Vipul: /* Force diagram and acceleration analysis */

2024-04-27T23:39:58Z

Force diagram and acceleration analysis

← Older revision		Revision as of 23:39, 27 April 2024
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	- The magnitude of normal force decreases for <math>\theta</math> increasing from 0 to <math>\tan^{-1}(\mu)</math> and increases for <math>\theta</math> increasing from <math>\tan^{-1}(\mu)</math> to <math>\pi/2</math>		- The magnitude of normal force decreases for <math>\theta</math> increasing from 0 to <math>\tan^{-1}(\mu)</math> and increases for <math>\theta</math> increasing from <math>\tan^{-1}(\mu)</math> to <math>\pi/2</math>

	{Consider a situation where <math>\mu_s = mu_k = \mu</math> is the coefficient of static as well as kinetic friction between the block and the incline. Once the angle of the incline (denoted <math>\theta</math>) exceeds <math>\tan^{-1}(\mu_s)</math>, the magnitude of downward acceleration <math>a</math> is an increasing function of <math>\theta</math>. What is its derivative with respect to <math>\theta</math>?		{Consider a situation where <math>\mu_s = \mu_k = \mu</math> is the coefficient of static as well as kinetic friction between the block and the incline. Once the angle of the incline (denoted <math>\theta</math>) exceeds <math>\tan^{-1}(\mu_s)</math>, the magnitude of downward acceleration <math>a</math> is an increasing function of <math>\theta</math>. What is its derivative with respect to <math>\theta</math>?
	\|type="()"}		\|type="()"}
	- <math>g(\sin \theta + \mu \cos \theta)</math>		- <math>g(\sin \theta + \mu \cos \theta)</math>

Vipul: Created page with "See sliding motion along an inclined plane for background information. ==Force diagram and acceleration analysis== {Consider a situation where $..."$

2011-10-20T00:16:50Z

Created page with "See sliding motion along an inclined plane for background information. ==Force diagram and acceleration analysis== <quiz display=simple> {Consider a situation where <math>..."

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See [[sliding motion along an inclined plane]] for background information.

==Force diagram and acceleration analysis==

<quiz display=simple>

{Consider a situation where <math>\mu_s = mu_k = \mu</math> is the coefficient of static as well as kinetic friction between the block and the incline. What can we say about the normal force between the block (of mass <math>m</math>) and the incline as a function of the angle of incline <math>\theta</math> (this is the angle that the incline makes with the horizontal)?
|type="()"}
- The magnitude of normal force equals <math>mg</math> and is independent of <math>\theta</math>
+ The magnitude of normal force decreases from <math>mg</math> to 0 as <math>\theta</math> increases from 0 to <math>\pi/2</math>
- The magnitude of normal force increases from 0 to <math>mg</math> as <math>\theta</math> increases from 0 to <math>\pi/2</math>
- The magnitude of normal force increases for <math>\theta</math> increasing from 0 to <math>\tan^{-1}(\mu)</math> and decreases for <math>\theta</math> increasing from <math>\tan^{-1}(\mu)</math> to <math>\pi/2</math>
- The magnitude of normal force decreases for <math>\theta</math> increasing from 0 to <math>\tan^{-1}(\mu)</math> and increases for <math>\theta</math> increasing from <math>\tan^{-1}(\mu)</math> to <math>\pi/2</math>

{Consider a situation where <math>\mu_s = mu_k = \mu</math> is the coefficient of static as well as kinetic friction between the block and the incline. Once the angle of the incline (denoted <math>\theta</math>) exceeds <math>\tan^{-1}(\mu_s)</math>, the magnitude of downward acceleration <math>a</math> is an increasing function of <math>\theta</math>. What is its derivative with respect to <math>\theta</math>?
|type="()"}
- <math>g(\sin \theta + \mu \cos \theta)</math>
- <math>g(\sin \theta - \mu \cos \theta)</math>
- <math>g(\cos \theta - \mu \sin \theta)</math>
+ <math>g(\cos \theta + \mu \sin \theta)</math>

</quiz>

Quiz:Sliding motion along an inclined plane - Revision history

Vipul: /* Force diagram and acceleration analysis */

Vipul: Created page with "See sliding motion along an inclined plane for background information. ==Force diagram and acceleration analysis== {Consider a situation where ..."

Vipul: Created page with "See sliding motion along an inclined plane for background information. ==Force diagram and acceleration analysis== {Consider a situation where $..."$