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My understanding is that normal force is always equal to the applied force vector that is in line with it. Like weight going down, normal force going up along the same line, equal in magnitude.

Here is a case where I guess Newton's third law somehow doesn't apply:

I push a object with one of my hands. It starts to move and then accelerate. Therefore, I know the net force is bigger than zero.

According to user Wolphram Jonny in his answer to a similar question, the force received by the object as I push it is defined by the interaction.

Can someone perhaps answer this question by explaining how the "interaction" is involved here? the question I am talking about

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I would rather answer the question in a different way than the previous answer you have pointed at.

So, you are analysing the motion of the object and hence you need to find out all the forces that are being applied "on" the object. And hence, you take into account the force you apply. Because of your applied force, the body starts to move and henceforth accelerate.

Now, yes the said object is also "pushing" you. But this (normal) force applied by the object does not effect it's own motion; it will effect your own motion. ( Simply because this normal force is applied by the box on you). But because of your larger mass and hence greater friction with the ground; this normal force cannot move you.

So the bottomline is:- Newton's Third Law is perfectly valid here! The normal force exerted by the object on you does not effect the object's motion in any manner.

Aritra
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