How does Newton's Third Law hold in cases of net force?

Question

In a case where there is a net force, how does Newton's Third Law hold? For example, if I give a book a push and it starts to slide across the table, that means it was not able to neutralize the force I exerted on it with normal/frictional force. What force is opposite in direction and equal in magnitude to the one exerted by me? If this requires a deeper explanation involving gravitation or electromagnetism please don't shy away.

Answer 1

For example, if I give a book a push and it starts to slide across the table, that means it was not able to neutralize the force I exerted on it with normal/frictional force.

The book moved because the static friction force between the book and the table that opposed the force you applied to the book did not "neutralize" the force you applied to the book. That has nothing to do with Newton's 3rd law. It's due to Newtons 2nd law. The third law still holds.

Newton's third law always applies to the interaction between objects whether or not the objects move. The objects move or don't move based on the net force of all the forces acting on each object applying Newton's second law to each object individually.

The book applied an a force on you equal and opposite to the force you applied to the book. The book slid because the friction force between the book and table opposing your force was less than the force you applied. You did not slide because the equal and opposite force the book applied to you per Newton's 3rd law did not exceed the opposing static friction force between your feet and the floor.

Hope this helps.

Answer 2

What force is opposite in direction and equal in magnitude to the one exerted by me?

This would be the book pushing you in the opposite direction, but since your mass is much larger you get more friction and as a result you do not move. If the surface on which you stand was frictionless, you would end up moving in the opposite direction but much slower than the book due to much larger mass.

Try to understand much simpler example - there are two ice skaters initially at rest, and then one decides to push the other. Since the friction force is negligible on ice, both of them would start moving in opposite direction. The acceleration for the two is not same if they do not have the same mass, but the force (impulse) is the same at all times. This is a simple example of the law of conservation of (linear) momentum which directly follows from the third Newton’s law of motion.

And please note that when calculating net force on a book, you must include only the forces exerted on the book. The force that book exerts on you does enter equation for the net force that acts on the book! This is a common mistake people usually do - they include both action and reaction forces in the same free-body diagram which then cancel out.