Friction-Statics

Friction

Friction is the force that opposes movement.

The 3 Laws of Friction
1.
The limiting frictional force ( F_L )is directly proportional to the normal contact force ( N )

note: limiting frictional force is the maximum frictional force

2.
The ratio of the limiting frictional force ( F_L ) to the normal contact force ( N ) is called the coefficient of friction (μ )

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:

F_L = μ N

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

F_L< 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)

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 .

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The Angle of Friction

If we examine the normal reaction force( N ) and the frictional force( F_L ) when it is limiting, then the equation F_L = μ N applies.
If the resultant between N and F_L is R , and it is inclined at an angle α(alpha) to the normal N, then we can write equations for F_L and N in terms of R .

In example #2(above) the angle of friction = tan ^-1(√3 / 3)
= tan ^-1(0.5773) = 30^o (the angle of the plane)