Question

Action and reaction are equal and opposite. Why cannot they cancel each other?

Answer 1

Hint- We know that according to Newton's third law if a body A exerts a force on a body B, then body B will exert an equal and opposite force on the body A. The action and reaction forces are exerted by two bodies on each other.

Complete step by step answer:
According to Newton's third law every action has an equal and opposite reaction.

So, we can say that the forces always act in pairs. Either of them can be named as action and the other one will be the reaction. The action and reaction forces are exerted by two bodies on each other. They are equal and opposite but they do not cancel each other.

Let us analyze why they don't cancel each other.

Suppose a body A exerts a force on a body B. Then according to Newton's third law the body B should exert an equal and opposite reaction back on A.
If $f$ is the force supplied by A, then force applied back by B will be $- f$.
The force applied by A on B can be denoted as ${F_{AB}}$ .
Force applied by B on A can be denoted as ${F_{BA}}$ .
Then, we can write Newton’s third law in equation form as
${F_{AB}} = - {F_{BA}}$
The subscript AB means that it denotes the action of A on B and the subscript BA means that the reaction is from B on A.

Here we can see that the action and reaction are happening on two different objects the action force is applied on B and the reaction is applied on A.

If two equal and opposite forces should cancel each other then they should act on the same body.

But, in our case both the action and reaction happen on two different bodies so they cannot cancel each other.

Note: Remember that if two equal and opposite forces are acting on the same object then they will cancel each other but in the case of Newton's third law the action and reaction are acting on two different bodies. In that case they will not cancel each other.