# Difference between revisions of "Dragging motion for pile of blocks"

From Mech

Line 2: | Line 2: | ||

==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: | ||

Line 10: | Line 12: | ||

* <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: | + | 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== | ||

## Revision as of 01:08, 23 November 2010

This article discusses a scenario/arrangement whose statics/dynamics/kinematics can be understood using the ideas of classical mechanics.

View other mechanics scenarios

## Contents

## 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 and the upper block is , and the lower block is resting on a fixed floor. Suppose the coefficients of friction are:

- is the limiting coefficient of static friction between and the floor.
- is the coefficient of kinetic friction between and the floor.
- is the limiting coefficient of static friction between and .
- is the coefficient of kinetic friction between and .

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

KEY FORCE CONCEPT (ACTION-REACTION): Just because two forces are equal in magnitude and opposite in direction doesnotimply that they form an action-reaction pair in the sense of Newton's third law of motion. An action-reaction pair is a pair occurs between two bodies that exert forceson each other,notfor a pair of forces both actingon the same body. The normal force on the upper block and (the gravitational force) are equal and opposite but donotform an action reaction pair.

If we denote by the normal force between the blocks, then acts upward on the upper block. The gravitational force acts downward. Since there is no net acceleration in the vertical direction, we get:

## Case of force on lower block

*Fill this in later*

## Case of force on upper block

*Fill this in later*