ES-150 Friction
When two real surfaces are in contact, an attempt to move either body with respect to the other will results in tangential friction forces developing.


The static frictional force builds up to match the applied horizontal component of force until it reaches its maximum value, at which point motion starts and a kinetic friction force acts.


The maximum value of the static friction force is shown here...

where is the coefficient of static friction
and N is the normal force (perpendicular to contact surface).


For static conditions, before the maximum friction force is generated...

For dynamic conditions, the frictional force is invariant and equal to where is the coefficient of kinetic friction.
Note: The coefficient of friction depends on materials and surfaces roughness.

When a force is applied to a body, the locations of the normal force changes.

identically Moments can be taken about the point indicated by 0.
For case (1)...


For case (2)...


For case (3)...

The normal force moves to keep the object in rotational equilibrium. When the normal force is a an extreme point (corner) of an object, tipping is imminent. Note the magnitude and point of application of P affects the tipping point.

Sometimes the friction and normal forces are combined into a resultant force and a friction angle is utilized.



thus,
The friction angle is the angle between the normal and resultant force.
The maximum static friction angle is determined as shown here...

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