# Newton's third Law of Motion complete explanation

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

1. Recoil of a gun
2. Motion of rocket
3. While drawing water from the well, if the string breaks up the man drawing water falls back.
4. 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.

[ FAB = -FAB ] (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.