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# Coefficient of Static Friction Formula

Friction is the resistance that one surface or object encounters when moving over another. It occurs in two ways the first way is Kinetic friction acts on an object that slides on a surface, whereas static friction is the second way it occurs when friction prevents the object from moving. The coefficient is different for every pair of materials that contact each other, including a material that interacts with itself. Let us now discuss in detail about the coefficient of static friction formula.

## What is Static Friction?

Friction may be a force that creates it harder for two objects to slip alongside each other. Static friction is that friction, which exists between the surfaces on which, the object is resting and a stationary object. In other words, static friction is a force that keeps an object at rest. As an object start moving or we can say that it is in motion, it experiences kinetic friction. If a very less amount of force is applied to an object, the static friction has an equal magnitude in the opposite direction.

### Formula for Coefficient of Static Friction

Force of static friction = (coefficient of static friction) × (normal force)

$$F_s = \mu_s \times N$$

Where,

 Fs the force of static friction $$\mu_s$$ coefficient of static friction N normal force

The coefficient of friction is dimensionless i.e. it does not have any unit. It is a scalar quantity, which implies that the direction of the force shall not affect the physical quantity. The value of the coefficient of static friction depends on the objects that are causing friction. It’s value is generally between 0 and 1 but it can be greater than 1. The value equal to 0 means there is no friction between two objects. All objects will have some friction when they come in contact with each other. The value equal to 1 means the frictional force is equal to the normal force.

It is often a misconception that the coefficient of friction is limited to values between zero and one. A coefficient of friction that is more than one just means that the frictional force is stronger than the normal force such as silicone rubber, can have a coefficient of static friction much greater than one.

## Solved Examples for Coefficient of Static Friction Formula

Q. 1. A 5500 N force is applied to a sled. The skis of the sled have a coefficient of static friction $$\mu_s = 0.75$$ with the snow. If the fully loaded sled has a mass of 700 kg, what is the maximum force of static friction, and is the force applied enough to overcome it? Use Coefficient of Static Friction Formula.

Answer: On a flat surface, the normal force on an object is N= mg.

Using this, the force of static friction can be found:

$$F_s = \mu_s N$$

$$= \mu_s mg$$

=  0.75 x 700 kg x 9.8 m/s2

= 5145 kg∙m/s2

= 5145 N

The maximum force of static friction is 5145 N, and thus the applied force of 5500 N is enough to beat it, and begin moving the sled.

Q.2: The normal force and the static frictional force of an object are 50N and 80N respectively. Find the coefficient of static friction?

Solution: Given,

N = 50N, F = 80N and $$\mu_s= ?$$

The formula for coefficient of static friction is,

$$\mu_s = F/N$$

= 80/50

= 1.6

So, the coefficient of static friction is 1.6.

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