# Upward force on a object at rest

Is there an upward force on a object at rest? If yes, where does it come from?

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Can you be more specific about the situation? I have a feeling you're referring to an object in the Earth's gravitational field resting on some kind of surface? – dbrane Mar 12 '11 at 22:53
You mean on an object lying on the ground? If so, the answer is yes. It comes from the ground. Do you want more precise microscopic description of this? – Marek Mar 12 '11 at 22:54
No, there is no force on an object at rest. – user1708 Mar 13 '11 at 2:26
You should add why, we people get tired keeping a lifted weight in our hands but tables don't! :))) – Val May 12 '13 at 9:42

Lennard-Jones potential is a big answer to the confusion

The force is a spacial deriviative of the energy, F = dE/dr. So, positive derivative, where plot goes up you get attractive force, and where it goes down you will have repulsion. You see that there is a huge reuplsion between atoms when the distance between them, r, is very small. So, they cannot be pulled very closely. As gravity pulls book to the molecules of table, they repel very strongly. Atoms tend to stay at distance $r_m$, producing molecular structures. Please note that the repulisve force appears at distances smaller than distance between molecules. So, you do not feel it normally, when keep your book is above the table. The reaction force is zero at that distance.

You can make it visible at visible distances, though, by chaining zillions of atoms in one chain. Then, when you compress the chain by 1 mm, the distance between atoms varies by fraction of $r_m$. You get into the parabolic potential well $r_m$. You call such setup a spring. You expand it - you see that atoms attract. You contract it -- and see that they repel.

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The upward force on an object at rest is called the Normal force and is always perpendicular to the surface. If you recall from Newton's Third law, "Every action has an equal and opposite reaction."

So an example is a block sitting on a table. The block is exerting a force DOWN on the table from the gravitational force, its weight. By Newton's Third law, there is an equal an opposite reaction due to this downward force. The block is "pushing" down on the table, so the table must also push UP on the block. This pushing from the table is the normal force. If this force were not present, the block would accelerate right through the table due to Newton's Second Law.

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This is my second most hated thing about physics, personally it seems as though the upward force was just invented to fit the law. and that the reason the book doesn't fall through the table is simply because there is a table in the way :) – Jonathan. Apr 15 '11 at 20:58
One of the first things to check with such old (and quiet) threads is to look when the starter of it, in this case user2123, was seen last. It happens that this was Mar 12. – Georg Apr 15 '11 at 20:59
@Jonathan: for one thing, you can measure the upward force by pressing a scale against the table. So it's real, it wasn't just invented. Besides, how else would you mathematically express the fact "there is a table in the way"? (I guess you could do it with a Lagrange multiplier and a constraint function but that's another story) – David Z Apr 15 '11 at 21:17

It is all electrostatics. The electrons on the outer shells of the atoms of the object don't want to be anywhere near the electrons of the atoms on the resting surface providing a repelling force which increases with proximity. When this force balances with gravity you have reached "equilibrium". In fact, everything is somewhat fluid as the atoms move and vibrate nothing is really static. But on a macroscopic scale it is unnoticeable.

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I don't think this is relevant; you're referring to electrostatics in a very newtonian situation. – Garan May 12 '13 at 9:02
I do not think that crystals are sorta fluid, even at the microscopic level. And, I do not think that it is appropriate to ground the repulsion on the liquidness. – Val May 12 '13 at 9:37

Yes, it's called the normal force. It comes from the rigidity of the stuff separating the object from the center of gravitational attraction, i.e. the rigidity of the rocks, dirt, floor, table, etc. If you'd like, you could think of this stuff as behaving like a spring with a huge spring constant.

Any first-year physics textbook will cover this; there's a very incomplete list of books in another question.

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It's normal force equals its weight per Newton's third law. – Michael Luciuk Mar 12 '11 at 23:10
Michael Lucluk: You mean Newton's second law! Normal force equals weight (for an object that's subject only to those two forces and is not accelerating) because the total force on the object is zero in those circumstances. The third law says that the normal force on A due to B equals the normal force on B due to A; it doesn't say that normal force equals weight. – Ted Bunn Mar 12 '11 at 23:17
Sorry Ted. As usual my pen exceeded my brainpower. – Michael Luciuk Mar 13 '11 at 0:13
Stupid question: where does the energy come from to provide this upward force? – Jonathan. Apr 15 '11 at 20:59
@jonathan It does not require any energy transfer to provide a force. Energy will be transferred if there is a force on an object in the direction of its motion. – Mark Eichenlaub Apr 15 '11 at 21:05

## protected by Qmechanic♦May 12 '13 at 8:24

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