F RICTION ON AN INCLINE PUTTING “FRICTION ON AN

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Friction on an Incline

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Putting “Friction on an Incline” in Recognizable terms: Friction on an Incline is a special case of friction on a horizontal surface. An incline is created by taking a surface and raising one end. Friction on an incline has the same basic results as friction on a horizontal surface and uses the same basic equations. The force of friction (Ff) still depends on the perpendicular force between the object and the surface, called the normal force (Fn). The different types of friction, static and kinetic can still occur on an incline.


Putting “Friction on an Incline” in Conceptual terms: With an incline, the force of gravity is not perpendicular to the surface. As the angle of the incline is increased, the normal force is decreased, which decreases the frictional force. The incline can be raised until the object just begins to slide. At this angle of the incline friction is at its maximum or ready to be over come. It is at this angle that the coefficient of static friction can be calculated. If the incline is raised until the object slides with a constant speed then the parallel forces are equal in magnitude but opposite in direction and at this angle of the incline the coefficient of kinetic friction can be found.

F RICTION ON AN INCLINE PUTTING “FRICTION ON AN

Putting “Friction on an Incline” in Mathematical terms: The coefficient of friction, µ, is defined as µ = Ff / Fn. On an incline, gravity or force of weight, Fw, is resolved into two components, Fx (or Fll) and Fy (or F┴). Since the angle between FW and Fy is equal to the angle of the incline, a component triangle (see Figure 2) can be used to show that

Fx = FW sin θ Fy = FW cos θ

In the case of an incline being raised to an angle where the object just begins to slide or moves at a constant speed (see Figure 3), we assume Ff = Fx. Also, with no other forces acting but weight and friction, we know that Fn = Fy. Putting these results together we can show that µ = tan θ

F RICTION ON AN INCLINE PUTTING “FRICTION ON AN F RICTION ON AN INCLINE PUTTING “FRICTION ON AN

Remember this result assumes the object is just starting to slide (static) or moving at constant speed (kinetic).


Putting “Friction on an Incline” in Process terms: Friction on an incline is a generalization of friction on a horizontal surface. As the angle of the incline is increased, the force of friction will decrease due to the change in normal force.


Putting “Friction on an Incline” in Applicable terms: Friction on an Incline occurs when you walk up a steep hill or roof top. By applying the concepts of friction on an incline you can determine at what angle your feet will begin to slide. It is also viewed anytime a type of dump truck raises its bed to release it load.

 2009 Board of Regents University of Nebraska


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