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Physics Formulas

Friction Formula

Friction is something that every kid learns in her/his school life. The friction force is very important to identify and understand the nature if forces on any stationary or moving object in physics. Besides, we will study friction, friction formula, formula’s derivation, and solved example in this topic.

Friction Formula


It refers to the stopping force that acts in the opposite direction of the motion. Furthermore, friction produces heat. For, example, suppose you push a book across the table, the book will move. Moreover, the force of the push moves the book and as the book slides across the desk it slows down and stops moving. In addition, the force that opposes the motion of an object is friction.

Types of Friction

Friction has many types of book in the example above was an example of sliding friction. Also, during the sliding, the bottom surface of the book is touching the desk and this is where friction was working. Furthermore, the weight of the book determines the amount of sliding friction present between two objects. Moreover, a heavy object will exert more pressure on the surface it slides over, and so the sliding friction will be greater.

Water, oil, and air are all fluids. Besides, air resistance is a type of fluid friction. Also, when an object falls the air resistance tries to push the object upward.

Moreover, when you ride a bicycle, the contact between the wheel and the road is an example of rolling friction. Furthermore, while the object rolls over a surface, the force needed to overcome rolling friction is quite less than that needed to overcome sliding friction.

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Friction Formula

Friction happens when two surfaces move over one another. Also, it is a force that resists the motion of an object. Moreover, it causes motion energy to be lost in the form of heat. Besides, we use the coefficient of friction to describe how two surfaces interact. Furthermore, the Greek letter ‘mu’ (\(\mu\)), and it is unitless. In addition, the force of friction is \(\eta\) times the normal force on an object. Most noteworthy, the unit of friction is Newton (N).

Friction = (coefficient of friction) (normal force)
\(F_{f}\) = \(\mu \eta\)

Derivation of the formula

\(F_{f}\) = refers to the force of friction acting on the object
\(\mu\) = refers to the coefficient of friction
\(\eta\) = refers to the normal force acting on the object

Solved Example on Friction Formula 

Example 1

Assume a large block of ice is being pulled across a frozen lake. Furthermore, the mass of the block of ice is 250 kg. Also, the coefficient of friction between the two surfaces is small \(\mu_{k}\) = 0.05. So, find the force of friction that acts on the block of ice?


The normal force of an object on a flat surface is \(\eta\) = mg. Also, by using this formula we can calculate the force of friction

\(F_{f}\) = \(\mu \eta\)
\(F_{f}\) = \(\mu\) mg
\(F_{k}\) = (0.05) (250 kg) (9.8 \(m/s^{2}\))
\(F_{k}\) = 122.5 \(kg \cdot m/s^{2}\)
\(F_{k}\) = 122.5 N

Hence, the force of friction acting upon the block of ice while it is being pulled is 122.5 N.

Example 2

Think that a man’s boat was stuck on shore when the tide went out. So, he began pushing his boat across the mud to get to the water. Also, the coefficient of friction among his wooden boat and the mud is \(\mu\) = 0.400. Furthermore, the mass of the boat is 50.0 kg. Then find the magnitude of the force of friction acting on the boat?


This is quite similar to the first example so we will use mg in place of \(\eta\) because both are equal.

So, \(F_{f}\) = \(\mu \eta\)
\(F_{f}\) = \(\mu\) mg
\(F_{f}\) = (0.400) (50.0 kg) (9.8 \(m/s^{2}\))
\(F_{f}\) = 196 \(kg \cdot m/s^{2}\)
\(F_{f}\) = 196 N

So, the force due to friction acting on the boat is 196 N.

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