# Limiting friction Vs static friction

#### LogU16

Hello, members.

What are static, limiting, kinetic, rolling frictions and sliding frictions? I'm unable to grasp what exactly the difference is.

Could somebody give me an example that covers all of them (or some other example that could easily tell me the difference) so that it can be easy for me to understand what actually they are and how do they relate with each other.

Many many thanks.

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#### PWiz

Actually, there are only two types of friction in the case of two solid objects being in touch with each other (no fluids involved). These are static and dynamic (kinetic friction). In simple words, when there is no relative motion between two solid objects in contact with each other, we describe the frictional force between them to static. When an opposing force acts on one of the objects at any acute angle (not normal to the surface of contact) to overcome friction (cause motion), the resultant force determines if the object remains stationary or begins accelerating (relative to the surface of course). When the force acting on the object (which is trying to bring about motion) just equals the static friction, the friction between the objects is described as limiting, and the object on which the force is acting is said to be in limiting equilibrium. Once there is relative motion though, the frictional force between the objects is reduced, and is now called dynamic (kinetic) friction. There is a simple formula relating kinetic and static friction to the normal contact force of the object (on which the unbalanced force acts to cause relative motion):
$F=μ_sR$ (static) and $F=μ_kR$ (kinetic), where $μ_s$ represents the coefficient of static friction, and $ημ_k$ represents the coefficient of dynamic friction. Their values completely dependent on the type of surfaces which are in contact. The coefficient for kinetic friction is typically lower than that for static friction.

#### LogU16

Thanks a lot, PWiz. I'm still confused about static and limiting friction, they sound same to me. Could you please elaborate the difference between these two by giving some suitable example?

#### PWiz

Okay, let's take it from the top. If a resultant force acts on a body, the body will accelerate. If no external force acts on a stationary object, the static friction will be 0 (it has to be, otherwise the objects will accelerate due to the resultant frictional force!). Now I start applying a force on the object parallel to the surface (as I said before, you can apply at any angle except 90 degrees, but I'm simplifying the scenario here), and I gradually increase the magnitude of the force. Initially when the applied force is still "small", the object will stay stationary, which tells me that the static friction force is increasing along with the force which I'm applying to make sure the resultant stays 0 (friction always opposes motion). However, a point will be reached, as you would expect, when the force I apply on the object is enough to make it move. That means I have exceeded the maximum resistive force static friction can provide, and that is why the resultant is non-zero, and the object starts to accelerate. The formula for static friction which I gave above gives the maximum value static friction can reach. Let's say this value is 10N. So for all external forces less than 10N, the object will stay stationary because static friction can "match" the magnitude from the opposite direction and cancel the effect. When the external force is greater than 10N, for example 12N, then the resultant on the object on the instant it starts to move will be 2N. From that point on, the resistive force will decrease from 10N to whatever the kinetic friction value is, causing the resultant force on the object to increase (assuming I don't decrease my "driving force"). The case when the external force equals 10N is when static friction is providing it's maximum value to just keep the object from moving. This condition is known as limiting equilibrium (there is an equilibrium between the forces). Limiting friction is the maximum value static friction can take. Mathematically, $F≤μ_sR$. This means that static friction can take any value between 0 and $μ_sR$ depending upon the external force.

#### LogU16

Thank you very much, I want you to please explain the following formula to me relating (Fs, μs) and (Fs, R) so that I can understand what actually this formulas says.
Fs=μs R (static)

For horizontal surface, we take (R=mg), m=mass of the block lying on a surface (say it is a table)

What does this formula (R=mg) tell us? What is meant by "horizontal surface" here?

#### Philip Wood

Gold Member
R is the magnitude of the normal contact force between the surfaces, that is the component of the contact force which is at right angles to the surfaces. In the case of a body resting on a horizontal surface (such as a book resting on a table), we can say that R = mg in which m is the body's mass. This is true if the body is in equilibrium, as the up and down forces on it must balance. But R will be greater than mg if someone is pressing down on the body!

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