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Why won't two blocks kept in contact on a horizontal frictionless surface move, due to the normal force? No exterior force is applied to them from any direction (except for gravity).

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Ok here's more info

Actually in our physics text there were numerical where two boxes of mass m1 and m2 are kept on frictionless surface and a force is applied to one of them and we have to calculate their acceleration(a = F/(m1+ m2)) and normal force(N = m2/(m1+m2) *F)

And my physics teacher also said that "whenever two bodies are in contact there always exist normal force"(exact words)

So I thought if no external force is applied horizontally or vertical upwards to such a system of blocks(here m1 and m2) on a frictionless surface then why they don't move?

And what is the max N for a system of blocks(for simplification lets take two blocks only) and can that max N overcome friction if kept on a surface with friction

I hope you guys understand my confusion here

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    $\begingroup$ On horizontal surface, gravity and normal force are equal but opposite direction, cancelling each other out. If you have something else in mind, draw a picture and add it to your question. $\endgroup$
    – mbeckish
    Commented Sep 6, 2016 at 13:25
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    $\begingroup$ What keeps them in contact? $\endgroup$
    – nasu
    Commented Sep 6, 2016 at 13:27
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    $\begingroup$ In your diagram, the horizontal normal forces due to the blocks touching each other are also equal and opposite (and zero magnitude, as long as the blocks are not accelerating horizontally). $\endgroup$
    – mbeckish
    Commented Sep 6, 2016 at 14:07
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    $\begingroup$ @JiK: Answering off-topic questions is frowned upon. Just being downvoted doesn't mean you should answer it, there's even a badge for doing so brilliantly. $\endgroup$
    – ACuriousMind ♦
    Commented Sep 6, 2016 at 14:07
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    $\begingroup$ The two normal forces are due to the same interaction, so they are a "Third Law pair". Consequently, this question is in essence a duplicate of this one $\endgroup$
    – garyp
    Commented Sep 6, 2016 at 14:30

3 Answers 3

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In short, you are making a simplifying approximation ("frictionless surface"), while keeping another as negligible force in place ("whenever two bodies are in contact there always exist normal force"). This will quickly lead to an apparent contradiction.

(Also even saying "in contact" is an simplification (it just means that atoms are very close to each other), so you'll really run into trouble if you'll try to account for only some of the forces.)

Here's an example which hopefully explains this in more detail:

  1. Stand next to a wall so that the wall is on your right-hand side. Push the wall with all force you can without slipping. Now there are external forces acting on you: The wall pushes you left with force $N$, gravity pulls you down with force $G$, and between your feet and the ground, there is a normal force $F$ pointing (that is equal in magnitude to gravity) and a friction force $F_\mu$ that pushes you right.

    If the friction is strong enough, $F_\mu$ and $N$ are equal in magnitude, so there is no net force on you and you don't move. However, if your shoes are slippery, the friction force will not be enough, and you'll start moving to left.

  2. Push with slightly less force. You'll feel that $N$ is smaller than in the previous case. Consequently, the friction required to keep you in place is smaller, and you can stay without moving with more slippery shoes, too. Again, if you don't move, $F_\mu$ and $N$ are equal in magnitude.

  3. Now stand next to the wall so that your sleeve slightly touches the wall. In principle, your physics teacher is correct: there is a normal force between your sleeve and the wall, because the atoms in your sleeve are close enough to the atoms in the wall to cause electromagnetic interaction. However, the force $N$ is very very tiny, so you probably can't feel it. Similarly, there is a very very tiny friction force $F_\mu$ keeping you in place.

  4. Consider a frictionless surface, so $F_\mu=0$. Now in principle the force $N$ would move you. However, usually "a frictionless surface" is just an assumption to make things easier to calculate when $F_\mu$ is very very tiny. But the force $N$ is also very very tiny, so if you want to ignore very very tiny forces, you shouldn't need to think about the force $N$ either.

  5. But what if we consider an ideal unrealistic world where frictionless surfaces do really exist, but want to be very accurate? Well, then to be this accurate, you'll need to calculate what the interactions between the atoms in your sleeve and in the wall actually are.

    If there indeed is a repulsive force there, you will start slowly accelerating towards left. However, that acceleration will decrease quickly when your sleeve is far from the wall compared to the effective interaction distance between the atoms. In real life, the distance doesn't get very big (a few micrometers is probably enough) before the force $N$ will be smaller than other forces (such as the wind caused by air conditioning pushing you etc. etc.) that are acting on you. So what happens to you in the micrometer scale is unpredictable anyway so accounting for the force $N$ isn't really useful.

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    $\begingroup$ Nice answer. In the OP's situation, the teacher is technically correct (as you point out) but not correct in a practical sense. The teacher should make that clear. If the objects are held together closely enough so that their electrons interact and the objects slightly compress, then they will indeed move apart when the hold is released if the surface is perfectly frictionless. But in questions at this level we usually take simple models of our objects and ignore electrostatic forces and compression forces. $\endgroup$
    – garyp
    Commented Sep 6, 2016 at 18:16
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I see the problem as being the statement "whenever two bodies are in contact there always exist normal force". That really isn't true, because there are many situations where you might wish to have two bodies in contact, and you might not wish there to be any repulsive forces between the bodies. Your example is one of them. So don't think of the normal force as something that automatically appears any time two bodies touch, think of it as a force that can appear whenever two bodies touch. Its strength will always be whatever is necessary to keep one body from penetrating the other, but if there is no tendency for one body to penetrate the other anyway, then there's no need for any normal force. In short, it's a force that always depends on the rest of the situation.

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the misconception is that you are thinking whenever two bodies are in contact there must be a normal force, this is not true. Normal force arise when one body is in contact with other body and also exert a force on it.since in your case the blocks are rest so no force is applied on either body by another. that is why there is no normal force.

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