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Kinetic Friction Formula

We witness in our daily life about the frictional force taking place in moving bodies which are in mutual interaction. There are many types of friction which are possible. But kinetic friction also known as sliding friction is much important with moving bodies. Also, static friction affects the object before it starts moving. And rolling friction specifically relates to the rolling objects like wheels. In this topic, we will discuss the kinetic friction concepts with kinetic friction formula and examples. Let us begin the topic!

Kinetic Friction Formula

Definition of Kinetic Friction

The most straightforward kinetic friction definition is given as the resistance towards the motion caused by the contact between a surface and the moving object against it. The force of kinetic friction acts in the oppose of the moving object. Therefore, if we push something forward, friction will push it backward.

The kinetic friction force only applies to an object that is moving and it is otherwise known as sliding friction. Another major type of friction between the solids is static friction. It is the resistance to motion caused by the friction between a still object and some surface. The coefficient of static friction is generally found larger than the coefficient of kinetic friction.

The Formula for Kinetic Friction

The friction force is best defined using the following equation. The force of friction depends on the friction coefficient for the particular type of friction under consideration. It also depends on the magnitude of the normal force.

The Retarding force between the two moving planes when they are in interaction with each other is popularly termed as Kinetic Friction. Kinetic Friction Formula is given as:

\(F_k = \mu_k F_n\)

Also, if the problem involves a horizontal surface and no other vertical forces are acting i.e., \(F_n = mg\),

Where,

\(F_k\) Force of kinetic friction
\(\mu_k\) Coefficient of sliding friction or kinetic friction
\(F_n\) Normal force, equal to the object’s weight
m Object’s mass
g Acceleration due to gravity

 Since friction is a force, the unit of the frictional force is the newton (N). Also, the coefficient of kinetic friction will be a unitless quantity.

The equation for static friction will be basically the same. But the exception is that the sliding friction coefficient will be replaced by the static friction coefficient \(\mu_s\). This is really best thought of as a maximum value because it increases up to a certain point, and then if you apply more force to the object, it will start moving:

Following is the table explaining other related concepts of friction:

Solved Examples

Q.1: A boy is playing with the football. Compute the kinetic friction here, if the friction coefficient is 0.5 and the football is kicked with the force of 150 N?

Solution:

Given here,

Coefficient of friction \(\mu_k  = 0.5\),

Normal force\( F_n\) = 150 N,

The Kinetic friction is computed as,

\(F_k = \mu_k F_n \)

\(F_k = 0.5 \times 150\)

kinetic friction = 75 N

Q.2: A car is moving at a uniform speed with the normal force of 1000 N. If the kinetic friction applied on this car is 500 N. Then compute the coefficient of the kinetic friction involved here?

Answer: Known:

Normal force \(F_n = 1000 N\),

Kinetic friction\( F_k = 500 N\),

Formula for, the coefficient of kinetic energy is:

\(F_k = \mu_k F_n \)

Rearranging it,

\(\mu_k = \frac{F_k}{F_n} \)

\(\mu_k = \frac{500}{1000}\)

coefficient of the kinetic friction = 0.5

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