Vipul: /* Basic components of force diagram */

2011-08-14T02:02:12Z

Basic components of force diagram

@@ Line 18: / Line 18: @@
 | <math>mg</math> || [[gravitational force]] || unconditional || <math>mg</math> || vertical, downward
 |-
-| <math>N</math> || [[normal force]] || assuming that <math>F \sin \theta \le mg</math>, otherwise the block will lift off the floor. || vertical, upward
+| <math>N</math> || [[normal force]] || assuming that <math>F \sin \theta \le mg</math>, otherwise the block will lift off the floor. || adjusts so that there is no net force in the vertical direction || vertical, upward
 |-
-| <math>f_s</math> || [[static friction]] || no sliding || horizontal, opposite to horizontal component of <math>F</math>
+| <math>f_s</math> || [[static friction]] || no sliding || adjusts so that there is no net force in the horizontal direction || horizontal, opposite to horizontal component of <math>F</math>
 |-
-| <math>f_k</math> || [[kinetic friction]] || sliding || horizontal, opposite to direction of slipping. Assuming initially at rest, direction of slipping = horizontal component of <math>F</math>, so this is opposite to horizontal component of <math>F</math>.
+| <math>f_k</math> || [[kinetic friction]] || sliding || <math>\mu_kN</math> || horizontal, opposite to direction of slipping. Assuming initially at rest, direction of slipping = horizontal component of <math>F</math>, so this is opposite to horizontal component of <math>F</math>.
 |}

Vipul: Created page with "{{mechanics scenario}} ==The scenario== Suppose a block $m$ rests on a fixed horizontal floor. The limiting coefficient of static friction between $m$ ..."

2011-08-14T01:51:16Z

Created page with "{{mechanics scenario}} ==The scenario== Suppose a block <math>m</math> rests on a fixed horizontal floor. The limiting coefficient of static friction between <math>m</math>..."

New page

{{mechanics scenario}}

==The scenario==

Suppose a block <math>m</math> rests on a fixed horizontal floor. The [[limiting coefficient of static friction]] between <math>m</math> and the floor is <math>\mu_s</math> and the [[coefficient of kinetic friction]] is <math>\mu_k</math>. A force <math>F</math> is applied on the block in a diagonal direction at an angle <math>\theta</math> with the horizontal. The questions are as follows:

* For a given angle <math>\theta</math>, what is the minimum magnitude of force needed to get the block to start sliding, and how is the acceleration of the block given as a function of <math>F</math>?
* For what value of <math>\theta</math> is the minimum magnitude of force needed to get the block to start sliding as low as possible, and what is this minimum magnitude of force?
* For what value of <math>\theta</math> is the minimum magnitude of force needed to get the block to ''keep'' sliding as low as possible, and what is this minimum magnitude of force?

==Basic components of force diagram==

{| class="sortable" border="1"
! Force (letter) !! Nature of force !! Condition for existence !! Magnitude !! Direction
|-
| <math>F</math> || external force being applied || given to us that it's being applied || <math>F</math> || angle <math>\theta</math> with horizontal. The horizontal component is <math>F \cos \theta</math> and the vertical component is <math>F \sin \theta</math>.
|-
| <math>mg</math> || [[gravitational force]] || unconditional || <math>mg</math> || vertical, downward
|-
| <math>N</math> || [[normal force]] || assuming that <math>F \sin \theta \le mg</math>, otherwise the block will lift off the floor. || vertical, upward
|-
| <math>f_s</math> || [[static friction]] || no sliding || horizontal, opposite to horizontal component of <math>F</math>
|-
| <math>f_k</math> || [[kinetic friction]] || sliding || horizontal, opposite to direction of slipping. Assuming initially at rest, direction of slipping = horizontal component of <math>F</math>, so this is opposite to horizontal component of <math>F</math>.
|}

Dragging problem - Revision history

Vipul: /* Basic components of force diagram */

Vipul: Created page with "{{mechanics scenario}} ==The scenario== Suppose a block m rests on a fixed horizontal floor. The limiting coefficient of static friction between m..."

Vipul: Created page with "{{mechanics scenario}} ==The scenario== Suppose a block $m$ rests on a fixed horizontal floor. The limiting coefficient of static friction between $m$ ..."