# How is an object kept on a table is at rest?

When there are two bodies A and B lying in contact we can apply Newton's third law which says that the action and the reaction act on different bodies and not on the same body. That is why two forces don't cancel out each other. Fine till now. If this is the case then how can an object kept on a table sit at rest? My teacher says that in this case both the forces are acting on the object kept on the table. Aren't the action and the reaction acting on different bodies that is the table and the object. Is he right?

As usual for mechanical statics problems, the entire thing becomes clear if you draw a free body diagram.

Here we have the object (red) sitting on top of a table (blue) which is sitting on the Earth (black curved line). The object experiences two forces

1. It's weight $W_o$ which is caused by gravitational interaction with the Earth.

2. A normal force $N_{o,T}$ from the table top. Read the subscript $o,T$ as the force "on the object from the Table".

The "reaction" force to $W_o$ is an equally strong gravitational pull acting on the Earth itself. The reaction to the normal force is an equally strong normal force pushing down on the table. The table also experiences a normal force $N_{T,o}$ from the object. This is the reaction to $N_{o,T}$ and has equal magnitude to $N_{o,T}$. the table of course also has a weight force $W_T$ and the Earth feels a reaction as shown.

Because the system is static we know that the forces on the object are balanced $$N_{o,T}=W_o \, .$$ We also know that the forces on the table must be balanced $$N_{T,E} = W_T + N_{T,o} \, .$$ As we said, the normal force on the table from the object is a reaction to the normal force on the object from the table, so their mangitudes are equal, $$N_{T,o} = N_{o,T} \, .$$ Therefore $$N_{T,E} = W_T + N_{o,T} = W_T + W_o \, .$$ This is just a careful derivation of the fact that the upward normal force on the table from the Earth must be the sum of the weight of the table and the object! It's just saying that if you pick up the table you feel the weight of both the table and the object on the table.

• But you are still pretending that you are actually working in an inertial system and that gravity is a force, both of which are not true. No offense, but I don't think one should argue this way since it's physically false, even if it fits the false narrative of "free body diagrams are all of Newton" of high school physics. No offense, but we shouldn't be teaching it this way. What have you accomplished? You have reduced the problem from the table holding things to the floor holding things the same way against the same miraculous "force" that doesn't exist. – CuriousOne Sep 6 '15 at 10:18
• @CuriousOne look, I agree that gravity is not a force. However, I also think one should go one step at a time. I hope OP will read your answer. Between mine and yours hopefully something will be learned. The trouble with your answer alone is that it doesn't actually answer OP's question, it just tells him/her that what he/she thinks is wrong. – DanielSank Sep 6 '15 at 10:37
• @CuriousOne I also don't know what you mean about "holding things the same way against the same miraculous 'force' that doesn't exist". – DanielSank Sep 6 '15 at 10:42
• @adosar of course not. If the object is too heavy, it will break the table and fall down. – DanielSank Mar 16 '20 at 15:11

Imagine there are 3 objects. The Earth, a table on the Earth and a book on the table.

The book has 3 main forces acting on it. The table gravitationally attracts the book but its negligible. There is the Earth pulling it down and the table pushing it up with an equal force that cancels out the Earth. If the book were made heavier, then the atoms in the table would be compressed further resulting in a greater repulsive force. Either way they cancel out.

There is a normal force which is perpendicular to the underside of the object and to the surface of the table. This force is an acceleration of 1g, or 9.8 meters/sec^2. It is equal but in opposite direction to the gravitational force applied to the object by the Earth's gravitational field. The table prevents the object from falling to the ground by imparting the normal force to the object. As the table pushes up against the object, the object presses down on the table, and the table must bear the weight of the object, which is the object's mass * 9.8 meters/sec^2. Therefore, an equal amount of force acts on both the object and the table, in opposite directions.

The object has potential energy equal to its mass * 1g * height of the table. If the table were removed, or if the object were pushed off the table, it would go into free fall and its potential energy would become kinetic energy in the reference frame of the Earth.

(I posted this without seeing that the question had already been clearly and completely answered by Daniel Sank. I'll leave the post because there are a few links that might be helpful.)

According to the 3rd newton law which state that every action has reaction so the weight of the object is the actin a reaction made by the table in the opposite direction is equal to the magnitude of the object weight so the total force is zero

F=-w where : f is the reaction in the upper direction w is the weight of the object

An object resting on a table in a gravity field of 1g is not at rest in an inertial system. Instead it is being accelerated upwards with an acceleration of 1g. The problem is that the surface of the table and the floor are NOT inertial systems and Newton's laws are valid in inertial systems only. The only near inertial systems that humans have access to these days are the International Space Station, the vomit comet and other free falling systems.

• While I agree on everything you say here I think the simpler answer to the question is that "the object" is acted upon by two forces: its weight and the normal force from the table. Not sure we need to get into relativity here. – DanielSank Sep 6 '15 at 4:45
• Yes i was searching for THAT simple answer. Could you elaborate a bit more? – Tajammul Saleem Sep 6 '15 at 4:49
• @DanielSank: I am merely giving the OP the physically correct answer that I was given by my high school physics teacher. One does not need relativity to see that an object resting on a table is not in an inertial system. Newton's laws simply don't apply. They do apply in the ISS, where an apple resting on a table is not experiencing any forces, whatsoever. I think it's good teaching practice to make it absolutely clear to students that the surface of Earth is not an inertial system. Inertial system physics is what the astronauts are experiencing, floating liquid bubbles and all... – CuriousOne Sep 6 '15 at 4:49
• @TajammulSaleem ok, I posted an answer with a diagram. – DanielSank Sep 6 '15 at 5:16