Kinetic Friction: Definition, Formula, Examples, Direction & Properties

Why do we change the tyre of our car periodically? It is because after some time the surface of the tyre becomes smooth. So when we apply brakes, smooth tyres will not stop suddenly and that may lead to an accident. When tyres are new there is enough friction that stops the car from slipping. Friction is portrayed as a negative thing in daily conversation, but it is very important and necessary for everyday activity. Let’s understand friction in detail. 

Table of Contents

• Friction Force
• Kinetic Friction
• Direction of Kinetic Friction
• Properties of Coefficient of Kinetic Friction
• Practice Problems of Kinetic Friction
• FAQs of Kinetic Friction

Friction Force

Friction is a force related to two surfaces in contact, which opposes the relative motion or prevents the two surfaces from going in relative motion between them. Friction can be understood through two different views, macroscopic view and microscopic view.

Macroscopic View

At macroscopic level, when two bodies are kept in contact, particles of each body in contact exert electromagnetic force on the particles of the other body. As a result, each body exerts a contact force on the other. Contact forces can act in any direction.

Friction is the component of the contact force which is parallel to the surface in contact. Normal reaction is the perpendicular component of contact force.

Microscopic View

On a microscopic level, every surface has irregularities (projections and depressions). These irregularities cause friction by two different mechanisms.

• Interlocking 

Projections of one surface lock into depressions of another surface and hence resist the relative motion between them.

• Cold Welding

When two surfaces are in contact, only a few points touch each other, which implies that the effective contact area decreases. Due to reduction in the contact area, resultant pressure increases. Due to this, high pressure bonds are formed at contact points, which oppose the relative motion that leads to friction.

There are two types of friction:

Kinetic Friction

Kinetic friction exists between surfaces in contact only when there is a relative motion between those two surfaces.

Example: While surfing on ice there is relative motion between ice and surfboard as shown in the picture.

The magnitude of kinetic friction is proportional to the normal reaction force acting on the contact surface.

Kinetic friction force (F_k) is directly proportional to normal reaction force (N). 

$$\begin{gathered} f_k \propto N \\ {f}_k={\mu }_{k}N \end{gathered}$$

Here, U_k is the proportionality constant known as the coefficient of kinetic friction.

U_k is a unitless and dimensionless quantity. 

Note: Since normal force is the reaction force that opposes the net downward force on the surface of contact, it is not necessarily equal to the weight of the body. So, we can’t say that kinetic friction is proportional to the weight of the body.

Direction of Kinetic Friction

Kinetic friction opposes the relative motion between objects. So, for an object, the direction of kinetic friction is opposite to its relative velocity with respect to the other object in contact.

Example:

In this figure, block A is slipping in the backward direction with respect to B, so kinetic friction on A acts in the forward direction. Kinetic friction on B is equal and opposite to kinetic friction on A. Hence, kinetic friction on B is acting in the backward direction.

In other words, the direction of kinetic friction on the body A is opposite to the relative velocity of A with respect to B.

Note:

• Kinetic friction is always opposite to the relative motion and not necessarily opposite to the force applied. For example, in the above figure, kinetic friction on block A is parallel to the external force applied.
• When two bodies are under relative motion, the kinetic frictional force acting on one body is equal and opposite to the kinetic frictional force acting on the other body.

Properties of Coefficient of Kinetic Friction

• Coefficient of kinetic friction (U_k) depends on the nature of surfaces of materials in contact. It is not defined for a material alone but for a pair of material surfaces in contact.

For example, the coefficient of kinetic friction is different for each of the pairs shown.

• Coefficient of kinetic friction is independent of the area of the surface in contact.

For example, whether a body rests on its bigger face or smaller face, the frictional force remains the same. 

• Coefficient of kinetic friction is independent of the relative speed of the surfaces in contact.

Note:

• Magnitude of kinetic friction depends only on the normal reaction force and coefficient of kinetic friction which is independent of relative velocity.
• Direction of kinetic friction will always be opposite to the direction of relative velocity.

Video Explanation: Kinetic Friction 

Practice Problems of Kinetic Friction

Question 1. Find the direction of kinetic frictional force at the given instant on the block, exerted by the ground.

Answer:

Kinetic friction on the block, exerted by the ground:

Direction of kinetic friction is opposite to the relative velocity and independent of the force applied. So kinetic friction on the block acts in the leftward direction. 

Question 2. Find the direction of kinetic frictional force at the given instant on the ground, exerted by the block.

Answer:

Kinetic friction on the ground, exerted by the block:

The kinetic frictional force acting on the ground will be equal and opposite to the kinetic frictional force acting on the block. So kinetic friction on the ground acts in the rightward direction. 

Question 3. All surfaces shown are rough. Draw the kinetic friction force on 𝐴 and 𝐵.

Answer: Block 𝐴 is in contact with only block B. Hence, there is only one kinetic frictional force acting on block ??. While block B is in contact with block 𝐴 and the ground. Hence, there are two kinetic frictional forces acting on block B. 

Direction of kinetic friction force on 𝐴 exerted by B

Kinetic friction acts opposite to the relative velocity of the object with respect to the other object  in contact.

To find relative velocity of 𝐴 with respect to B,

$$\begin{gathered} \overrightarrow{V_{AB}}=\overrightarrow{V_A}-\overrightarrow{V_B} \\ =10i -20i \\ =-10i m{s}^{-1} \end{gathered}$$

Relative velocity of 𝐴 with respect to B is in the negative x direction. So, the direction of kinetic friction exerted on 𝐴 by B is in the positive x direction.

Direction of kinetic friction force on B exerted by A

To find relative velocity of B with respect to 𝐴, take 𝐴 as the frame of reference.

$$\begin{gathered} \overrightarrow{V_{BA}}=\overrightarrow{V_B}-\overrightarrow{V_A} \\ =20i -10i \\ =10i m{s}^{-1} \end{gathered}$$

Relative velocity of B with respect to 𝐴 is in positive x direction. So, the kinetic friction force on B is acting in negative x direction.

Kinetic friction on B exerted by ground

To find the relative velocity of B with respect to the ground, take ground as the frame of reference.

$$\begin{gathered} \overrightarrow{V_{BG}}=\overrightarrow{V_B}-\overrightarrow{V_G} \\ =20i -0i \\ =20i m{s}^{-1} \end{gathered}$$

Relative velocity of B with respect to the ground is in the positive x direction. So, the direction of kinetic friction on B exerted by ground is in the negative x direction.

Question 4. A block of mass M is sliding down on a fixed wedge that is making an angle 𝜃 with the horizontal. The coefficient of friction between the block and the wedge is 𝜇. Find the magnitude and direction of the friction on the block and its acceleration.

Answer:

In the question, it is given that the block is sliding down. So, there will be a kinetic friction acting along the inclined plane in the upward direction.

In y-direction,

$$\begin{gathered} Mg sin\theta -f_k=Ma \\ Mg sin\theta -\mu (Mg cos\theta )=Ma \\ a=g(sin\theta -\mu cos\theta ) \\ \overrightarrow{a}=g(sin\theta -\mu cos\theta )i \end{gathered}$$                     

FAQs of Kinetic Friction

Question 1. What is friction?
Answer: Friction is a force related to two surfaces in contact, which opposes the relative motion between them.

Question 2. What are types of friction?
Answer: Friction is of two types: 1) Kinetic friction 2) Static friction

Question 3. What is kinetic friction?
Answer: Kinetic friction exists between surfaces in contact only when there is a relative motion between those two surfaces.

Question 4. What is the direction of kinetic friction?
Answer: Kinetic friction opposes the relative motion between objects. So, for an object, the direction of kinetic friction is opposite to its relative velocity with respect to the other object in contact.`