Frictional force-Definition, Types, Practice problems,FAQs

Let me ask you a question: if you pushed or pulled a box which is kept on a rough surface, would you be able to do it easily without applying much effort? The answer is no. There is always an opposing force to this motion. Friction is the name given to this opposing force. We are able to walk on the ground because of the frictional force between our feet and the ground. Friction exists not only between solids. When a ball or a raindrop starts to fall from a height, the speed of descent doesn't increase continuously. The resistive forces exerted by the air molecules slows it down. It is also an example of friction–hence they fall slower. In this article, we will explore friction in detail.

Table of contents

• Definition of friction
• Static friction
• Kinetic friction
• Rolling friction
• Angle of friction
• Friction graph
• Practice problems
• FAQs

Definition of friction

Friction is the resistance offered by surfaces that are in contact with each other – it opposes the relative motion between two surfaces in contact. Friction is both helpful and not desired. For instance, it is necessary for humans to stay in contact with the ground. But in the case of a block sliding down an inclined plane, if the friction is high, there is energy dissipation.

Consider the above figure in which a block is lying on a rough surface. The reaction force exerted by the ground on the block is N. Friction being a contact force,

$f=\mu N ; \mu -$ coefficient of friction.

The coefficient of friction has no unit. It depends upon the surfaces that are in contact. Friction arises due to irregularities in the surface.

Static friction

Static friction (f_s) is a variable resistive force which is equal and opposite to the external force applied, till a maximum point. It is a self adjusting force. We can say that the static friction exists as long as there is no relative motion between the surfaces in contact.

Let us consider a block of mass m lying on rest on an inclined plane. If $\mu$_s indicates the coefficient of static friction, $f_s \le {\mu }_{s}mg$.

The maximum value of static friction is called limiting friction (f_L). Once this is exceeded, the friction becomes kinetic in nature. The kinetic friction is slightly less than the static friction.

From figure,

(f_s)_max = ^$\mu$N is the limiting friction.

Kinetic friction

Kinetic friction (f_k) exists between surfaces in contact when there is a relative motion between the two surfaces.

$f_k={\mu }_{k}N; {\mu }_k-$coefficient of kinetic friction.

Rolling friction

Rolling friction comes into play when an object rolls on a surface. During pure rolling, the frictional torque (τ) is equal to the product of the rolling frictional force and the radius of the object.

$$\begin{gathered} \tau =F_r\times R \\ {F}_r={\mu }_r N \end{gathered}$$

$\mu$_r- coefficient of rolling friction.

Angle of friction

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

From the figure, the resultant force $R=\sqrt{{(f_s{)}_{max}}^2+({N)}^2}$

If $(f_s{)}_{max}$ denotes the limiting friction

$(f_s{)}_{max}=\mu N,N-$ normal reaction.

$$\begin{gathered} \mathit{t}\mathit{a}\mathit{n}\mathit{ }\mathit{\alpha }=\frac{({\mathit{f}}_{\mathit{s}}{)}_{\mathit{m}\mathit{a}\mathit{x}}}{\mathit{N}};\alpha =\mathit{t}\mathit{a}{\mathit{n}}^{-1}\left(\frac{\mathit{\mu }\mathit{N}}{\mathit{N}}\right) \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathit{\alpha }\mathbf{=}\mathit{t}\mathit{a}{\mathit{n}}^{\mathbf{-}\mathbf{1}}\left(\mu \right) \end{gathered}$$

Friction graph

The following plot explains the variation of frictional force with the external applied force. The value of friction increases linearly, then reduces, and then becomes constant. The constant value of friction is the kinetic friction.

Practice problems:

Q1. A block of mass m is placed on top of another block of mass M. The coefficient of friction between them is $\mu$. The minimum acceleration to be provided on the lower block, so that m moves over M would be,

$\left(a\right) \mu g \left(b\right) \mu \frac{m}{M}g \left(c\right) \mu \frac{M}{m}g \left(d\right) \frac{g}{\mu }$

A. a

The maximum value of static friction between the blocks, (f_s)_max = $\mu$mg

Let, the minimum acceleration to be provided be, a_min

So the pseudo force on the upper bock ma_min

By the question, ma_min = $\mu$mg

Hence, the minimum acceleration to be provided, a_min = $\mu$g

Q2. A block of mass 5 kg is given a force of 15 N. What is the coefficient of friction between the block and the ground so that the block does not move? Assume g=10 ms^-2

A. Given, m=5 kg,F=15 N.

The maximum value of frictional force can be provided in static friction is the limiting friction, f_L = $\mu$mg.

For the block to not move, $F=f_L\Rightarrow \mu mg=15;$

$\mu =\frac{15}{5\left(10\right)}=0.3$

Q3. A block of weight 10 N rests on a surface where the limiting friction between the surface and the block is 5 N. Calculate (i) The resultant force (ii) Angle of friction.

A. Given, f_L = 5 N, N = 10 N (Normal reaction is equal to the weight of the block.

$R=\sqrt{(f_L{)}^2+({N)}^2}=\sqrt{(5{)}^2+({10)}^2}=\sqrt{125}=11.18 N$

Here the maximum static friction is f_L = 5 N

The normal reaction force N=10 N

So the coefficient of friction ${\mu }_s=\frac{f_L}{N}=0.5$

Angle of friction= tan^-1(0.5) = 26.56^o.

Q4. A block of mass M is lying on rest over an inclined plane of inclination . The coefficient of friction between the block and the inclined plane is $\mu$. The block starts sliding down the inclined plane. Find the expression for its acceleration ?

A.

The weight the block Mg can be resolved into two components, one along the plane and another perpendicular to the plane as Mg sin$\theta$ and Mg cos^$\theta$ respectively as shown in the figure.

Let the block is descending with an acceleration, a.

The normal reaction is N. We have,

$$\begin{gathered} \Rightarrow Mgsin\theta -f_k=Ma \\ \Rightarrow N=Mg cos \theta \\ \Rightarrow Mgsin\theta -\mu N=Ma \\ Mgsin\theta -\mu \left(Mgcos \theta \right)=Ma\Rightarrow a=g(sin\theta -\mu cos\theta ) \end{gathered}$$

FAQs

Q1. What is the reason behind frictional force?

A. Friction between two surfaces arises due to the surface irregularities. This gives rise to a contact force between the two surfaces in contact which slide against each other. This depends on the angle and position of the surfaces with respect to each other. This affects the quantity of friction between them. Also, the roughness of the surfaces cause them to generate frictional force when brought in contact with each other. Adhesion refers to the molecular force that arises between two surfaces when they are brought in contact with each other. This leads to the friction

Q2. What happens when we don’t have frictional force?

A. Friction stops objects from sliding against each other. If there were no friction, objects would continue to move indefinitely. A skater would continue to skate without control if there is no friction between the ice surface and the skating wheels. We walk on the floor pleasantly because of friction. Even the slippery floors and surfaces have some friction in it. But we still struggle to walk on them.

Q3. Give 3 facts about friction?

A. Here are three facts on friction:

1) Frictional force can generate static electricity and the bodies involved get charged.
2) The harder the two surfaces are pressed together, more force is needed to overcome the friction between the surfaces. This is due to the existing normal force between the two surfaces.
3) Friction can be minimised by reducing the area of contact between the surfaces and also by oiling or lubricating the surfaces.

Q4. Which type of friction is the weakest ?

A. There are three types of friction we regularly encounter. They are static friction, sliding friction and rolling friction. Rolling friction is the weakest type of friction among them. This is the reason why tyres/wheels are able to move with ease on roads. Rolling friction is vital to prevent skidding between the tyres and the road. It gives necessary traction to the wheels.