# Question Regarding the Normal Force

Suppose I place a lighter on a wooden table, the lighter has a weight, so it wants to go down, but the table exerts a normal force on it, preventing it from going down trough the table, so the lighter does not move. We can say that this is consistent with Newton's first principle of dynamics, in fact the normal force is equal and opposite to the weight force of the lighter, so the net sum of the forces is zero.

But where does the normal force comes from? What implies the presence of a normal force? Well, at a subatomic level the atoms of the lighter and the atoms of the table get really close together and repel each other thanks to the electromagnetic force.

Great! But suppose that now I remove the lighter from the table and place on it an heavy object made of steal, with approximately the same dimension of the lighter. In this case, assuming that the table does not break, the heavy steal object will stay still just like the lighter lighter (fun). Ok, but this implies that in this case the normal force is greater, because it has to equal in module the weight of the steal object.

Note that in both cases the atoms of the object do not "touch" the atoms of the table, they simply get repelled and "hover" at a certain small distance from the atoms of the table.

My question is: In both cases the distance between the atoms of the object and the atoms of the table is the same? Or in the case of an heavier object the distance becomes smaller? Or, since we are talking about subatomic interaction, makes no sense at all to talk about distances between objects?

I was thinking that since in one case the normal force is smaller and in another case the normal force is greater, but the table and the surface of interaction remain the same, then something must change, a change in configuration of the system has to occur in order to motivate a change in the interaction force.

Placing an object on the table causes a small deformation of the table. For a heavy object the deformation may be visible. For a light object the deformation is invisible but is still there.

The deformation stretches some of the intermolecular bonds in the table, and compresses others. This results in a force that tries to restore the bonds to their normal (unstressed) length. It is this restorative force that appears as the normal force.

Of course, if the object is too heavy then the intermolecular bonds in the table will be stretched beyond their ability to recover and the table will be permanently deformed (dented) or may even break.

For more details (and many more fascinating facts) see J. E. Gordon’s excellent books Structure or Why Things Don’t Fall Down and The New Science of Strong Materials or Why You Don’t Fall Through The Floor.

• Wonderful, but still my doubt remains: the distance between the table and the object gets shorter or not? Can we even talk about distance in this subatomic context? Aug 17, 2020 at 11:45
• @Noumeno At the molecular level, the molecules of the object and the table are “close” at a relatively small number of places (because they are not at all smooth at this scale) and these distances do not change much. The main contribution to the normal force is the small changes in the lengths of many many more intermolecular bonds in the body of the table due to the deformation of the table. Aug 17, 2020 at 11:58

The reason ,probably, is that in case of the heavier object the number of interactions increases due to the presence of more mass.If you keep the dimensions of the heavier object same you are increasing the density so essentially you have reduced the region in which the same number of interactions happen. Hence the normal force does not reduce on decreasing the dimensions.

The something that changes here is the number of interactions that have increased in total such that the normal again equals the weight.

• Your explanation seems to come a bit out of the blue. What makes you say that the distance does not change? Do you have any book/article to cite? Do you have some proof for your statement or is it simply a guess? Aug 17, 2020 at 10:00
• I did not deny that distance could not change but it seemed improbable to me for the following reason: Suppose you have a table which breaks from the middle not from its legs when a certain heavy mass is kept. This according to you would mean that distance became so less that repulsion forces caused the break. But this does not take the weight of the table(rather strength) in consideration. That is to say same distance would be between another heavier or stronger table and the heavy mass but that does not break. Also my answer is a rough guess at best.
– Lost
Aug 17, 2020 at 10:15