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Let's say we have two blocks resting over a frictionless surface. The two blocks are next to each other and there is contact between them. Even though there is no force trying to push them closer to each other, is there a normal force between the two blocks?

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    $\begingroup$ Pedantic note, there will be some gravitational attraction between the blocks, so if they are indeed touching, there will be a normal force resisting the attraction. $\endgroup$ – Nuclear Wang Mar 30 at 15:04
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In this case, there wouldn't be a normal force between the blocks. Much like friction, the normal force only acts in opposition to other forces. From a logical real-world perspective, this makes sense too, since if the normal force acted between, say, two billiard balls sitting on a surface, they would start rolling away from each other, which isn't what we observe to happen.

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    $\begingroup$ "Much like friction, the normal force only acts in opposition to other forces." Friction doesn't act in opposition to other forces, it acts in opposition to movement, which might not require other forces present. Similarly, if a ball hits a wall in a gravityless environment, a normal force appears (without any other force) and compresses the ball until it bounces back. $\endgroup$ – JiK Mar 30 at 14:33
  • $\begingroup$ That force appears because the ball compresses the wall, and the wall wants to bounce back. But still there is no force pushing the ball and the wall closer to each other. $\endgroup$ – JiK Mar 30 at 14:37
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    $\begingroup$ @mascoj What do you mean by "force to the collision"? There's only one force-reaction force pair in play: the normal force both objects apply to each other. $\endgroup$ – JiK Mar 30 at 22:32
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    $\begingroup$ However, I wouldn't say that the normal force only acts necessarily in opposition to other forces. Lets say we have a ball in space going at constant velocity (and therefore without expiriencing force) and it´s about to hit a wall. Once they collide, there will be a normal force excerted on the ball and it will either stop or bounce off. $\endgroup$ – Bruce Wayne Mar 31 at 3:28
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    $\begingroup$ "Normal force by definition is a force in response to an applied force, no?" No. Normal force is by definition the force produced by contact between two solid objects. It pushes in a direction normal to the surface, hence the name. The reason the force appears is to stop the two objects from phasing into each other. $\endgroup$ – Michael Ferguson Mar 31 at 3:48
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Contrary to other answers so far, no force is needed to create a normal force. However, if there's no force counteracting the normal force, the situation is obviously not static. So in a static situation, there is always a force that balances the normal force.

Here's a brief explanation of the mechanism that causes the forces to be balanced in many real-life situations, and an example of a situation where a normal force exists without any other forces.


To start, we need to understand what makes a normal force appear.

Imagine putting a heavy box on a trampoline. First, the box pushes the trampoline down. But when the trampoline is stretched, the internal forces try to return it to its original position, which also pushes the box up.

This creates some oscillation, because after the trampoline is stretched too much, the restoring force is actually bigger than the gravity of the box. But eventually the energy dissipates and it settles to a point where the normal force balances the gravity of the box completely, and the box doesn't move.

Now consider a box lying on a floor. With a hard box on a hard floor, the oscillation is completely invisible as it's too small to see and dissipates fast. However, the main reason for the normal force is the same: The floor and the box get compressed a bit on the surface, and it is just enough to create a force that balances the gravity of the box.

If the normal force was bigger than the gravity of the box, the box would start rising, thus decreasing the compression of the floor, thus decreasing the normal force. If the normal force was smaller than the gravity of the box, the box would start going down, thus increasing the compression of the floor, thus increasing the normal force.

So in a static situation, the normal force must balance the force pushing the objects together. Simply because otherwise the situation wouldn't be static.

So now consider your situation. If there was a normal force between the two side-by-side boxes, they would push each other away. But after a very tiny movement, there wouldn't be any more compression, so there would be nothing to cause a normal force. So there is no normal force between the boxes in your situation. Simply because otherwise the situation wouldn't be static.

However, normal forces can appear without any other forces in a dynamic situation. Consider a gravityless environment, where a ball is flying towards a wall. When the ball and the wall touch, a normal force appears for the exact same reasons it appears in the box-on-a-floor or box-on-a-trampoline cases described above. However, there's nothing to balance the normal force: The ball and the wall would first compress, and then start decompressing, and all the time the normal force would be changing the momentum of the ball. Finally, the ball starts flying backwards and leaves the wall, and the normal force gets down to zero.

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    $\begingroup$ Thank you for discussing the dynamic case. To add an idea for a dynamic case that looks static we could consider rotational motion. Consider your laundry inside a washing machine on the fastest spin cycle. The walls of the drum exert a fairly constant normal force on the laundry, but the normal force is not in response to some external force pressing the laundry into the drum. $\endgroup$ – Michael Ferguson Mar 31 at 3:51
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Does the normal force require other forces to exist?

Yes. In statics, the normal force happens when another force pushes something against a surface. The surface pushes back in a direction perpendicular (or normal) to the plane of the surface.

Under static conditions, the surface can't push unless another force pushes first.

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  • $\begingroup$ Would it be correct then to think of the normal force as a restoring force? $\endgroup$ – electronpusher Mar 30 at 11:12
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    $\begingroup$ If a ball hits a wall in a gravityless environment, a normal force appears and compresses the ball until it bounces back. There's no need for a force that pushes the ball towards the wall. $\endgroup$ – JiK Mar 30 at 14:35
  • $\begingroup$ The question has "Free-Body Diagram" as a tag, along with the text that clearly indicated this was a statics question. I updated the text of the answer to reflect that scope. $\endgroup$ – user1717828 Mar 30 at 19:55
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    $\begingroup$ While the text implies statics I wouldn't say it does so clearly. And I don't see how "free body diagram" contributes. I use free body diagrams in dynamics all the time. $\endgroup$ – Michael Ferguson Mar 31 at 3:55

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