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Static Sliding Friction on an Incline

by Ron Kurtus (22 November 2016)

When an object is placed on a flat incline or ramp, it will not slide down the surface if the force caused by gravity acting on the object is less than the resistance from static sliding friction.

The static coefficient of sliding friction can easily be determined by the incline angle when the gravity force equals the static sliding friction resistance.

Questions you may have include:

This lesson will answer those questions. Useful tool: Units Conversion



Static sliding friction equation on incline

The static sliding friction equation is:

Fss = μssN

where

Normal force

When the object is on an incline, the normal force is:

N = W*cos(β)

where

Equation for static sliding friction

Thus, the equation for static sliding friction is:

Fss = μssW*cos(β)

Static forces on object on inclined surface

Static forces on object on inclined surface

Gravity force for object on incline

The force from gravity acting down the incline is the weight times the sine of the angle of inclination:

Fg = W*sin(β)

where

Will not slide

When the resistance from static sliding friction is greater than the sliding force from gravity, the object will not slide:

Fss > Fg

Coefficient of friction

The static coefficient of sliding friction can be found experimentally by adjusting the angle of the ramp or incline until the object just starts to slide. At this point, the forces are equal:

Fss = Fg

Since

Fss = μssW*cos(β)

Fg = W*sin(β)

then

μssW*cos(β) = W*sin(β)

and

μss = sin(β)/cos(β)

μss = tan(β)

Tangent

The tangent of β is simply the height divided by the length of the base:

Measure sides to determine tangent

Measure sides to determine tangent

Thus:

μss = A/B

(See Friction Experiment: Measure Coefficient of Friction with a Ramp)

Summary

An object is placed on a flat incline or ramp will not slide down the surface if the force caused by gravity is less than the resistance from static sliding friction.

The static coefficient of sliding friction can easily be determined by the incline angle when the gravity force equals the static sliding friction resistance.


Be clever


Resources and references

Ron Kurtus' Credentials

Websites

Friction Concepts - HyperPhysics

Friction Resources - Extensive list

Books

Top-rated books on Friction Science

Top-rated books on Friction Experiments


Questions and comments

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.


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