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Static Friction Formula

Friction is a force that holds back the movement of some sliding objects. We can find friction everywhere in our surroundings. This force acts in the opposite direction to the way an object wants to slide. If we run down the sidewalk and stop quickly, we can stop because of the friction between our shoes and the cement. Friction may be with a moving body or with a non-moving body. Thus it may be dynamic as well as static. In this topic, we will discuss the concept of static friction and static friction formula with examples. Let us learn it!

Concept of Friction

Friction refers to the resistance which an object encounters in moving over another. Friction only happens with solid objects, but we do get resistance to motion in both liquids as well as gases. Imagine that someone is trying to push a book along with a table with his finger.

If he applies a very small force, the book will not move. If he further pushes slightly harder, then the book will start to move. Thus, if a body is moving, then friction will be taking its limiting value.

The Formula for Static Friction

Let us imagine a car at rest. To start this car without using the accelerator, we have to use a lot of force. This is due to static friction. Here the object at rest is a force to move to conflict the frictional force. Static friction is a kind of resistive force perceived in a body that is at rest. It is given as:

\(F_s = \mu_s \times F_n\)

\(F_n\) Normal force
\(\mu_s\) Coefficient of static friction
\(F_s\) Static friction

This formula will help us to compute the frictional force, co-efficient of friction or normal force in any asked numerically.

Static Friction Formula


Coefficient of Friction

The measure of friction is based on the type of materials that are in contact. Concrete material will have a very high coefficient of friction. This coefficient of friction will measure how easily one object moves in relation to the other one. Thus, a high coefficient of friction represents that there is a lot of friction between the materials. The coefficient of friction is a unit-less value and it represents the friction between two surfaces.

Solved Examples for Static Friction Formula

Q.1: A force of 300 N is acted on some box of 5kg put static on the floor. If the coefficient of friction is 0.3, then determine the static friction using Static Friction Formula

Solution: Known values are as follows

Normal force, \(F_n = 300 N,\)

Coefficient of friction , \(\mu_s = 0.3,\)

Static friction is given by the formula:

\(F_s = \mu_s \times F_n\)

\(= 0.3 \times 300 N\)

= 90 N.

Therefore, the static friction will be 90 N.

Q.2: A person is pushing a toy car of mass 4 kg which was at rest position on the floor. If 100 N is the value of the static frictional force, then determine the friction coefficient?

Answer: Known values are as,

Mass, m = 4 kg,

Static frictional force, \(F_s = 100 N,\)

Normal force, \(F_n = m \times g\)

\(F_n = 5 \times 10\)  , for acceleration due to gravity, \(g = 10 m s^{-2}\)

\(F_n = 50 N\)

Now, Formula is,

\(F_s = \mu_s \times F_n\\\)

After rearranging it,

\(\mu_s = \frac{F_s}{F_n} \\\)

Putting the values,

\(\mu_s = \frac{100}{50} \\\)

\(\mu_s = 2\)

Therefore, the friction coefficient is 2.

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