# Action - Reaction?

I got to know that when a book is kept on a table.

1. Earth attracts it due to Gravitational force. The book responds by attracting the earth with same force. (An action-reaction pair)
2. The book is kept on table therefore it pushes it with a force which is nothing but the same force with which it was attracted by the earth. Thus, the book exerts a force on the table. (Am I correct up to here ?)
3. Now the table responds by pushing the book back which is the normal force. This force is due the Electromagnetic Force between the table and the book molecules.

So, the force with which the book pushes the table is at core due to Gravitational Force. And the force due to which the table pushes the book (i.e. normal force) is at core due to Electromagnet Force. And the both are in turn action-reaction pairs ? Is it true that the reaction of a gravitational force can be electromagnetic force ??

• To your last question: no. An action-reaction pair must consist of the same type of force, exerted in exactly opposite directions and always equal in magnitude. In your example, if the book was on a table in an elevator accelerating upward, the force exerted by the book on the table (and vice versa) would be larger than the force exerted on the book by gravity. You are confusing the causal chain of events (book pulled down by gravity, book pushes into table because table gets in the way, table gets compressed so exerts a force upwards, etc.) with action/reaction. – march Feb 4 '16 at 17:22
• @march Copy that into the answer box - seems like a good answer to me. – Brionius Feb 4 '16 at 17:23

To your last question: no. An action-reaction pair must consist of the same type of force, exerted in exactly opposite directions and always equal in magnitude. That is the content of Newton's 3rd Law, given in mathematical form by $$\vec{F}_{\textrm{1 on 2}} = -\vec{F}_{\textrm{2 on 1}}.$$

In your example, if the book was on a table in an elevator accelerating upward, the force exerted by the book on the table (and vice versa) would be larger than the force exerted on the book by gravity. We infer this by noting that there is a net force upwards on the book (because it is accelerating), and so the force upwards must be larger than the force downwards (which is the gravitational force). The scalar equation looks like $$0\neq m a = F_{\textrm{net}} = F_{\textrm{N, table on book}} - mg.$$ Thus, the force (whatever its nature) exerted by the book on the table and the gravitational force exerted by the Earth on the book do not have to be equal, and therefore cannot compose an action/reaction pair.

You are confusing the causal chain of events with "action/reaction" (which is understandable since the phrase "action/reaction" implies some sort of causal chain, although that is not really the conceptual content of the 3rd Law). In this case, the book is pulled down by the gravitational force exerted by the Earth. The table is in the way, and as a consequence, the book pushes into the table. The table gets compressed (think of the table as a very stiff spring), and so it then exerts a force upwards on the book.

So, to be clear, the statement

So, the force with which the book pushes the table is at core due to Gravitational Force.

is correct, but it is irrelevant. That force might come about as a consequence of the fact that the gravitational force is acting, but that force is not a gravitational force itself.

• Thank you very much..... but I still don't get the normal force (Electromagnetic Force) is reaction force to Electromagnetic force, the book exerts on the table. What is the force called with which book pushes the table ? (Electromagnetic or Gravitational) – I Am K Feb 5 '16 at 5:08
• @KunalInvincible. Any time you have an action/reaction pair, the two forces are of the same type. The book and the table exert forces on each other that are---microscopically---due to electromagnetic forces, although the details of that are a little complicated. At the level of macroscopic objects exerting contact forces on each other, we usually just call the force exerted by two objects on each other perpendicular to the surfaces of contact the normal force and leave it at that. But yes: microscopically, these are electromagnetic forces. – march Feb 5 '16 at 5:11
• I got your point. Thanks a lot.The conclusion is- the force with which the book pushes the table may be "due to" Gravitational Force but the "force itself is not Gravitation but electromagnetic" However, the book was able to apply ELECTROMAGNETIC FORCE on table because it was brought closer to table (on contact) due Gravitational Force. The amount of net electromagnetic force the book applies on the table is in turn equal to the force with which it is being pushed on table. "Which in this case is gravitational force". If book is Pushed harder on table,the EMF the book applies increases – I Am K Feb 5 '16 at 13:33