Applying the Coulomb model of friction - Revision history

Vipul: /* Ignoring rotational issues */

2011-08-13T17:41:51Z

Ignoring rotational issues

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	\| [[pulley system on a double inclined plane]] \|\| [[File:Pulleysystemondoubleinclinedplane.png\|200px]] \|\| Section not yet created, see page anyway.		\| [[pulley system on a double inclined plane]] \|\| [[File:Pulleysystemondoubleinclinedplane.png\|200px]] \|\| Section not yet created, see page anyway.
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Vipul: /* Assuming static friction */

2011-08-13T17:35:12Z

Assuming static friction

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	\| [[sliding motion along an inclined plane]] \|\| [[File:Blockonincline.png\|200px]] \|\| [[Sliding motion along an inclined plane#Component along (down) the inclined plane]]		\| [[sliding motion along an inclined plane]] \|\| [[File:Blockonincline.png\|200px]] \|\| [[Sliding motion along an inclined plane#Component along (down) the inclined plane]]
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			\| [[pulley system on a double inclined plane]] \|\| [[File:Pulleysystemondoubleinclinedplane.png\|200px]] \|\| Section not yet created, see page anyway.
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Vipul: /* Ignoring rotational issues */

2011-08-13T17:24:45Z

Ignoring rotational issues

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	! Scenario !! Picture !! Section in page for static friction analysis		! Scenario !! Picture !! Section in page for static friction analysis
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	\| [[sliding motion along an inclined plane]] \|\| [[File:~~Blokonincline~~.png\|200px]] \|\| [[Sliding motion along an inclined plane#Component along (down) the inclined plane]]		\| [[sliding motion along an inclined plane]] \|\| [[File:Blockonincline.png\|200px]] \|\| [[Sliding motion along an inclined plane#Component along (down) the inclined plane]]
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Vipul: /* Ignoring rotational issues */

2011-08-13T17:24:19Z

Ignoring rotational issues

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 * Equality constraint: The ''force of static friction'' exerted by one body on the other is equal in magnitude and opposite in direction to the force of static friction exerted by the other body on the first.
 * Inequality constraint: The magnitude of force of static friction is bounded from above by the [[limiting coefficient of static friction]] (denoted <math>\mu_s</math>) times the magnitude of [[normal force]]. In the ''limiting case'' for this, equality occurs.
 ==Assuming kinetic friction==

Vipul at 17:19, 13 August 2011

2011-08-13T17:19:37Z

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 * Solve ''assuming'' kinetic friction.
 * Predict which of the cases (static and kinetic friction) arises.
 Some general observations:
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 * Equality constraint: The ''force of kinetic friction'' is equal in magnitude to the [[coefficient of kinetic friction]] times the magnitude of the normal force, and its direction is opposite the direction of slipping/relative motion along the plane of contact.

Vipul: Created page with "This article discusses how the Coulomb model of friction can be applied to predict values of acceleration and force in given mechanics scenario. There are three parts to the..."

2011-08-13T01:03:44Z

Created page with "This article discusses how the Coulomb model of friction can be applied to predict values of acceleration and force in given mechanics scenario. There are three parts to the..."

New page

This article discusses how the [[Coulomb model of friction]] can be applied to predict values of acceleration and force in given mechanics scenario.

There are three parts to the application:

* Solve ''assuming'' static friction.
* Solve ''assuming'' kinetic friction.
* Predict which of the cases (static and kinetic friction) arises.

Some general observations:

* If the [[limiting coefficient of static friction]] and the [[coefficient of kinetic friction]] are equal for all pairs of surfaces in contact, then the Coulomb model of friction can be used to correctly predict all accelerations and the accelerations are continuous (though not differentiable) as functions of various parameters in the scenario (such as angles, external force magnitudes, masses).
* If there is a pair of surfaces for which the coefficient of kinetic friction is strictly smaller than the limiting coefficient of static friction, then there can be a discontinuity at certain values of force or certain angles in the predicted value of acceleration. Further, the predicted values of acceleration are not stable under mild perturbations in these regions of discontinuity.
* The system is generally correctly determined (i.e., neither overdetermined nor underdetermined) to predict values of accelerations once we decide whether static or kinetic friction is operative. However, in the situation of multiple surfaces of contact that are experiencing static friction, it may not be possible using mechanics alone to figure out the magnitudes of static friction operating between multiple surface pairs, even though some sort of ''total'' across the surface pairs may be computable.

==Assuming static friction==

===Ignoring rotational issues===

We get the following information about the system of equations:

* Equality constraint: The ''accelerations'' on both bodies are equal. This follows from the fact that the ''velocity'' on both bodies are equal, and when two quantities are identically equal through time, their derivatives are also equal. This can be incorporated either by choosing a single acceleration variable for both bodies, ''or'' by choosing different acceleration variables and setting up an equality constraint between them. Note that if one of the bodies is stationary, ''or'' moving at constant velocity (so its acceleration is zero) the other body also has acceleration zero.
* Equality constraint: The ''force of static friction'' exerted by one body on the other is equal in magnitude and opposite in direction to the force of static friction exerted by the other body on the first.
* Inequality constraint: The magnitude of force of static friction is bounded from above by the [[limiting coefficient of static friction]] (denoted <math>\mu_s</math>) times the magnitude of [[normal force]]. In the ''limiting case'' for this, equality occurs.

==Assuming kinetic friction==

===Ignoring rotational issues===

We get the following information about the system of equations:

* Equality constraint: The ''force of kinetic friction'' is equal in magnitude to the [[coefficient of kinetic friction]] times the magnitude of the normal force, and its direction is opposite the direction of slipping/relative motion along the plane of contact.