Newton's Third Law: Contact Interactions (Normal, Frictional, Tensional, and Applied Forces Are Examples of

Newton's Third Law
A force is a push or a pull upon an object that results from its interaction with another
object. Forces result from interactions! As discussed in Lesson 2, some forces result from
contact interactions (normal, frictional, tensional, and applied forces are examples of
contact forces) and other forces are the result of action-at-a-distance interactions (gravitational,
electrical, and magnetic forces). According to Newton, whenever objects A and B interact with
each other, they exert forces upon each other. When you sit in your chair, your body exerts a
downward force on the chair and the chair exerts an upward force on your body. There are two
forces resulting from this interaction - a force on the chair and a force on your body. These two
forces are called action and reaction forces and are the subject of Newton's third law of motion.
Formally stated, Newton's third law is:
For every action, there is an equal and opposite reaction.
The statement means that in every interaction, there is a pair of forces acting on the two
interacting objects. The size of the forces on the first object equals the size of the force on the
second object. The direction of the force on the first object is opposite to the direction of the
force on the second object. Forces always come in pairs - equal and opposite action-reaction
force pairs.
A variety of action-reaction force pairs are evident in nature. Consider the propulsion of a fish
through the water. A fish uses its fins to push water backwards. But a push on the water will
only serve to accelerate the water. Since forces result from mutual interactions, the water must
also be pushing the fish forwards, propelling the fish through the water. The size of the force on
the water equals the size of the force on the fish; the direction of the force on the water
(backwards) is opposite the direction of the force on the fish (forwards). For every action, there
is an equal (in size) and opposite (in direction) reaction force. Action-reaction force pairs make it
possible for fish to swim.
Consider the flying motion of birds. A bird flies by use of its wings. The wings of a bird push air
downwards. Since forces result from mutual interactions, the air must also be pushing the bird
upwards. The size of the force on the air equals the size of the force on the bird; the direction of
the force on the air (downwards) is opposite the direction of the force on the bird (upwards). For
every action, there is an equal (in size) and opposite (in direction) reaction. Action-reaction force
pairs make it possible for birds to fly.
Consider the motion of a car on the way to school. A car is equipped with wheels that spin in a
clockwise direction. As the wheels spin clockwise, they grip the road and push the road
backwards. Since forces result from mutual interactions, the road must also be pushing the
wheels forward. The size of the force on the road equals the size of the force on the wheels (or
car); the direction of the force on the road (backwards) is opposite the direction of the force on
the wheels (forwards). For every action, there is an equal (in size) and opposite (in direction)
reaction. Action-reaction force pairs make it possible for cars to move along a roadway surface.
……………………………………………………………………………………………
Third law of motion is different to other two laws of motion in what it describes. This law
states about an important characteristic of force rather than the relation between force and
motion as described by the first two laws.
Definition 1: Newton’s third law of motion
One body interacts with other body exerting force on each other, which are equal in
magnitude, but opposite in direction.
The action and reaction pair acts along the same line. Their points of application are
different as they act on different bodies. This is a distinguishing aspect of third law with
respect first two laws, which consider application of force on a single entity.
The law underlines the basic manner in which force comes into existence. Force results
from interaction of two bodies, always appearing in pair. In other words, the existence of
single force is impossible. In the figure below, we consider a block at rest on a table. The
block presses the table down with a force equal to its weight (mg). The horizontal table
surface, in turn, pushes the block up with an equal normal force (N), acting upwards.
Newton’s third law of motion
Figure 1: Two bodies exert equal but opposite

force on each other.
N=mg
In this case, the net force on the block and table is zero. The force applied by the table on
the block is equal and opposite to the force due to gravity acting on it. As such, there is
no change in the state of block. Similarly, net force on the table is zero as ground applies
upward reaction force on table to counterbalance the force applied by the block. We
should, however, be very clear that these action and reaction force arising from the
contact are capable to change the state of motion of individual bodies, provided they are
free to move. Consider collision of two billiard balls. The action and reaction forces
during collision change the course of motion (acceleration of each ball).
The "action" and "reaction" forces are external forces on individual bodies. Depending on
the state of a body (i.e. the state of other forces on the body), the individual "action" or
"reaction" will cause acceleration in the particular body. For this reason, book and table
do not move on contact, but balls after collision actually moves with certain acceleration.
The scope of this force is not limited to interactions involving physical contact. This law
appears to apply only when two bodies come in contact. But, in reality, the
characterization of force by third law is applicable to all force types. This requirement of
pair existence is equally applicable to forces like electrostatic or gravitational force,
which act at a distance without coming in contact.
Let us consider the force between two charges q1 and −q2 placed at a distance "r" apart.
The magnitude of electrostatic force is given by :
F=
q1q2
4πε0r2
The charge q1 applies a force F21 on the charge q2 and charge q2 applies a force F12 on
q1 . The two forces are equal in magnitude, but opposite in direction such that :
Electrostatic force
Figure 2: Force appears in pair.

F12=−F21
⇒F12+F21=0
(1)
Note:
Here, we read the subscripted symbol like this : F12 means that it is a force, which is
applied on body 1 by body 2.
It should be emphasized that though vector sum of two forces is zero, but this condition
does not indicate a state of equilibrium. This is so because two forces, often called as
action and reaction pair, are acting on different bodies. Equilibrium of a body, on the
other hand, involves consideration of external forces on the particular body.
Deduction of Third law from Newton’s Second law
We have pointed out that “action” and “reaction” forces are external forces on the
individual bodies. However, if we consider two bodies forming a “system of two bodies”,
then action and reaction pairs are internal to the system of two bodies. The forces on the
system of bodies are :
∑F=∑Fint+∑Fext (2)
If no external forces act on the system of bodies, then :
∑Fext=0
From second law of motion, we know that only external force causes acceleration to the
body system under consideration. As such, acceleration of the “system of two bodies”
due to net internal forces should be zero. Hence,
∑Fint=0
This is possible when internal forces are pair forces of equal magnitude, which are
directed in opposite directions.
The internal forces are incapable to produce acceleration of the system of bodies. The
term “system of bodies” is important (we shall discuss the concept of system of bodies
and their motion in separate module). The acceleration of the system of bodies is
identified with a point known as center of mass. When we say that no acceleration is
caused by the pair of third law forces, we mean that the “center of mass” has no
acceleration. Even though individual body of the system is accelerated, but “center of
mass” is not accelerated and hence, we say that "system of bodies" is not accelerated.
Referring to two charged body system that we referred earlier, we can consider forces F12
and F21 being the internal forces with respect to the system of two charged bodies. As
such, applying Newton’s second law,
Electrostatic force
Figure 3: Force appears in pair.

∑Fint=F12+F21=0
⇒F12=−F21
The “action” and “reaction” forces are, therefore, equal in magnitude, but opposite in
direction. Clearly, third law is deducible from second law of motion.
The important point to realize here is that “action” and “reaction” forces are external
forces, when considered in relation to individual bodies. Each of the two forces is capable
to produce acceleration in individual bodies. The same forces constitute a pair of equal
and opposite internal forces, when considered in relation to the system of bodies. In this
consideration, the center of mass of the body system has no acceleration and net internal
force is zero

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Newton's Third Law

For every action, there is an equal and opposite reaction.

Figure 1: Two bodies exert equal but opposite

Figure 2: Force appears in pair.

Figure 3: Force appears in pair.

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