Inclined plane: Difference between revisions

Latest revision as of 12:11, 7 September 2011

Definition

The term inclined plane is used for a fixed plane that is maintained at an angle with the horizontal, i.e., it is not completely horizontal. An inclined plane is typically represented geometrically using a two-dimensional profile perpendicular to the horizontal direction within the incline. The significance of an inclined plane is that work can be done moving objects up and down the incline.

The inclined plane is one of the six simple machines.

Inclined planes may be combined with pulley systems to create more complicated mechanics scenarios.

Typical scenarios

The most standard scenario associated with an inclined plane is sliding motion along an inclined plane, where a block is placed (or given an initial speed) on an inclined plane, and the subsequent analysis of the statics, dynamics, and kinematics of the situation.

Scenario	Key addition/complication	Picture
sliding motion along a frictionless inclined plane	$\mu _{k}=\mu _{s}=0$
toppling motion along an inclined plane	The block can topple
sliding motion for adjacent blocks along an inclined plane	Two blocks instead of one, with a normal force between them
sliding-cum-rotational motion along an inclined plane	A sphere or cylinder on an inclined plane
pulley system on a double inclined plane	Two sliding blocks, connected by a string over a pulley, forcing a relationship between their motion
sliding motion along a frictionless circular incline	Incline is frictionless, but circular instead of linear (planar)
sliding motion along a circular incline	Incline is circular instead of linear (planar)
block on free wedge on horizontal floor	A block on the incline of a wedge that is free to move on a horizontal floor.
blocks on two inclines of a free wedge	Blocks on two inclines of a wedge that is free to move on a horizontal floor.

@@ Line 6: / Line 6: @@
 Inclined planes may be combined with [[pulley]] systems to create more complicated mechanics scenarios.
+==Typical scenarios==
+The most standard scenario associated with an inclined plane is [[sliding motion along an inclined plane]], where a block is placed (or given an initial speed) on an inclined plane, and the subsequent analysis of the statics, dynamics, and kinematics of the situation.
+[[File:Blockonincline.png|400px]]
+{| class="sortable" border="1"
+! Scenario !! Key addition/complication !! Picture
+|-
+| [[sliding motion along a frictionless inclined plane]] || <math>\mu_k = \mu_s = 0</math> || [[File:Blockonincline.png|100px]]
+|-
+| [[toppling motion along an inclined plane]] || The block can topple || [[File:Topplableblockonincline.png|100px]]
+|-
+| [[sliding motion for adjacent blocks along an inclined plane]] || Two blocks instead of one, with a normal force between them || [[File:Adjacentblocksonincline.png|100px]]
+|-
+| [[sliding-cum-rotational motion along an inclined plane]] || A sphere or cylinder on an inclined plane || [[File:Rotatoronincline.png|100px]]
+|-
+| [[pulley system on a double inclined plane]] || Two sliding blocks, connected by a string over a pulley, forcing a relationship between their motion || [[File:Pulleysystemondoubleinclinedplane.png|100px]]
+|-
+| [[sliding motion along a frictionless circular incline]] || Incline is frictionless, but circular instead of linear (planar) || [[File:Blockoncircularincline.png|100px]]
+|-
+| [[sliding motion along a circular incline]] || Incline is circular instead of linear (planar) || [[File:Blockoncircularincline.png|100px]]
+|-
+| [[block on free wedge on horizontal floor]] || A block on the incline of a wedge that is free to move on a horizontal floor. || [[File:Blockonwedge.png|100px]]
+|-
+| [[blocks on two inclines of a free wedge]] || Blocks on two inclines of a wedge that is free to move on a horizontal floor. || [[File:Blocksontwoinclinesoffreewedge.png|100px]]
+|}