Newton's Third Law states that action reactions are equal and opposite. Why is the resultant force is not zero?

This is a really common misconception among students, and it's due to the fact that people often shorten Newton's third law to "for every action there is an equal and opposite reaction".

More precisely, Newton's Third Law says that if an object A applies a Force on object B, then object B applies and equal and opposite force to object A.

So the action and reaction forces affect different objects.

This means there's no reason that the resultant force on either object A or B should be zero, and we need to consider what other forces are acting on A and B to determine the resultant force.

Newtons Third Law should not be taught using the "Action and Reaction" version. This question is a common misunderstanding of it with A-level students as well as at GCSE. You should know it as "Object A forces object B, object B forces object A with equal opposite force". This is a clearer to understand version. As stated above, the two Newton's 3rd Law forces act on DIFFERENT objects so can not make a resultant force of zero. Only two forces acting on the SAME object can make zero resultant force.

Another way to see it is that the 2 forces in a Newton's 3rd Law pair must meet all 4 of these conditions:- 1. Be equal size, 2. Be opposite direction, 3. Act on DIFFERENT objects 4. Be of the same type. Two cancelling forces on an object at rest/in equilibrium meet only conditions 1 and 2 therefore arent Newtons 3rd Law.

A particular example is a person of weight 800N standing on the floor at rest. The common mistake is that his Weight of 800N down and the floor's Normal Contact force pushing him up are a Newtons 3rd Law Pair.,They are not as yes they are equal and opposite, but they act on the same object (the person) not different objects, and are of different type( one Weight one Normal Contact).

Each force is in a Newtons 3rd Law pair. The weight is the Earth pulling the person down with 800N gravitational force. Now "reverse" the statement for Newtons 3rd Law (its a bit like revenge). So the N3 Pair of the Weight is the person pulling the Earth UP with 800N gravitational force. The Normal Contact force is the floor pushing the person up with 800N Normal Contact force, therefore by Newton's 3rd Law the person forces the floor DOWN with 800N Normal Contact force.

You will understand this more clearly if you study similar examples with the other force types you know.

The resultant force is not zero because the two forces (action and reaction) do not apply to the same body.

In general, when body A exerts a force onto a body B (action), body B will in turn exert the same force in the opposite direction onto the body A (reaction).

Since the two forces in question don't act onto the same body, they cannot be added together, and hence there is no resultant force.