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Friction

Key Concepts: Sliding may or may not occur between contiguous (connecting) surfaces.

If relative motion is about to start between two connecting surfaces, we say that sliding impends. Frictional forces always oppose sliding or the tendency to slide.

In a Nutshell: If sliding impends or occurs, then the friction force, F, reaches its maximum amount, F_max, where F_max = μ N . μ is the coefficient of friction, μ_s is the static coefficient of friction, μ_K is the kinetic coefficient of friction (slightly less than μ_S), and N is the normal

force acting between the contiguous or connecting surfaces.

If sliding is not impending, then the friction force, F, is less than its maximum amount or

F < μN. You then determine F from the equilibrium equations. In all cases start with a “complete free body diagram” of each part or collection of parts.

Belt Friction: Friction forces acting on a rope or belt wrapped around a fixed circular cylinder or pulley require a different model. Click here to skip to a discussion of belt friction.

The general strategy for solving friction problems.

To determine the different possibilities where motion might impend,

construct a FBD for each part and for each possibility.

Write the equations of equilibrium for each part and for each possibility.

Solve the friction forces for each case.

Check results for each case to determine where motion first impends or where sliding

occurs. Compare the friction forces calculated from the equilibrium equations with

the maximum values, μN. As a check, in each case, F < μN.

Iron Clad Rule You must ALWAYS have the same number of unknowns as independent equations in order to solve a system of equations. So you might need to supplement the

equations of equilibrium with other equations such as F = μ N (where motion impends or

sliding occurs), geometrical relations, and any related equations of constraint.

Click here for examples.

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