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# Static Friction, Limiting Friction, Friction Graph, Angle of friction, Angle of Repose, Practice Problems, FAQs

If I ask you to walk on an ice surface, will you be able to do that? No. Because there isn’t enough friction between your feet and the ice surface. We can not walk without frictional force. Also if you look at the sole of sports shoes then you will see that it is designed in such a way that there will be maximum friction and no slipping takes place. This is because sportspeople have to run fast for that high friction force is required. In this article we will learn about static friction.

• Static friction
• Limiting friction
• Friction graph
• Angle of friction
• Angle of repose
• Practice problems
• FAQs

## Static friction

When someone pushes an object resting on a surface, it will only start to move when the applied force is greater than a particular value. So, there is a force developed which opposes the tendency of motion known as static friction.

Static friction acts when an individual tries to move a stationary object on a surface, without actually triggering any relative motion between the body and the surface which it is on.

Static friction is a variable resistive force which is equal and opposite to the external force until it surpasses the threshold of motion when the slipping starts. Hence, static friction is a self-adjusting force.

## Limiting friction

The maximum possible friction force between the two surfaces before sliding begins is known as limiting friction.

If the applied external force exceeds the value of the limiting friction, then the slipping starts and the nature of friction changes to kinetic friction.

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

Limiting Friction ∝ Normal reaction

(fs)max ∝ N

(fs)max=μsN

where μs is the coefficient of static friction.

μs is a unitless and dimensionless quantity.

Direction of static friction will be opposite to the tendency of relative motion.

In the given example, blocks A and B move together in positive x - direction when external force is applied, the tendency of motion of with respect to B is in negative x-direction. Hence, the direction of static friction on block A will be in the positive - direction.

## Friction graph

limiting friction with the normal reaction.

Let’s analyse the graph between friction and applied force.

From the friction graph, it is clear that the limiting friction force is more than the kinetic friction force. Why so?

We know that interlocking and cold welding causes friction at a microscopic level.

When the object is at rest, it has both interlocking and cold welding. So, both interlocking and cold welding contributes to static friction. When there is a relative motion between the surfaces, the bonds due to cold welding breaks and hence only interlocking contribute to kinetic friction. So, the kinetic friction is less than the limiting friction.

(fs)max > fk

μsN>μkN

μs>μk

This is why it is more difficult to start a relative motion between surfaces in contact than to maintain it.

Note: Normally (fs)max=μsN and fk=μkN. However in a question μs and μk are not given separately we can assume μs=μk=μgiven.

## Angle of friction ()

It is the angle made by the resultant of the normal reaction and limiting friction with the normal reaction.

Tan()=(fs)max N

=μsNN

=μs

Therefore, Angle of friction =tan-1(μs)

## Angle of Repose (r)

It is the minimum angle (r) made by an inclined plane with the horizontal such that an object placed on the inclined surface just begins to slide.

N=mg cos

Case1: <r

In this case friction force will be static in nature.

fs=mgsin From the graph below, you can see that friction force is increasing from zero to maximum value sinusoidally.

Case2: =r

In this case friction force will be limiting friction.

At this point the object is at the verge of sliding.

(fs)max=μsN=μsmg cos

(fs)max=mg sin

μsmg cosr=mg sinr

tanr=μs

Therefore, Angle of repose r=tan-1(μs).

Case3: >r

In this case friction is kinetic.

fk=μkN

fk=μsmgcos

From the above graph you can see that friction force is decreasing according to cosine function.

Video Explanation: Static Friction

## Practice problems

Question.1 Consider a block kept on a horizontal surface as shown in the figure. For the given values of F=10 N, find the acceleration of the block, force of friction, and nature of friction in each case. (Given, μs=0.5μk=0.2and g=10 ms-2)

N=mg=410=40 N

(fs)max=μsN=0.540=20 N

When F=10 N

F<(fs)max No motion Static friction

Friction force f=fs=F=10 N

Acceleration, a=0 ms-2

Question.2 Consider a block kept on a horizontal surface as shown in the figure. For the given values of F=15 N, find the acceleration of the block, force of friction, and nature of friction in each case. (Given, μs=0.5μk=0.2and g=10 ms-2)

N=mg=410=40 N

(fs)max=μsN=0.540=20 N

When F=15 N

F<(fs)max No motion Static friction

Friction force f=fs=F=15 N

Acceleration, a=0 ms-2

Question.3 Consider a block kept on a horizontal surface as shown in the figure. For the given values of F=20 N, find the acceleration of the block, force of friction, and nature of friction in each case. (Given, μs=0.5μk=0.2and g=10 ms-2)

N=mg=410=40 N

(fs)max=μsN=0.540=20 N

When F=20 N

F=(fs)max Just start to move Limiting friction

Friction force f=(fs)max=20 N

Acceleration, a=0 ms-2

Question.4 Consider a block kept on a horizontal surface as shown in the figure. For the given values of F=24 N, find the acceleration of the block, force of friction, and nature of friction in each case. (Given, μs=0.5μk=0.2and g=10 ms-2)

N=mg=410=40 N

(fs)max=μsN=0.540=20 N

When F=24 N

F>(fs)max Slipping Kinetic friction

Friction force f=fk=μkN=0.240=8 N

Applying Newton’s second law of motion,

F-fk=ma

24-8=4a

a=4ms-2

## FAQs

Question.1 What is static friction?

Answer: Static friction is a variable resistive force which is equal and opposite to the external force until it surpasses the threshold of motion when the slipping starts. Hence, static friction is a self-adjusting force.

Question.2 What is limiting friction?

Answer: The maximum possible friction force between the two surfaces before sliding begins is known as limiting friction.

Question.3 What is the angle of friction?

Answer: It is the angle made by the resultant of the normal reaction and limiting friction with the normal reaction.

Question.4 What is the direction of static friction?

Answer: Direction of static friction will be opposite to the tendency of relative motion.

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