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the laws of friction

the angle of friction




Friction is the force that opposes movement.



limiting friction



The 3 Laws of Friction


1. The limiting frictional force (FL) is directly proportional to the normal contact force (N)


limiting friction proportional to normal reaction


note: the limiting frictional force is the maximum frictional force



2. The ratio of the limiting frictional force ( FL ) to the normal contact force( N ) is called the coefficient of friction (μ) ... the Greek letter 'mu'


coefficient of friction



3. When there is no motion, but the object is on the point of moving,


applied force = frictional force (limiting friction)


and when there is motion,


applied force > frictional force(limiting friction)


then this equality applies:

FL = μ N



Up to this point, when the frictional force is less than limiting friction(maximum)*, then the inequality below applies.


FL< μ N


*object is static and not on the point of moving



Example #1


A flat stone is thrown horizontally across a frozen lake.

If the stone decelerates at 2.5 ms-2 , what is the coefficient of friction between the stone and the ice? (take g=10 ms-2)



friction prob #01



Example #2


A 2 kg mass in limiting equilibrium rests on a rough plane inclined at an angle of 30 deg. to the horizontal.

Show that the coefficient of friction between the mass and the plane is √3 / 3 .




inclined plane friction problem


friction prob #2



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The Angle of Friction



angle of friction



If we examine the normal reaction force( N ) and the frictional force( FL ) when it is limiting, then the equation FL = μ N applies.


If the resultant between N and FL is R , and it is inclined at an angle α(alpha) to the normal N, then we can write equations for FL and N in terms of R .



angle of friction



In Example #2(above) the angle of friction = tan -1(√3 / 3)

= tan -1(0.5773) = 30o (the angle of the plane)









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