Sliding Friction on an Inclined Surface
About 2 min read
The sliding friction of an object on a flat inclined surface is different than the friction for the same object on a level surface. The reason is that the resistive force of friction is a function of the normal or perpendicular force of the object on the surface. When the surface is at an angle, that force is reduced according to the angle of inclination.
Questions you may have include:
- What is the general friction equation?
- What is the friction equation at an angle?
- How can static coefficient be determined?
This lesson will answer those questions. Useful tool: Units Conversion
Friction equation
The resistive force of friction equals the coefficient of friction times the normal or perpendicular force. The general friction equation is:
Fr = μN
where:
- Fr is the resistive force of friction
- μ is the coefficient of friction for the two surfaces (Greek letter “mu”)
- N is the normal or perpendicular force pushing the two objects together
If the object is not yet moving, the static coefficient of friction (μS) is used.
If the object is sliding, the kinetic coefficient of friction (μK) is used.
Equation at an angle
When the object is on a level surface, the normal force is the sum of the weight (W) of the object plus any forces pushing the objects together. For the sake of simplicity, let’s only consider the weight of the object. Thus, on a level surface, the friction is:
Fr = μW
However, when the object is situated on an incline, the normal force pushing the object against the surface is the weight times the cosine of the angle of inclination.
Fra = μWcos(a)
where
- Fra is the friction force on the incline at angle a
- a is the angle of inclination
- cos(a) is the cosine of angle a
The weight of the object is a vector quantity pointing downward. It can be divided into its vector components Wcos(a), perpendicular to the incline surface, and Wsin(a), parallel to the surface.
Note that Wsin(a) is a force that could cause the object to slide down the incline or ramp. When Wsin(a) is greater than μSWcos(a), the object will start to slide.
Finding static coefficient of friction
One way to determine the static coefficient of friction is by changing the inclination of the ramp until the object just starts to slide. That is when the kinetic friction takes over from the static friction.
At that angle:
Wsin(a) = μSWcos(a)
μS = Wsin(a)/Wcos(a)
Thus:
μS = tan(a)
Summary
The sliding friction of an object on a flat inclined surface is a function of the normal or perpendicular force of the object on the surface. When the surface is at an angle, that force is reduced according to the angle of inclination.
You can use this information to determine the static coefficient of friction between the surfaces.
Help others learn
Resources and references
Websites
Friction Concepts – HyperPhysics
Friction – Wolfram Research Science World
Friction Resources – Extensive list
Books
The following books are available from Amazon.com.
Questions and comments
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