2

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.

Qmechanic
  • 201,751
Ethan Dandelion
  • 725
  • 1
    Why does it matter whether the book moves or not? The "equal but opposite" force something you push exerts back on you/your fingers doesn't have anything to do with friction. – ACuriousMind Mar 07 '22 at 20:00
  • 1
    Related/possible duplicate: https://physics.stackexchange.com/q/45653/50583 – ACuriousMind Mar 07 '22 at 20:01

2 Answers2

3

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.

Bob D
  • 71,527
1

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.

Marko Gulin
  • 5,210
  • I understand, thank you. Does this technically mean that if I managed to exert an absurd amount of force on the book, it would be possible for me to move as well? – Ethan Dandelion Mar 07 '22 at 20:13
  • @EthanDandelion Correct, whether or not you will move all comes down to the net force, and the “reaction” force of the book is just one of the forces acting on you. – Marko Gulin Mar 07 '22 at 20:15
  • So how is it possible that there is a "net force"? Doesn't that, by definition, mean an unbalanced force? Or is there perhaps a better definition? It seems that there cannot technically be a net force if every force in the universe is balanced, and net force is more an indicator of direction of motion. – Ethan Dandelion Mar 07 '22 at 20:19
  • @EthanDandelion Please check my last paragraph I’ve just added. To calculate the net force that acts on an object you take into account only forces exerted on that particular object. Take weight for example - have you ever included the force that pulls the Earth towards you? That one also comes in pair :) – Marko Gulin Mar 07 '22 at 20:21
  • I understand. So technically, all forces ARE balanced – it is simply the closed system that we are describing that is not in equilibrium. – Ethan Dandelion Mar 07 '22 at 20:23
  • @EthanDandelion That is correct, and instead of “closed” I would rather use adjectice “particular”. – Marko Gulin Mar 07 '22 at 20:24
  • I understand. Another question arises. If I try to imagine all the forces present, then we could say that ultimately the reason I don't move when I push the book is because of the friction between myself and the floor. Which force, then is balancing that friction? Thank you. – Ethan Dandelion Mar 07 '22 at 20:25
  • @EthanDandelion If you were standing on a big solid sphere, the reaction to friction force would be tangential force (torque) on the sphere which would start rotating the sphere. Just try to imagine this situation and try to guess how the sphere would be rotating - it is intuitive. – Marko Gulin Mar 07 '22 at 20:29
  • Let us continue this discussion in chat. – Ethan Dandelion Mar 07 '22 at 20:31
  • @EthanDandelion "I understand. So technically, all forces ARE balanced – it is simply the closed system that we are describing that is not in equilibrium." I wouldn't normally interject myself into another's conversation, but forces are not always balanced. If that were the case, nothing would accelerate. But maybe I misunderstand your comment. – Bob D Mar 07 '22 at 23:51
  • @BobD I read his comment as “all forces in the universe are balanced”, which is true according to 3rd Newton’s law – Marko Gulin Mar 08 '22 at 06:29