Statics : Friction

[ the laws of friction ][ the angle of friction]





Friction is the force that opposes movement.

limiting friction

The 3 Laws of Friction


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

limiting friction proportional to normal reaction

note: limiting frictional force is the maximum frictional force


The ratio of the limiting frictional force ( FL ) to the normal contact force ( N ) is called the coefficient of friction (μ )

coefficient of friction


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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