Newtonian Mechanics – Difference Between Normal Force and Reaction Force

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So I'm just wondering about three scenarios:

You've got a book on the table. It's got a gravitational force acting downwards. This is the force on the book by the earth. Apparently there is an equal and opposite force on the earth by the book.

But then there is also a normal force involved. The normal force is the force of the table pushing back against the book. Does this have a reaction force of the book pushing back on the table? And isn't this already accounted for with the gravitational force? What?

And then another massive question: If everything has equal and opposite forces on each other then how can there be net forces? Seriously that is pretty weird. For example when you push a cube with a non-constant velocity along a horizontal plane then there are net forces which is confusing because according to the third law there are equal and opposite forces on every interaction.

Lastly if you walk along a floor it pushes out against you with an equal and opposite reaction normal force. But surely if you are really heavy such that the surface breaks and you fall through then there is no equal and opposite reaction force? So what's up with that?

Update: Thanks for all the good answers guys but I am still low key really confused so I hope you don't mind if I don't accept anyone's answer as of yet. The quality of your answers are great but I just want to make sure I understand these concepts 100% before I resolve my issue

Best Answer

The normal force is the force of the table pushing back against the book. Does this have a reaction force of the book pushing back on the table? And isn't this already accounted for with the gravitational force? What?

  • The book feels weight downwards. Reaction: the Earth feels a gravitational pull upwards.
  • The book feels a normal force upwards. Reaction: the Earth feels a push downwards.

Another example:

  • An billard ball feels a "push" backwards at impact (equivalent to the normal force before). Reaction: The other billard ball feels the same "push" but oppositely (equivalent to the push before).

If everything has equal and opposite forces on each other then how can there be net forces? Seriously that is pretty weird. For example when you push a cube with a non-constant velocity along a horizontal plane then there are net forces which is confusing because according to the third law there are equal and opposite forces on every interaction.

There is a reaction force to every force exerted, yes. Just remember that you are talking about another object then.

  • The book feels the normal force, but it's reaction is not felt by the book; the reaction is felt by the Earth.
  • The billard ball feels the impact "push" and thus has a net force and flies back (accelerates). The reaction is not felt by the same billard ball but by the other ball, which then also has a net force and flies off (accelerates).

When setting up Newton's 2nd law, always look at only one object/system at a time.

Lastly if you walk along a floor it pushes out against you with an equal and opposite reaction normal force. But surely if you are really heavy such that the surface breaks and you fall through then there is no equal and opposite reaction force? So what's up with that?

  • If a ninja karate-chops a plank without breaking it by applying force $F$, then the plank is able to hold back with the entire same force $-F$.
  • If the ninja karate-chops a plank that breaks, then he did not need all the force $F$. He only applied force up until the plank stopped reacting with the same force. After that point he did not increase his force. So the force he exerted equals the force the plank was able to do (plus the acceleration term it also causes), which is smaller than the $F$ that he could have done.

Think of the difference between throwing your karate-hand through the air vs. throwing it into a falling piece of paper vs. throwing it into a wall: When hitting the wall, you exert a force on that wall. When hitting the paper, you exert a force but much smaller (and you move it as well). When not hitting anything, you don't exert any force on anything - you just move.

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