# Newton III and normal force

quark001

## Homework Statement

A book rests on a table. Identify the NIII force pairs.

## The Attempt at a Solution

Downward force of book on table; upward force of table on book (N).
Downward force of book and table on ground; upward force of ground on book and table (N).
Downward force of earth on book, table and ground (gravity); upward force of book, table and ground on earth.

This is where I get confused. The earth and the ground are essentially the same thing, aren't they?

Also, the book is in equilibrium because the normal force of the table and gravity cancel.
The table is in equilibrium because the normal force of the ground and gravity cancel. So why is the ground in equilibrium? Are all normal forces essentially directed from the center of the earth, as is gravity?

cupid.callin
The earth is stable as it is very large having large mass!!!!

mass of earth is 10^24

the force on earth due to table would be ~50N

F = ma
50 = 10^24 * a
a = ~0

quark001
I'm trying to understand the whole gravity/normal force relationship better. I know the earth exerts a gravitational force on all objects, regardless of whether they touch the ground or not.

So does the earth only exert an opposite normal force on an object only once the object touches the ground, or some surface (like a table)?

And am I correct in saying that: I exert a downward force on the earth and the earth exerts an upward (normal) force on me? The earth also exerts a downward force on me (gravity) and therefore I must exert an upward force on the earth?

Mentor
I'm trying to understand the whole gravity/normal force relationship better. I know the earth exerts a gravitational force on all objects, regardless of whether they touch the ground or not.
Good.

So does the earth only exert an opposite normal force on an object only once the object touches the ground, or some surface (like a table)?
A normal force is a contact force between two objects. If there's no contact, there's no normal force. (Very different from gravity.)

And am I correct in saying that: I exert a downward force on the earth and the earth exerts an upward (normal) force on me? The earth also exerts a downward force on me (gravity) and therefore I must exert an upward force on the earth?
Yes. When you are standing on the earth there are two kinds of interaction between you: gravitational forces (which form third law pairs) and the contact/normal forces (which form a different set of third law pairs).

cupid.callin
So does the earth only exert an opposite normal force on an object only once the object touches the ground, or some surface (like a table)?

strictly speaking: earth exerts a gravitational force on everything. the bodies in contact with earth's surface are also acted by by a normal force due to "Surface of earth".
This force is not due to gravity but electromagnetism. and this force follows newton third Law and therefore act in pair!!! therefore WE remain in equilibrium on earth.

And am I correct in saying that: I exert a force on the earth and the earth exerts an upward (normal) force on me? The earth also exerts a downward force on me (gravity) and therefore I must exert an upward force on the earth?

Yes you are correct.
From this you can conclude that force on earth due to "you" is balanced!!! ad same is for you!!!

How ever this is not true when there is no contact. In that case, there will be no normal forces and therefore you and earth will be accelerated towards each other!!!

and you will have acceleration very larger than earth due to reason which i explained above

quark001
Thanks, the replies so far have been very useful!

strictly speaking: earth exerts a gravitational force on everything. the bodies in contact with earth's surface are also acted by by a normal force due to "Surface of earth".

Is it important to distinguish between the "earth" (when speaking of gravity) and the "surface of the earth" (when speaking of normal forces)?

Normal forces always counteract the weight of an object in equilibrium, right? So if an object doesn't have weight, it can't have a normal force working in on it? In other words, are normal forces dependent on gravity?

Staff Emeritus
Is it important to distinguish between the "earth" (when speaking of gravity) and the "surface of the earth" (when speaking of normal forces)?
Yes. The gravitational force exerted by the Earth on you is the sum of the gravitational forces exerted by all of the the Earth on you. The normal force only has to do with the surface at your location.

Normal forces always counteract the weight of an object in equilibrium, right?
No, they don't. Suppose the table is at 45 degrees latitude, making it about 4500 km from the Earth's rotation axis. The Earth rotates on its own axis, one revolution per sidereal day. This means the net force on the book resting on the table cannot be zero. It is necessarily equal to the mass of the book times the centripetal acceleration that results from this (more or less) uniform circular motion. For a 1 kg book, this is net force is about 0.024 newtons. The normal force does not counteract gravitation for a rotating Earth.

There is also atmosphere to consider. Assuming the book has a density of 2 grams/cc, the buoyant force from the atmosphere on a 1 kg book is about 0.000625 newtons. Even if the Earth was not rotating, the normal force still would not exactly balance gravitational force.

This net force and buoyancy might be small forces, but they are not zero. Some other small forces that come into play are the tidal forces. Bottom line: The normal force is not equal but opposite to the gravitational force.

zorro
A normal force is a contact force between two objects. If there's no contact, there's no normal force. (Very different from gravity.)

Will there be any contact force if there is no gravity?

cupid.callin
Will there be any contact force if there is no gravity?

Yes, there still can be coulumb forces

Mentor
Will there be any contact force if there is no gravity?
In general, sure. In this particular example of an object sitting on the ground, no. (Ignoring minor effects such as adhesion, etc.)

The point is that normal force is not directly dependent on gravity.

zorro
In general, sure. In this particular example of an object sitting on the ground, no. (Ignoring minor effects such as adhesion, etc.)

The point is that normal force is not directly dependent on gravity.

I am a bit confused.
The contact force between two bodies is of electromagnetic nature. Is that repulsive or attractive and why? Does it depend on the extent to which we press the ground?

Staff Emeritus
I am a bit confused.
The contact force between two bodies is of electromagnetic nature. Is that repulsive or attractive and why? Does it depend on the extent to which we press the ground?
Yes, it's repulsive.

For a true explanation you will have to delve into condensed matter physics. So instead, here is a cartoonish (but ultimately wrong) explanation: The electrons form a cloud around the nuclei. At a distance, the electrons and protons balance out; the net electric field essentially vanishes. At very close range, the electrons look close than the nuclei. It looks like the surface is negative charge. However, this appearance drops off very quickly to the null-charge view from afar. When two solid objects are in very close proximity, the electrons at the surface of each object repulse the other object. Note that because the objects are each electrically neutral as a whole, this repulsion drops off with increasing distance / builds up with decreasing distance much, much quicker than 1/r2.

In other words, the normal force only occurs when the two objects are "touching".

zorro
Yes, it's repulsive..............In other words, the normal force only occurs when the two objects are "touching".

If thats the case, then the coulumbic forces are of huge magnitude compared to gravitational force. The ratio of electric to gravitational force between two electrons is of the order of 10^42. Why don't we fly off from the earth's surface?

Mentor
If thats the case, then the coulumbic forces are of huge magnitude compared to gravitational force. The ratio of electric to gravitational force between two electrons is of the order of 10^42. Why don't we fly off from the earth's surface?
While the coulombic force between two electrons is much greater than their gravitational force, that's largely irrelevant when considering the normal force. (Reread D H's last post.) The normal force will be just enough to keep you from pushing through the floor.

zorro
that's largely irrelevant when considering the normal force. (Reread D H's last post.)

I don't understand why it is irrelevant here.
Are you referring to this "However, this appearance drops off very quickly to the null-charge view from afar." ?

That means if we jump a feet above the ground, there should be a greater gravitational force acting (neglecting the variation of 'g') because there is no repulsive force due to electrons at that distance.

Staff Emeritus
If you jump a millimeter off the ground there is no repulsive force due to the electrons. The force essentially disappears when the distance is greater than microscopic scale.

zorro
If you jump a millimeter off the ground there is no repulsive force due to the electrons. The force essentially disappears when the distance is greater than microscopic scale.

Yes I agree with that. But that repulsive force is so huge that it can provide you with an escape velocity against the gravity even if it is short ranged. Why do we stick to the earth inspite of that?

cupid.callin
The contact forces are not due to charges but "instantaneous partial charges"

Surface charge density of earth is ~3 x 10-9 C-m-2. and you will be taking like .01m2
Lets consider that you also contain same charge on four feet as the charge on earth in area of contact.

F = (K x 3 x 10-11 x 3 x 10-11)/(.00012 C) = ~ .008N

Is that force enough to give you escape velocity??

Staff Emeritus
Yes I agree with that. But that repulsive force is so huge that it can provide you with an escape velocity against the gravity even if it is short ranged. Why do we stick to the earth inspite of that?
Nobody said anything about escape velocity.

When you press on a spring scale the spring compresses a bit, just enough to counteract the force resulting from your pressing on the spring. Think of the normal force as resulting from an exceedingly stiff spring.

zorro
Nobody said anything about escape velocity.

I wanted to assert that the coulumbic forces are very huge in comparision to the gravitational force.

When you press on a spring scale the spring compresses a bit, just enough to counteract the force resulting from your pressing on the spring. Think of the normal force as resulting from an exceedingly stiff spring.

Thats just a way to exemplify the effect of normal force. I am interested in answering these questions - If the origin of the normal force (a component of the contact force) is of electromagnetic nature which is very huge compared to the gravitational force, why don't we fly off from the surface of earth?

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Mentor
I wanted to assert that the coulumbic forces are very huge in comparision to the gravitational force.
Not between uncharged objects. Unless you crush them together.

cupid.callin
Nobody said anything about escape velocity.

Yes he did !!! :tongue:

Thats just a way to exemplify the effect of normal force. I am interested in answering these questions - If the origin of the normal force (a component of the contact force) is of electromagnetic nature which is very huge compared to the gravitational force, why don't we fly off from the surface of earth? Why is the normal force self adjusting?

Think of a large charged sheet of charge density e-6 C
if you drop a small charge (say an electron) ... it will not just fly away but will stop at some place where its weight is balanced by electrostatic force, right? ...... (forget about SHM)
(you can easily find that in this case)

Consider normal forces in same manner.
The force i explained above (escape velocity one) is .08N which is very small even to balance our weight.
the rest force comes from where DH told (wrong, but still good explanations for now)

when you stand, you press the ground ..... the electrons of your feet's and ground's surface come closer upto a point where weight is balanced ( e-e, p-p repulsions)
now you may say that this distance must be very large as electrostatic force is very large than gravity, ..... the reason is in e-p attractions.
due to the attraction of e-p pair, the distance of equilibrium is reduced to is what we know.

as electrons will be closer than protons .... therefore repulsion dominates.

zorro
Lets end this discussion thinking normal force as a force which acts when a body presses against a surface. The more I think about its origin, the more it spins my head. Its beyond my scope of understanding and I am not going to research on it ( I have more important things to do )

Homework Helper
welcome to pf!

hi quark001! welcome to pf! Is it important to distinguish between the "earth" (when speaking of gravity) and the "surface of the earth" (when speaking of normal forces)?

I wouldn't even say "the earth", i'd always say "gravitational" or "weight" …

eg "the forces on the book are the normal force and the weight"

or "the forces on the book are the normal force and the gravitational force" Lets end this discussion thinking normal force as a force which acts when a body presses against a surface. The more I think about its origin, the more it spins my head. Its beyond my scope of understanding and I am not going to research on it ( I have more important things to do )

I agree! We simplify by talking about heat, rather than energy of molecules, about pressure, rather than collisions of molecules, and so on …

reaction forces are a perfectly legitimate simplification! 