# 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:

• What is the friction equation on an incline?
• What is the gravity force for object on incline?
• How can static coefficient of sliding friction be determined?

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

• Fss is the static force of sliding friction
• μss is the static coefficient of sliding friction for the two surfaces (Greek letter "mu")
• N is the normal force

### Normal force

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

N = W*cos(β)

where

• W is the weight of the object
• β is the angle of inclination (Greek letter "beta")
• cos(β) is the cosine of angle β

### Equation for static sliding friction

Thus, the equation for static sliding friction is:

Fss = μssW*cos(β)

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

• Fg is the force from gravity pulling the object down the incline
• sin(β) is the sine of angle β

### 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

Thus:

μss = A/B

## 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

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## Students and researchers

www.school-for-champions.com/science/
friction_sliding_static_incline.htm
.

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