BS Physics (Foundation) Series

1. 1
Module # 17
Force, Friction & Elasticity
Force
Force is that agency which moves or tends to move or stops or
tends to stop the motion of a body. Alternatively, force is an agent
which produces or tries to produce motion in the body, stops or
tries to stop a moving body.
Thus, force is that which changes a body's state of rest or of
uniform motion in a straight line.
Measurement of Force
Force can be measured according to the second law of motion
which gives the relationship as follows:
F = ma
Units of Force
In MKS system or in SI system, the unit of force is newton and is
denoted by N.
A newton is the force required to give a mass of one kilogram an
acceleration of one meter per second2
.
1 kg force = 9.81 Newtons
&

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1 lb force = 4.45 Newtons
Net Force
Rate of change of momentum is called net force.
Forces in Nature
From our everyday observations, we realize that different kinds of
forces come into play in different circumstances i.e. we come
across various kinds of forces in nature. They are:
(1) Gravitational force
(2) Electrostatic force
(3) Magnetic force
(4) Electromagnetic force
(5) Strong nuclear force
(6) Weak nuclear force.
The gravitational force is the weakest force in nature. The nuclear
forces which hold the protons and neutrons in the nucleus are
strongest in nature. These forces are attractive forces and are
strong enough to overcome the electrostatic repulsive forces in
the nucleus. During radioactive decay, the nucleus emits a -
particle and a neutrino. The -particle and neutrino interact
though a weak force.

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Unification of the Forces
The unification of the various kinds of forces in nature has been a
major theme in the history of physics. Some years earlier,
magnetism and weak forces were listed separately and physicists
counted four fundamental forces i.e. it was thought that the nature
is controlled by only four forces. These four basic forces along
with their relative strength are given in the table below.
Table: The Four Forces in Nature
Type Relative
Strength
Range
Strong Nuclear
Force
1 1.4 x 10-15
m limited to the
nucleus
Electromagnetic
Force
10-2 Long range, can be screened
by a conductor.
Weak Nuclear
Force
10-13
Almost zero
Gravitational Force 10-40
Long range, cannot be
screened by any known
means.

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Three scientists, Dr. Abdus Salam, Sheldon Glashow and Steven
Weinberg developed a unified theory of the electromagnetic and
weak interactions, and in a sense, this presentation reduced the
number of classes of forces from four to three. So, now, there are
three basic forces in nature, namely, gravitational force, weak
electromagnetic force and strong nuclear force. For their theory,
linking the weak and electromagnetic forces, they received the
1979 Nobel Prize for Physics. That theory was confirmed
experimentally in 1983 by a group working under the Italian
physicist Carlo Rubbia, a Harvard professor working at CERN, the
European Centre for Nuclear Research. The 1984 Nobel Prize for
Physics went very quickly to Rubbia and his Dutch colleague
Simon Van der Meer.
There was a long held hope of Einstein to find a unified basis for
these different forces, but, he was never able to realize this hope.
Attempts similar to the unified theory have been made to
understand all strong, electromagnetic and weak interaction on
the basis of a single unified theory called a grand unified theory
(GUT). Such theories are still speculative, and there are many
unanswered questions. The entire area is a very active field of
current research.

5. 5
Friction
According to Newton's first law of motion, a body in motion will
continue to move with constant velocity unless acted upon by an
external net force. A body moving through a viscous medium such
as air or water eventually comes to rest. Similarly, a body in
motion on a solid surface eventually comes to rest. There are
always forces which resist the motion of a body. These forces
arise as a result of the interaction of the moving body with its
environment. Such a force, which resists the motion of a body, is
called a resistive force or a force of friction. Force of friction plays
a very important role in our everyday life, for example, forces of
friction allow us to walk or run and are necessary for the motion of
wheeled vehicles.
Thus, friction is the force which opposes the relative sliding
motion of two surfaces in contact with one another.
When a body is made to slide over the surface of another body,
its motion is opposed by some force due to the roughness of the
two surfaces. If we see the surfaces through microscope we
observe that they are not smooth. When one surface is placed
over another the elevations of one get interlocked with the
depressions of the other. Thus they will oppose relative motion.
Thus, the force which opposes the sliding motion of one surface

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over another is called force of friction or simply friction.
Friction Good or Bad
Whether friction proves to be useful or otherwise depends upon
the circumstances under which it comes into action. Friction
between rubber and concrete is certainly desirable, because it will
be impossible to walk if the friction between the soles of the shoes
and the ground were absent. Every mean of surface
transportation is based upon friction between the wheels and the
road. On the other hand, machines, clothes, shoes etc. wear out
due to friction.
Fluid Friction
A body experiences a resistive force when it moves through a
fluid, which can be either air/gas or liquid. Just as in the case of a
body moving over a solid surface experiences a frictional force
opposing its motion, similarly the fluid also exerts a frictional force
on the body.
The size, shape, orientation and velocity of an object determine
the fluid friction on it. Swimmers and sky divers change their
effective size and orientation of their bodies by bending, twisting
or stretching their arms and legs in and out. This allows them to
manipulate the fluid forces and consequently to control their
speed and direction of motion.

7. 7
Hover Crafts and Friction
Hover Crafts are those machines which are used for
transportation over water, marshes and land. They make use of
the comparatively low frictional forces offered by air at moderate
speeds. Hover crafts have the ability to hover just above land or
water. Hover crafts move very fast on a cushion of air that is
formed between the bottom of the vehicle and the surface on
which it hovers, irrespective of whether it is land or water. The air
is continuously forced downward by the engines of the hover
craft. These vehicles are now in regular use as ferries for short
distance travel across channels and islands. They can attain
speed over 150 km hr-1
as compared to the speed of the surface
boats of around 60 km hr-1
.
Rolling Friction
When an object rolls over a surface, the force of friction is called
the rolling friction.
If a heavy spherical ball is allowed to roll, the ball appears partly
sunk in the surface due to its weight or softness of the surface.
Thus when it rolls it appears to move up an incline and so it
experiences an opposing force called rolling friction.
The rolling friction is much less than the sliding friction. For
example, the rolling friction between steel is 1/100 of the sliding

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friction between them. Besides, in rolling the contact surface is
much less than that in sliding friction.
Limiting Friction
When a certain force is applied to slide or move some body over
another, then before the motion starts the force of friction
increases as the applied force is increased.
The maximum force of friction which just stops the body from
moving is called limiting friction.
This limiting friction is directly proportional to the normal reaction
or the weight of the body.
Let Fs is the magnitude of limiting friction and R is the normal
reaction of the body having weight (W = mg), then mathematically
we can write
Fs  R
or
Fs = R
or
Fs = mg (R = W = mg)
Where  is a constant of proportionality and depends on the
nature of the surfaces of the bodies.

9. 9
Methods of Reducing Friction
1. The various parts of the machines which are moving over
one another are properly lubricated. A lot of research is being
done all over the world to develop newer and newer lubricants to
minimize friction in machines. Lubricants provide a film of fluid
between the two moving surfaces and, therefore, tend to reduce
the friction.
2. In machines the sliding of various parts is usually replaced
by rolling and this is done by using ball bearing. Friction can be
reduced by using ball bearings because they convert sliding
friction into rolling friction.
3. Where sliding is unavoidable a thick layer of greasing
material is used between the sliding surfaces.
4. The front of the fast moving objects e.g. car and aeroplane
is made oblong to minimize air friction.
Advantages of Friction
Friction is necessary for our everyday activities
1 In the absence of friction, motion would not be possible i.e. it
is not possible for a man to walk on earth without friction. When
we walk we push the ground backward, the ground reacts and

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pushes us forward due to friction (in accordance with Newton’s 3rd
Law of Motion).
2 Without friction it is impossible to stop a moving body (in
accordance with Newton’s 1st
Law of Motion).
3. In the absence of friction a horse will not be able to pull a
cart / wagon (in accordance with Newton’s 3rd Law of Motion).
4 A nail stays in the wood because of friction similarly we can
tie a knot because of this force.
Disadvantages of Friction
1 Friction produces heat in various parts of the machines thus
some useful energy is wasted as heat energy.
2 Vehicles like cars, buses and trains lose part of their useful
energy in overcoming friction.
Coefficient of Friction
The ratios of the static and kinetic friction to the force pressing the
surfaces together are called the coefficients of static and kinetic
friction respectively.
F
 = -------
R

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Where,  is the coefficient of friction, F is the force of friction and
R is the force pressing surfaces together.
Co-efficient of Friction Never to Exceed One
Value of co-efficient of friction cannot be greater than one
because the force of friction increases with the increase of normal
reaction (i.e. the force acting vertically upward). Therefore, we
write
Fs  R
OR
Fs = R
Where  is the co-efficient of friction.
If the value of  is greater than one, then there will be an increase
in the value of product R beyond Fs and the body will not move.
In other words, we can say that when a force acts on a body, a
part of acting force is used in balancing the friction force and the
remaining portion causes motion in the body. Thus if value of 
becomes greater than one then the value of R will become so
high that a body cannot move.

12. 12
The ratio of limiting friction to normal reaction is known as the co-
efficient of friction. It is denoted by ‘’. Limiting friction Fs is
directly proportional to the Normal Reaction i.e.
Fs  R
OR
Fs = R
OR
 = Fs / R
Thus  is a constant of proportionality.
The co-efficient of friction depends upon two factors.
1. Nature of surfaces.
2. Cleanliness and dryness of the surfaces.
Elasticity
Elasticity is the property of solid materials due to which they
regain their original shape when an applied force is removed.
Thus, the property of the matter by virtue of which it resists any
force which tends to produce deformation in it is called elasticity.
If we apply a force to pull a body like a rubber band (strip) or a
spring, it is stretched. On removing the force, the rubber band or

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the spring regains its original length, that is, it returns to its
original shape.
The phenomenon of returning a solid body to its original shape
and size after applied force is removed is known as elasticity.
A wooden meter rod can be slightly bent into an arc and when the
force applied is removed, it becomes straight again. The meter
rod will break if it is bent too far. Thus, there is a limit to the
applied force from which the rod will recover when the force is
removed. This limit of the applied force is called the elastic limit.
Its value is different for different materials. Once a body (material)
crosses this limit, it will not regain its original shape even after the
removal of the applied force.
According to Kinetic or molecular theory of matter, the molecules
in a solid are very close to each other and, therefore, there exist
strong forces of attraction between them. When the applied force
is removed, the attractive force between them pulls the molecules
back again and the material is restored to its original shape.
Materials have different elasticities depending upon the nature of
the material.

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Elastic Potential Energy
When work is done in compressing and stretching a spring
against the elastic force, then, potential energy is stored in it.
Such a potential energy is called elastic potential energy.
It is to be noted here that potential energy is not always due to
work against the force of gravity (which is called gravitational
potential energy), e.g. if we wind our watch, then, its spring is
tightened. During this process, some work is done. This energy is
stored in the spring as its potential energy, which is then used to
run the watch.
Constant of Elasticity
The ratio of stress and strain is equal to the constant value. This
constant quantity is called constant of elasticity.
Hook’s Law
Robert Hook discovered that the strain produced is directly
proportional to the stress exerted within elastic limits. This is
known as Hook's law.
Thus,
stress  strain

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In other words, the deformation of a material is proportional to the
force applied to it, provided the elastic limit is not exceeded.
Hence, if the deformation of a material is proportional to the force
applied, then, the material is said to obey Hook's Law.
Application of Hook's Law
When a spring is fixed at one end and a force is applied to the
other end, then, the extension of the spring is proportional to the
applied force, provided the force is not large enough to stretch the
spring permanently i.e. when an elastic spring is stretched by a
force, then, the extension produced in the spring is proportional to
the exerted force. This is known as Hook's law.