Inclined plane

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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.

Blockonincline.png

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