Laelelenr1 2009.png has been proposed for deletion because of the following concern:
Unused. Superseded by File:Capstan-derivation-diagram.svg.
While all constructive contributions to Wikipedia are appreciated, pages may be deleted for any of several reasons.
You may prevent the proposed deletion by removing the {{proposed deletion/dated files}}
notice, but please explain why in your
edit summary or on
the file's talk page.
Please consider addressing the issues raised. Removing {{proposed deletion/dated files}}
will stop the
proposed deletion process, but other
deletion processes exist. In particular, the
speedy deletion process can result in deletion without discussion, and
files for discussion allows discussion to reach
consensus for deletion. --
Minorax«¦
talk¦»
23:54, 5 August 2022 (UTC)