Dragging motion for pile of blocks - Revision history

Vipul: /* Situation where neither block moves */

2011-08-13T00:48:30Z

Situation where neither block moves

← Older revision		Revision as of 00:48, 13 August 2011
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	<math>F_{\max} = g[\mu_{s1}(m_A + m_B)] \qquad (2.7)</math>		<math>F_{\max} = g[\mu_{s1}(m_A + m_B)] \qquad (2.7)</math>

	{{quotation\|'''ANSWER FORMAT CHECK''': For these kinds of situations, the critical values of external forces are always of the form <math>g</math> times a homogeneous linear polynomial involving the masses, with coefficients drawn from various possible friction coefficient.		{{quotation\|'''ANSWER FORMAT CHECK''': For these kinds of situations, the critical values of external forces are always of the form <math>g</math> times a homogeneous linear polynomial involving the masses, with coefficients drawn from various possible friction coefficient.}}

	===Situation where blocks move together as a system===		===Situation where blocks move together as a system===

Vipul: /* Summary of cases */

2011-08-13T00:47:51Z

Summary of cases

← Older revision		Revision as of 00:47, 13 August 2011
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	! Verbal description of case !! Lower bound on <math>F</math> for this case !! Upper bound on <math>F</math> for this case !! Acceleration of <math>A</math> !! Acceleration of <math>B</math>		! Verbal description of case !! Lower bound on <math>F</math> for this case !! Upper bound on <math>F</math> for this case !! Acceleration of <math>A</math> !! Acceleration of <math>B</math>
	\|-		\|-
	\| Neither block moves \|\| 0 \|\| <math>g[\mu_{s1}(m_A + m_B)]</math> \|\| 0 \|\| 0		\| Neither block moves \|\| 0 \|\| <math>\! g[\mu_{s1}(m_A + m_B)]</math> \|\| 0 \|\| 0
	\|-		\|-
	\| Both blocks move together with the same acceleration \|\| <math>g[\mu_{s1}(m_A + m_B)]</math> \|\| <math>g(\mu_{s2} + \mu_{k1})(m_A + m_B)</math> \|\| <math>\frac{F}{m_A + m_B} - \mu_{k1}g</math> \|\| <math>\frac{F}{m_A + m_B} - \mu_{k1}g</math>		\| Both blocks move together with the same acceleration \|\| <math>\! g[\mu_{s1}(m_A + m_B)]</math> \|\| <math>g(\mu_{s2} + \mu_{k1})(m_A + m_B)</math> \|\| <math>\frac{F}{m_A + m_B} - \mu_{k1}g</math> \|\| <math>\frac{F}{m_A + m_B} - \mu_{k1}g</math>
	\|-		\|-
	\| The blocks move with different accelerations \|\| <math>\frac{F}{m_A + m_B} - \mu_{k1}g</math> \|\| infinite \|\| <math>\frac{1}{m_A}\left[F - g(\mu_{k1}(m_A + m_B) + \mu_{k2}m_B)\right]</math> \|\| <math>\mu_{k2}g</math>		\| The blocks move with different accelerations \|\| <math>\frac{F}{m_A + m_B} - \mu_{k1}g</math> \|\| infinite \|\| <math>\frac{1}{m_A}\left[F - g(\mu_{k1}(m_A + m_B) + \mu_{k2}m_B)\right]</math> \|\| <math>\mu_{k2}g</math>

Vipul: /* Case of force on lower block */

2011-08-13T00:47:04Z

Case of force on lower block

@@ Line 41: / Line 41: @@
 Suppose an external horizontal force <math>F</math> is applied on the lower block. We determine the conditions under which both blocks start moving together, the two blocks start moving but not together, and neither block moves.
 ===Situation where neither block moves===
@@ Line 157: / Line 169: @@
 <math>F \ge (\mu_{s2} + \mu_{k1})(m_A + m_B)g \qquad (3.11)</math>
 ==Case of force on upper block==

Vipul at 00:42, 13 August 2011

2011-08-13T00:42:27Z

Show changes

Vipul at 01:08, 23 November 2010

2010-11-23T01:08:03Z

← Older revision		Revision as of 01:08, 23 November 2010
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	==The two blocks scenario==		==The two blocks scenario==

			[[File:Pileoftwoblocks.png\|thumb\|500px\|right]]

	Consider one block placed on top of another. The blocks are cuboidal with a horizontal surface of contact. Suppose the lower block is <math>A</math> and the upper block is <math>B</math>, and the lower block is resting on a fixed floor. Suppose the coefficients of friction are:		Consider one block placed on top of another. The blocks are cuboidal with a horizontal surface of contact. Suppose the lower block is <math>A</math> and the upper block is <math>B</math>, and the lower block is resting on a fixed floor. Suppose the coefficients of friction are:
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	* <math>\mu_{k2}</math> is the coefficient of kinetic friction between <math>A</math> and <math>B</math>.		* <math>\mu_{k2}</math> is the coefficient of kinetic friction between <math>A</math> and <math>B</math>.

	[[File:~~Pileoftwoblocks~~.png\|thumb\|500px\|right]]		We assume that there are no external forces in the vertical direction, other than the gravitational and normal force.

			==Normal force and gravitational force==

			===On the upper block===

			[[File:Upperblockforcediagram.png\|thumb\|500px\|right]]

			{{action reaction force concept\|The normal force on the upper block and <math>m_Bg</math> (the gravitational force) are equal and opposite but do ''not'' form an action reaction pair.}}

			If we denote by <math>N_{AB}</math> the normal force between the blocks, then <math>N_{AB}</math> acts upward on the upper block. The gravitational force <math>m_Bg</math> acts downward. Since there is no net acceleration in the vertical direction, we get:

			<math>\! N_{AB} = m_Bg \qquad (1)</math>
	==Case of force on lower block==		==Case of force on lower block==

Vipul at 00:55, 23 November 2010

2010-11-23T00:55:05Z

← Older revision		Revision as of 00:55, 23 November 2010
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	* <math>\mu_{s2}</math> is the limiting coefficient of static friction between <math>A</math> and <math>B</math>.		* <math>\mu_{s2}</math> is the limiting coefficient of static friction between <math>A</math> and <math>B</math>.
	* <math>\mu_{k2}</math> is the coefficient of kinetic friction between <math>A</math> and <math>B</math>.		* <math>\mu_{k2}</math> is the coefficient of kinetic friction between <math>A</math> and <math>B</math>.

			[[File:Pileoftwoblocks.png\|thumb\|500px\|right]]

	==Case of force on lower block==		==Case of force on lower block==

Vipul: Created page with '{{mechanics scenario}} ==The two blocks scenario== Consider one block placed on top of another. The blocks are cuboidal with a horizontal surface of contact. Suppose the lower …'

2009-11-22T16:41:35Z

Created page with '{{mechanics scenario}} ==The two blocks scenario== Consider one block placed on top of another. The blocks are cuboidal with a horizontal surface of contact. Suppose the lower …'

New page

{{mechanics scenario}}

==The two blocks scenario==

Consider one block placed on top of another. The blocks are cuboidal with a horizontal surface of contact. Suppose the lower block is <math>A</math> and the upper block is <math>B</math>, and the lower block is resting on a fixed floor. Suppose the coefficients of friction are:

* <math>\mu_{s1}</math> is the limiting coefficient of static friction between <math>A</math> and the floor.
* <math>\mu_{k1}</math> is the coefficient of kinetic friction between <math>A</math> and the floor.
* <math>\mu_{s2}</math> is the limiting coefficient of static friction between <math>A</math> and <math>B</math>.
* <math>\mu_{k2}</math> is the coefficient of kinetic friction between <math>A</math> and <math>B</math>.

==Case of force on lower block==

{{fillin}}

==Case of force on upper block==

{{fillin}}