Index of a Lie algebra: Difference between revisions

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'''Belt friction''' is a term describing the friction forces between a [[Belt (mechanical)|belt]] and a surface, such as a belt wrapped around a [[bollard]]. When one end of the belt is being pulled only part of this force is transmitted to the other end wrapped about a surface. The friction force increases with the amount of wrap about a surface and makes it so the [[tension (physics)|tension]] in the belt can be different at both ends of the belt. Belt friction can be modeled by the [[Capstan equation|Belt friction equation]].<ref name=Attaway>{{cite conference | last = Attaway | first = Stephen W. | title = The Mechanics of Friction in Rope Rescue | url = http://www.jrre.org/att_frict.pdf | format = PDF | accessdate = February 1, 2010 | conference = International Technical Rescue Symposium | year = 1999}}</ref>


In practice, the theoretical tension acting on the belt or rope calculated by the belt friction equation can be compared to the maximum tension the belt can support. This helps a designer of such a rig to know how many times the belt or rope must be wrapped around the pulley to prevent it from slipping. Mountain climbers and sailing crews demonstrate a standard knowledge of belt friction when accomplishing basic tasks.


== Equation ==
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{{main|Capstan equation}}
The equation used to model belt friction is, assuming the belt has no [[mass]] and its material is a fixed composition:<ref>{{cite web
| last = Mann
| first = Herman
| title = Belt Friction
| date = May 5, 2005
| url = http://www.esr.ruhr-uni-bochum.de/rt1/currentcourse/node57.html
| publisher = Ruhr-Universität
| accessdate = 2010-02-01}}</ref>
 
: <math>T_2=T_1e^{\mu_s\beta} \, </math>
 
where <math>T_2</math> is the tension of the pulling side, <math>T_1</math> is the tension of the resisting side, <math>\mu_s</math> is the [[static friction]] coefficient, which has no units, and <math>\beta</math> is the angle, in [[radian]]s, formed by the first and last spots the belt touches the pulley, with the vertex at the center of the pulley.<ref>{{cite web
| last = Chandoo
| title = Couloumb Belt Friction
| url = http://web.mst.edu/~bestmech/preview/chandoo/8_2_2_1/8_2_2_1.htm
| publisher = Missouri University of Science and Technology
| accessdate = 2010-02-01}}</ref>
 
The tension on the pulling side of the belt and pulley has the ability to increase [[exponential growth|exponentially]]<ref name=Attaway/> if the magnitude of the belt angle increases (e.g. it is wrapped around the pulley segment numerous times).
 
== Friction coefficient ==
 
There are certain factors that help determine the value of the [[friction coefficient]]. These determining factors are:<ref>{{cite web
| title = Belt Tension Theory
| url = http://www.ckit.co.za/secure/conveyor/troughed/belt_tension/belt_tension_factors.htm
| publisher = CKIT – The Bulk Materials Handling Knowledge Base
| accessdate = 2010-02-01}}</ref>
 
* Belting material used – The age of the material also plays a part, where worn out and older material may become more rough or smoother, changing the sliding friction.
* Construction of the drive-pulley system – This involves strength and stability of the material used, like the pulley, and how greatly it will oppose the motion of the belt or rope.
* Conditions under which the belt and pulleys are operating – The friction between the belt and pulley may decrease substantially if the belt happens to be muddy or wet, as it may act as a lubricant between the surfaces. This also applies to extremely dry or warm conditions which will evaporate any water naturally found in the belt, nominally making friction greater.
* Overall design of the setup – The setup involves the initial conditions of the construction, such as the angle which the belt is wrapped around and geometry of the belt and pulley system.
 
== Applications ==
 
An understanding of belt friction is essential for sailing crews and mountain climbers.<ref name=Attaway/> Their professions require being able to understand the amount of weight a rope with a certain tension capacity can hold versus the amount of wraps around a pulley. Too many revolutions around a pulley make it inefficient to retract or release rope, and too few may cause the rope to slip. Misjudging the ability of a rope and capstan system to maintain the proper frictional forces may lead to failure and injury.
 
==See also==
*[[Capstan equation]]
*[[Frictional contact mechanics]]
 
==References==
{{reflist}}
 
[[Category:Mechanics]]

Latest revision as of 04:46, 27 June 2014


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Adjust the tyre pressure too so it is at its optimum level. General Use (Commuting, Mountain Bike, Road Bike, BMX, and Universal Fit) General use helmets are usually about. Each rider has lanes, but some others only have a single lane. If biking is your passion or your favorite sport, then you know the worth of good accessories while riding. If you have any kind of questions relating to where and ways to use Popular mountain bike sizing., you can call us at our own page. A sports drink is better than water as they contain carbohydrates and electrolytes that speed absorption of fluids and can give you an energy boost.

you know, right before making myself all nice and pretty before climbing on my bike and heading to work. An Indian travois style trailer is very simple to make and very effective for heavy loads. Please remember the stem lengths can impact just how reactive the bike is. Once you have answered the above questions and you see all these features present in a bike, you are on your way to choosing the road bike that is right for you. One of the obvious things to check on both a bike and car are brakes.

For more info about Anyclean and the range of cleaning services on offer please visit:. There are also tires with detailed treads which are very prominent and these are very useful for the biker because of the grip they provide. Serious head injuries can be prevented with a helmet and today’s styles and designs make them more comfortable to wear. With a Shimano 105 groupset and FSA Gossamer chain set, it's a great choice for under. I've never been into cycling and wanted to give it a try for exercise.

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