Newton's laws of motion are of central importance in
classical physics. A large number of principles and results may be derived from Newton's
laws The first two laws relate to the type of motion of a system that
results from a given set of forces These laws may be interpreted in a
variety of ways and it is slightly uninteresting and annoying at the technical
outlet to go into the details of the interpretation The precise
definitions of **mass**, **force**, and **acceleration** should be
given before we relate them And these definitions themselves need the
use of Newton's laws Thus, these laws turn out to be definitions to
some extent We shall assume that we know how to assign mass to a body,
how to assign the magnitude and direction to a force and how to measure the
acceleration with respect to a given frame of reference. The development here
does not follow the historical track these laws have gone through, but are
explained to make them simple to apply.

# Newton's third law of motion definition

According to Newton's third law,
**To every action, there is an equal and opposite reaction.**

# Important Examples of Newton's third law of motion

**Recoil of a gun****Motion of rocket**-
**While drawing water from the well, if the string breaks up the man drawing water falls back.** **Swimming**

# Newton's third law of motion formula derivation

**"If a body A exerts a force F on another body B,**

**then B exerts a force -F on A.**

**[ F _{AB} = -F_{AB} ] **(negative force arise as the force is applied in
opposite direction)

" Thus, the force exerted by A on B and that by B on A is **equal in
magnitude but opposite in direction.** This law connects the forces
exerted by two bodies on one another

# Newton's third law of motion explanation with examples

The forces connected by the third law act on two different bodies and hence will never appear together in the list of forces at step 2 of applying Newton's first or second law.

For example, suppose a table exerts an upward force N on a block placed on it This force should be accounted for if we consider the block as the system The block pushes the table down with an equal force V. But this force acts on the table and should be considered only if we take the table as the system Thus, only one of the two forces connected by the third law may appear in the equation of motion depending on the system chosen.

The force exerted by the earth on a particle of mass M is Mg downward and therefore, by the particle on the earth is Mg upward These two forces will not cancel each other The downward force on the particle will cause acceleration of the particle and that on the earth will cause acceleration ( how large ? ) of the earth.

*Newton's third law of motion is not strictly correct when an interaction
between two bodies separated by a large distance is considered*. We come across such deviations when we study **electric** and
**magnetic forces**.

**Working with the Tension in a String**

Suppose a block of mass M is hanging through a string from the ceiling

Consider a cross-section of the string at A. The cross-section divides the string into two parts, the lower part, and the upper part The two parts are in physical contact at the cross-section at A. The lower part of the string will exert an electromagnetic force on the upper part and the upper part will exert an electromagnetic force on the lower part.

**According to the third law**, these two forces will have equal
magnitude The lower part pulls down the upper part with a force T and
the upper part pulls up the lower part with equal force T. The common
magnitude of the forces exerted by the two parts of the string on each other
is called the tension in the string at A.

**What is the tension in the string at the lower end? **The block and
the string are in contact at this end and exert electromagnetic forces on each
other The common magnitude of these forces is the tension in the string
at the lower end What is the tension in the string at the upper
end? At this end, the string and the ceiling meet The string
pulls the ceiling down and the ceiling pulls the string up.

The common magnitude of these forces is the tension in the string at the upper end.

Example

The mass of the part of the string below A in the given figure is m Find the tension of the string at the lower end and at A. Solution: To get the tension at the lower end we need the force exerted by the string on the block Take the block as the system The forces on it are

**pull of the string, T, upward,****pull of the earth, Mg, downward,**

The free body diagram for the block is shown in the given figure

As the acceleration of the block is zero, these forces should add to
zero Hence the tension at the lower end is **T = Mg.**

To get the tension T at A we need the force exerted by the upper part of the string on the lower part of the string For this, we may write the equation of motion for the lower part of the string So take the string below A as the system.

The forces acting on this part are

**( a ) T ', upward, by the upper part of the string****( b ) mg, downward, by the earth****( c ) T, downward, by the block.**

Note that in (c) we have written T for the force by the block on the string We have already used the symbol T for the force by the string on the block.

We have used Newton's third law here.
*The force exerted by the block on the string is equal in magnitude to the
force exerted by the string on the block* The free body diagram for this part is shown in the given figure As the system under consideration ( the lower part of the string ) is
in equilibrium, **Newton's first law gives T ” = T + mg but T = Mg**

**hence , T ' = (M + m )g**.

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