Frictional Force - Formula, Examples, Types, FAQs

When a body is placed on the surface of another body, then due to the irregularities in their surfaces, the contact between them occurs at a large number of points. at each point of contact, a small area of the two surfaces comes in contact with each other. At these points of contact, the atoms and molecules of the two surfaces come very close to each other and they attract strongly. When we try to move a body places over the other body, the bonds of attraction oppose the motion. This opposing force is recognized as the force of friction.

In this article, we will discuss Friction, the laws of friction and a brief overview of the types of friction

Laws of friction

• The friction of the moving object is proportional to the normal force( numerically equal to the pressing force).

f∝N

• The friction experienced by the object is dependent on the nature of the surface it is in contact with.
• Friction is independent of the area of contact as long as there is an area of contact(as for solid apparent area is not equal to the actual area of contact).
• It acts tangentially along with the contact.
• The direction of friction is always opposite to the direction of relative motion.
• It can be also defined as the component of contact force which is parallel to the surfaces in contact.

The frictional force is a contact force, which is a force that arises due to contact with some other object solid or fluid. It is the property that arises due to which force is set up at the surface of contact of two body preventing any relative motion in between.
Friction is a dissipative force that is in most of the cases due to the frictional force there is the liberation of heat.

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Now we can look onto more about friction

Causes of friction

Suppose a body is moving above a surface from east to west then the direction of the frictional force will be in the exact opposite direction that is from west to east.

The frictional force will be less if the surface of interaction is small and smooth, for providing more friction the interacting surface should be rough. The breaking of a vehicle moving on the road occurs by taking advantage of the frictional force between the tyres and the road. You can see that the tyres get worn out after running for a while this is due to the friction acting between the tyre and the road. The rougher the tyres are it will be much easy for the vehicle to stop and difficult to gain speed and move smoothly. We can see the math regarding the friction against the motion of vehicles on the road in the coming sections.

Frictional force formula

F = μ x N

Where F – the frictional force

μ – the coefficient of friction which depends upon the two surfaces in contact with each other, it is a dimensionless quantity.

N – is the normal reaction to the ground

From this, it is clear that the frictional force depends on the weight as well as the nature of the surfaces

Unit of friction is Newton as it is a kind of force

Now let us consider a situation where we can see how to calculate the frictional force

Suppose there is a block of wood that weighs 5 kg resting on a table to be pushed from the rest. Considering the coefficient of friction as 0.5 then the frictional force can be calculated as below

The Normal reaction , N = 5 Kg x 9.8 N/kg = 49 N/Kg

Given, the coefficient of friction equal to, μ = 0.5

Then , the frictional force, F = 49 N/Kg x 0.5 = 24.5 N

We can define the coefficient of friction as the frictional force acting against a unit normal body

Frictional force examples

1. Rubbing of hands
2. The motion of a vehicle on the road
3. Dragging a box
4. Pushing a chair through the ground
5. Breaking system of cars
6. Viscous force on an object moving inside a fluid

Types of friction

There are different types of frictional forces depending upon the surfaces in contact they are

1. Fluid friction

It is the friction that occurs between the layers of the fluids moving relative to the ground, it depends upon the type of fluid and is determined by using a term called viscosity the more viscous fluid have more friction and hence moves less slowly compared to a less viscous fluid.

2. Dry friction

If the motion between two hard solid surfaces is considered it is called dry friction.it is again divided as static friction and sliding friction based on the state as the objects whether it is moving or not, which will be discussed in detail in the next session.

3. Lubricated friction

It is the case where a lubricant is present in between the two solid surfaces

4. Internal friction

It is such a type of frictional force that can be seen in between the elements of a solid material; it can be molecular or atomic in nature.

Sliding friction and Static friction

Sliding friction is the opposing force that occurs when one body attempts to slide across another's surface. Static friction is the friction between two solids that are not in relative motion with each other. or it can be said as the friction that prevents the motion to start in this case the body on the surface is at rest that is the frictional force balances the force due to the weight or that is provided externally and when the body starts moving it becomes kinetic friction.

The force that stops a vehicle wheel from sliding as it rolls on the ground is an example of static friction. Despite the fact that the wheel is spinning, the tyre patch in contact with the ground is fixed in relation to the ground, resulting in static rather than kinetic friction. When motion is imminent, the maximum amount of static friction is often referred to as limiting friction, however, this phrase is not widely used.

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Sliding friction – The friction that acts when a body slides over the surface of another body, is called sliding friction.

Dynamic friction – The friction that acts when a body is actually sliding over the surface of another body. Dynamic friction has another name called kinetic friction.

Work done by frictional force

This depends on the situation we are dealing with.

Assume a person is walking on the ground forward then we have to find the work done by the frictional force on the person’s foot,

We know that equation of work is force times displacement
W = F x S
Here the person lifts his foot on walking and there is no displacement with respect to the ground when considering the relative motion so the work done by the friction, in this case, is zero
Ie, S = 0
Hence W = 0

Now assume the case of a box sliding over a rough surface then there is a frictional force acting opposite to the motion of the box

Here if we consider it as static friction, then the displacement is zero and hence the work done is also zero(work done by a force is dot product of force and displacement)
Now if the box is actually moving then the case here is of sliding friction,
Here, work, W = – F x S x Cosθ
W = F_t x S x Cos (1800) since the force and the displacement is in opposite direction
W = F_t x S x (-1)
= - (F_t x S )
Where F_t is the frictional force and S is the displacement of the box relative due to the relative motion between the box and the surface.

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Solved Examples Based On Friction

Question 1: Friction is a force that acts in the ______ direction of the relative motion of two bodies.

1) Same

2) Parallel

3) Opposite

4) None of the above

Solution:

Frictional force offers resistance to the applied force opposing its motion. Thus, it always acts in the direction opposite to that of the object in motion. If force is applied to the left, then friction acts on the right.

example- when we try to push a box kept on the floor, friction acts opposite to the applied force on the box

Hence the force of friction always acts in the reverse direction to which an object moves or tries to move.

Hence, the answer is the option 3.

Question 2: A block of mass 1kg is at rest on a rough horizontal surface having a coefficient of static friction 0.2 and kinetic friction 0.15, find the friction force (in Newtons) if the horizontal force of 2.5N is applied on the block. (g=9.8m/s²)

1) 1.47

2) 2.5

3) 1.7

4) 2.3

Solution:

Friction

Opposing Force which is parallel to the surface and opposite to the direction of Relative Motion.

wherein

The direction of friction is always opposite the direction of Relative Motion.

fext. =2.5 N F1=0.2∗1∗9.8=1.96 N∵fext>Fl

body will be in a moving condition
friction force,

Fk=μkN=μkmg=0.15∗1∗9.8=1.47N

Question 3: A body of mass m=10−2 kg is moving in a medium and experiences a frictional force F=−kv2 Its initial speed is v0=10 ms−1. If, after 10 s , its energy is 18mv02 the value of k will be :

1) 10⁻³ kg m⁻¹

2) 10⁻³ kg s⁻¹

3) 10⁻⁴ kg m⁻¹

4) 10⁻¹ kg m⁻¹ s⁻¹

Solution:

m= 10^-2 kg

^{F= -kv2}

v₀ = 10m/s

initial energy= 1/2(V₀²)

final energy=1/8(mV₀²)

12mvf2=18mvo2vf=Vo2=5 m/s(10−2)dvdt=−KV2∫105=−100k∫010dt⇒15−110=100k(1∘)K=10−4

Hence, the answer is the option (3).

Question 4: What is true about rolling friction

1) for the same magnitude of normal reaction the sliding friction is much larger than the rolling friction

2) Rolling friction doesn't depend on the radius of the rolling body

3) Rolling friction depends only on the coefficient of rolling friction

4) none of the above

Solution:

For rolling friction

fr=μ0RrR= normal reaction r= radius of rolling body μr→ coefficient of the rolling body

Hence, the answer is the Option (2).

Summary

Friction is the force that opposes the relative motion between two surfaces in contact. It arises due to surface irregularities and the molecular attraction between the surfaces. There are different types of friction, including static and kinetic friction, each governed by specific laws. Kinetic friction occurs when one body moves over another, and it depends on factors such as the nature of the surfaces and the normal force.