FRICTION
(1) Introduction
- We all know that what would happen if we slide a book kept along a horizontal table .Yes it would first sliding and then finally would come to rest
- This force opposing continous motion of book on the table is called force of friction
- Whenever surface of one object slides over another ,both the bodies exerts force of friction on each other
- Here in this chapter,we will consider frictional forces acting between a pair of surfaces
- Frictional force comes into action whenever two surfaces of two bodies comes in contact with each other(Both the bodies could be moving or rest).Both the bodies exert a force on each other which is basically E.M in nature and this force is a contact force
- Magnitude of contact forces on two bodies are equal but they are opposite in direction
- Contact forces also depend on the nature of the surfaces of the two bodies kept in contact,how both the bodies are moving and all the forces acting on them
- Consider a block resting on the horizontal surface as shown below in the figure ,Now two bodies exert equal and opposite contact force on each other . Let Fc is the contact force both the bodies exert on each other
- Direction of the contact force acting on a body need not necessarily be perpendicular to the surface of contact
- Contact force Fc can be resolved into two components.The component of Fc along the normal to the surface is called Normal
contact force and component parallel to the surface is called friction (f) as shown in fig (b) - Friction is subdivided into two catagories namely
1. Static Friction
2. Kinetic Friction
Static friction is experienced betweem the non moving surfaces i.e the bodies at rest and kinetic friction or dynamic friction is experienced between the moving surfaces or between the bodies in motion - We shall now discuss both the static and kinetic friction in details
(2) Static Friction
- We already know that frictional forces can also act between the bodies in contact with each other even if they are not moving and such type frictional force is known as static friction
- Consider a heavy metal block kept on the floor and you are trying very hard to push it to another location and you are not able to slide it even by a centimeter
- Since the block is at rest resultant force on it should be zero.To counter balance the force applied by you ,floor exerts a frictional force on the block
s - Now if you begin to increase the magnitude of force gradually then bloack does not start moving until force applied is greater then a minimum value of force
- This force of static friction must be overcome by the applied force before the body at rest begin to move
- Force of friction is always equal and opposite to the external applied force as long as the body is at rest
- This means that static friction force is a self adjusting force.It adjust its value accordingly with the increase in magnitude of applied force
- This frictional force cannot be unlimited and its value cannot go beyond a maximum value fms
- This maximum value of static friction between the two surfaces in contact is known as limiting friction
- Thus magnitude of static friction can not go beyond the magnitude of the limiting friction i.e, fs <= fms
- This limiting friction is proportional to the normal contact force (N) between the bodies i.e,
fms is proportional to N
fms=μsN
Where N =Normal contact force
μs is the proportionality constant known as coefficent of static friction - Value of coefficent of static friction depends on the material and roughness of the surfaces of bodies in contact
- fms is the maximum value that force of static friction acting between two bodies can reach
- The actual force of static friction can be equal to zero or less then fms and its value depends on the force applied on the body thus
fs <= fms=μsN
(3) Kinetic or dynamic friction
- We already know that static frictional force exists between two surfaces in contact before there is relative motion between two surfaces
- When applied force becomes greater then limiting friction force,then motion of the body starts and kinetic friction comes into existence
- Thus when bodies in contact moves relative to each other then friction devloped between them is called kinetic or dynamic friction
- Consider the figure below in which a block of mass m is kept over the surface S
- Initially the block is at rest,now we push the block on the surface such that it begins to move or start sliding on the surface
- When the block is sliding over the surface each body exerts a frictional force on the other side parallel to the surface in contact
- The force of friction acting on the block B due to surface S is along the direction opposite to the motion of B with respect to S.Thus force of kinectic friction opposes the relative motion between the bodies in motion
- The frictional force acting on the block is along the direction towards the left and an equal force acts on the surface S directed towards the rights
- Thus we can say that sliding friction on a body B against surface S is opposite to the velocity of the body B with respect to S
- Force of kinetic friction is denoted by fk and its magnitude is always less then the magnitude of limting friction i.e maximum static friction
i.e fk < fms - kinetic friction force is proportional to the normal contact force between the surfaces i.e
fk is proportional to N
=> fk =μkN
Where N =Normal contact force
μk is the proportionality constant known as coefficent of kinetic friction and its value depends on the nature of the two surfaces in contact - fk < fms, this inequality shows that force required to start the motion is greater then the force required to maintail the further motion of the body
(4) Rolling Friction
- Consider a situation of the ring or a sphere rolling without slipping over a horizontal plane.In this case there is only one point of contact between the body and the plane
- The frictional forces developed between two surfaces in case described above is called rolling friction
- Rolling friction developes between two surfaces when one body rolls over the surface of another body
- We know that it is very difficult to pull a heavy metal box on a rough surface and if we attah four metal wheel to the box it becomes easiar to move the
- Thus resistance offered by the surface during rolling is relatively less than offered during sliding friction
- This is because while rolling surfaces in contact do not rub each other
- Rolling friction is negligible in comparision to the kinetic and static friction which are present simlutanously
- In many parts of the machine where this type of friction is undesirable ball bearings(small steel balls) are generally kept between the rotating parts of
(5) Angle of friction
- It is the angle which the normal force N makes with the contact force when the equlibrium is limiting i.e when the condition of maximum static friction
- Consider a block of mass m resting on a horizontal surface .Weight W=mg of this block is balanced by the normal force (N) of reaction as shown below in the figure.
Mathematically
W=mg=-N - if F is the contact force which each body exerts on the another body then this contact force can be resolved into two components
- Perpendicular Components which is normal force N
- Components parallel to the contact surface known as friction which is usually denoted by the fs,fk or fms
- Angle BCD respresented by λ is angle of friction
Since N and fms are components of the contact force F,so we can write
Fcosλ=N
and Fsinλ=fms
or we can say
tanλ=fms/N
Also from the defination of static friction we know that
fms=μsN So tan λ=μs
Thus we can conclude that coefficient of static friction is equal to the tangent of the angle of friction
(6) Methods to Reduce Friction
- Friction can be reduced by the numbers of methods.Some of them are listed below
(a)Lubrication: when a lubricant is applied between the two surfaces in contact then a thin layer of lubricant is formed between the two surfaces resulting in reduction in friction.Example of Lubricant Grease oil,graphite,compressed air
(b)Polishing : Irregularities of a surface can be reduced by polishing the surface smooth which results in reduction in friction
(c) Friction between the two surfaces can be reduced by using ball bearing between the two surfaces.Also sliding friction can be converted into rolling friction which is much less then sliding friction
Solved examples
Question 1 A block of Mass M is moving with a velocity v on straight surface.What is the shortest distance and shortest time in which the block can be stopped if μ is coefficent of friction
a.v2/2μg,v/μg
b. v2/μg,v/μg
c.v2/2Mg,v/μg
d none of the above
Solution 1
Force of friction opposes the motion
Force of friction=μN=μmg
Therefore retardation =μmg/m=μg
From v2=u2+2as
or
S=v2/2μg
from v=u+at
or t=v/μg
Question 2A horizontal force of F N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is μ. The weight of the block is
a.μF
b. F(1+μ)
c. F/μ
d none of these
Solution 2
Let W be the weight
Reaction force=F
Weight downward=W
weight Upward=frictional force=μr=μF
For no movement
weight Upward=Weight downward
W=μF
Question 3.A body is sliding down a rough inclined plane of angle of inclination θ for which coefficent of friction varies with distance y as μ(y)=Ky where K is constant.Here y is the distance moved by the body down the plane.The net force on the body is zero at A.Find the value of constant K
a. tanθ/A
b. Acotθ
c. cottanθ/A
d. Atantanθ
b>Solution 3
The downward force=mgsinθ
The upward force=μmgcosθ
Net force
f(y)=mgsinθ-μmgcosθ
=mg(sinθ-kycosθ)
at y=A, f(y)=0
0=sinθ-kAcosθ
or K=tanθ/A
Question 4A given object takes n times as much times to slide down a 45 rough incline as its takes to slide down a perfectly smooth 45 incline.The coefficent f kinectic friction between the objects and incline is gievn by.
a. 1/(1-n2)
b.1-1/n2
c. √1/(1-n2)
d. √(1-1/n2)
Solution 4
let μ be the coefficient of friction
Acceleration is smooth 45 inclined plane=gsinθ=g/(2)sup>1/2
Acceeration in friction 45 inclined plane=gsinθ-μqcosθ=[g/(2)sup>1/2(1-μ)
Now s=ut+(1/2)at2
or 2s=at2 as =0
For smooth plane
2s=g/(2)sup>1/2t2 ---(1)
for friction plane
2s=[g/(2)sup>1/2(1-μ)(nt)2 -(2)
so (1-μ)n2=1
or μ=1-1/n2
Question 5A uniform chain of length L is lying on the horizontal surface of a table.If the coefficent of friction between the chain and the table top is μ. what is the maximum length of the chain that can hang over the edge of the table without disturbing the rest of the chain on table.?
a.L/(1+μ)
b. μL/(1+μ)
c. L/(1-μ)
d. μL/(1-μ)
Solution 5
Let m be the mass per unit length
Let L be the full length and l be the length of chain hanging
So net force downwards=mlg
Net frictional force in opposite direction=μm(L-l)g
Now mlg=μm(L-l)g
or l=μ(L-l)
or l=μL/(1+μ)
Question 6The coefficent of static and kinectic friction between a body and the surface are .75 and .50 respectively.A force is applied to the body to make it just slide with a constant acceleration which is
a. g/4
b g/2
c. 3g/4
d g
Solution 6
Minimum force with which body will just move=μsmg
After the body start moving Frictional force becomes =μkmg
So ma=μsmg-μkmg
or a=g/4
Question 7 A block of mAss M is moving with a velocity v on straight surface.What is the shortest distance and shortest time in which the block can be stopped if μ is coefficent of friction
a.v2/2μg,v/μg
b. v2/μg,v/μg
c.v2/2Mg,v/μg
d none of the above
Solution 7
Force of friction opposes the motion
Force of friction=μN=μmg
Therefore retardation =μmg/m=μg
From v2=u2+2as
or
S=v2/2μg
from v=u+at
or t=v/μg
Question 8A horizontal force of F N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is μ. The weight of the block is
a.μF
b. F(1+μ)
c. F/μ
d none of these
Solution 8
Let W be the weight
Reaction force=F
Weight downward=W
weight Upward=frictional force=μr=μF
For no movement
weight Upward=Weight downward
W=μF
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