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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:
- 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
(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
Websites
Friction Concepts - HyperPhysics
Friction Resources - Extensive list
Books
Top-rated books on Friction Science
Top-rated books on Friction Experiments
Questions and comments
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Static Sliding Friction on an Incline