# If frictional force in system is <= us*N then there is no slipping

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• annamal
In summary: Frictional-forceIn summary, if the applied horizontal force is less than the threshold force, then there is no slipping. If the applied horizontal force is greater than the threshold force, then there is slipping.
annamal
TL;DR Summary
If frictional force in system is less than or equal to us*N then there is no slipping. Why is it that if the frictional force in the system is greater than us*N then there is slipping?
If frictional force in system (say a block being pushed on a horizontal surface) is less than or equal to us*N then there is no slipping. Why is it that if the frictional force (Ff) in the system is greater than us*N then there is slipping (I am finding it hard to wrap my head around this)? us is coefficient of static friction and N is normal force.

I think you are misstating your query. You mean to ask why this happens when the applied horizontal force is less than ##\mu_s N## ?

annamal said:
Why is it that if the frictional force in the system is greater than us*N then there is slipping?
Because the bonds between the two materials are breaking. Note that the dynamic friction force drops as soon as the threshold force is reached.

Imagine the parts glued together and then you break the bond; one part can now move with respect to the other.

Static friction:

Kinetic friction:

Lnewqban
berkeman said:
I think you are misstating your query. You mean to ask why this happens when the applied horizontal force is less than ##\mu_s N## ?
According to my notes if the frictional force <= us*N, then no slipping occurs, but if frictional force > us*N then there is slipping?

My notes say this, specifically what does part 3b mean? If Ff > us*N why are we now slipping because isn't the Ff < us*N if Ff = uk*N?

Last edited:
1. If there is slipping, the friction force is ##\mu_kN##;
2. If there is no slipping, the friction force may be anything between zero and ##\mu_sN##;
3. If there is no slipping and the force exceeds ##\mu_sN##, slipping occurs (thus going to condition 1, i.e. ##F_f = \mu_kN##, and this is as long as there is slipping).
You can feel this by pushing an object sitting on another object. While increasing the force slowly, the object doesn't move. Once you reach the threshold force, the block suddenly starts to move and the block becomes easier to push (i.e. less force required).

annamal said:
Why is it that if the frictional force in the system is greater than us*N then there is slipping?
Because that is what we see in the experiments

berkeman said:
I think you are misstating your query. You mean to ask why this happens when the applied horizontal force is less than ##\mu_s N## ?
annamal said:
According to my notes if the frictional force <= us*N, then no slipping occurs, but if frictional force > us*N then there is slipping?
My point was more about how you are thinking about the forces.

The frictional force opposes the applied force to the object. So for a static object, the object does not slide until the applied horizontal force exceeds ##\mu_s N##. To state that in terms of only the frictional force being less than ##\mu_s N## seems to me to miss an important part of the force balance situation.

The frictional force is the result of the external force applied to the object; it does not exist all by itself.

Lnewqban
annamal said:
According to my notes if the frictional force <= us*N, then no slipping occurs, but if frictional force > us*N then there is slipping?

My notes say this, specifically what does part 3b mean? If Ff > us*N why are we now slipping because isn't the Ff < us*N if Ff = uk*N?
View attachment 329982
That value is a threshold between static and kinematic types of friction.
http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html

## What does "us" represent in the context of frictional force?

"us" represents the coefficient of static friction, which is a dimensionless quantity that characterizes the frictional force between two surfaces when there is no relative motion between them. It is a measure of how much force is needed to start moving one object over another.

## What is "N" in the equation "frictional force <= us*N"?

"N" stands for the normal force, which is the perpendicular force exerted by a surface on an object resting on it. It is equal in magnitude and opposite in direction to the force exerted by the object on the surface due to gravity.

## How is the maximum static frictional force calculated?

The maximum static frictional force can be calculated using the equation F_max = us * N, where F_max is the maximum force of static friction, us is the coefficient of static friction, and N is the normal force.

## What happens if the applied force exceeds the maximum static frictional force?

If the applied force exceeds the maximum static frictional force, the object will begin to slip or move, transitioning from static friction to kinetic friction. The kinetic frictional force is typically less than the maximum static frictional force.

## Does the coefficient of static friction depend on the contact area between surfaces?

No, the coefficient of static friction does not depend on the contact area between the surfaces. It depends on the materials and surface roughness of the two contacting surfaces. The normal force and the coefficient of static friction together determine the maximum static frictional force.

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