# Clarification on Newton's 3rd Law

I was looking for some clarifications on Newton's 3rd Law.

I've heard that a book resting on the surface of a table is not an example of Newton's 3rd law. The Earth's gravity pulls down on the book and the resultant force is not the support or normal force but rather the books pull on the Earth. If this is the case, What is the reaction force of the normal force?

Does this mean that Newton's 3rd Law requires the opposite forces to be of the same type? Consider a rocket fired into space. What is the reaction force of the weight of the rocket? My teacher said that the reaction force must be the gravitational force of the rocket on the Earth as this is the same type of force.

What does same type of force even mean? Is there some definition of Newton's 3rd Law that can help me clearly understand these problems? Any online resources or pdfs would help.

## 5 Answers

The reason why the book has no acceleration ("doesn't move") is that it feels two different forces - not one. Had it felt only gravity, it would have accellerated downwards toward the center of the earth, but it doesn't: The force of gravity is balanced by the "normal force" that the table exerts upward on the book - a force whose ultimate explanation is the electrons in the two object deflecting each other.

These two forces - gravity and the normal force - are two different forces that act on the same object (the book), and not the "action and reaction" of Newton's 3rd law which are forces on two different object.

Rather, each of these two forces on the book has an "equal and opposite reaction" of its own, each on a different object:

1. When the earth pulls the book ("gravity") with force F1, the book also pulls the earth with equal and opposite force, -F1 - which is a force that the earth (not the book!) feels. The actual impact on the earth of this force will be tiny, because remember from Newton's second law F=ma, so a=F/m, i.e., the acceleration of the earth due to the force will be the force divided by the huge mass of the earth - which will be tiny.
2. When the table pushes the book up ("normal force") with force F2, the book also pushes down on the table with force -F2. Again, this is a force on the table - not the book.

If this is the case, What is the reaction force of the normal force?

The Newton's 3rd law partner of the normal force on the book is normal force the book exerts on the table.

Does this mean that Newton's 3rd Law requires the opposite forces to be of the same type?

Yes.

Consider a rocket fired into space. What is the reaction force of the weight of the rocket? My teacher said that the reaction force must be the gravitational force of the rocket on the Earth as this is the same type of force.

It depends on what exactly you mean by "the weight of the rocket", but if this means the gravitational force exerted on the rocket by the Earth, then your teacher is correct.

What does same type of force even mean?

For example, if one force in a Newton's 3rd law pair is a gravitational force, then the other force must be a gravitational force as well. Or they are both friction forces, or electric forces, etc.

• Thanks for the clarification. How does the book also exert a normal force on the table? Does this force just happen to be of the same magnitude as the gravitational force on the book? Commented May 20, 2023 at 9:45
• Yes. The normal force that table exerts on the book is due to the table resisting bending. The book is also going to push on the table by resisting bending on its side too. Commented May 20, 2023 at 12:38
• @JamesChadwick The atoms in the table exert electric forces on the atoms in the book, and the atoms in the book exert the same electric forces on the atoms in the table. It's not merely a coincidence — the microscopic forces obey Newton's 3rd law, so the macroscopic forces do too.
– d_b
Commented May 20, 2023 at 18:18

There are two pairs of forces. First we have the gravitational force exerted by the earth on the book and the gravitational force exerted by the book on the earth. Secondly we have the normal force exerted by the book on the table and the normal force exerted by the table on the book. Because of Newton's third law, each of these pairs must be balanced. But Newton's third law doesn't say that the normal force should be equal to the gravitational attraction.

You can think of a force as an exchange of momentum, similar to how you can give money to people by transferring between bank account. When transferring money, no money can be lost. Let's say Alice pays €10 to Bob. Because of conservation of money, Alice must lose the exact amount that Bob gains. If Bob now pays €10 to Chloe, it will seem as if Alice paid €10 to Chloe. But conservation of money doesn't directly apply to the pair Alice-Chloe, it is just coincidentally the same amount. It applies to Alice-Bob and Bob-Chloe separately.

Similarly, the normal force can be different to the weight of an object. If you stand on a scale and bob your body up and down, your weight will fluctuate. The normal force doesn't have to be equal. It just happens to be equal when the object is at rest.

Newton's third law states that forces exist in pairs but they act on seperate bodies. In case1: gravity pulls down the book and books applies the same force on earth. The thing is both forces acts on different bodies. Normal force from the table cancels the gravitational force on book. Normal force is a kind a contact force and book also applies the reaction force which acts on table. There are two pairs $$1.Force_{(B\;due\;to\;E)}=-Force_{(E\;due\;to\;B)}$$ $$2.Force_{(B\;due\;to\;T)}=-Force_{(T\;due\;to\;B)}$$ $$(B\;=Book)$$ $$(T\;=Table)$$ $$(E\;=Earth)$$ There is 3rd pair between book table which also causes the book to remain at rest.

Well to understand your doubt we first need to get deep into what it means when we say that it is the normal force. Normal is basically electromagnetic force. You may ask ,how? Well everything is made up of atoms.When they are far apart there is no electromagnetic interaction but when you push them close enough, the electrons in the atoms start repelling each other. That force of replusion is called Normal force. We must understand that gravity necessarily dont cause the normal force but when atoms come really close(When 2 objects come close)the force of replusion is called Normal force. So you may wonder that why they book doesn't fly off? And the reason is gravity as it hold togeather everthing. It is such that the net force on body is zero.
There was a very beautiful line given in one of my favorite book. These laws are never wrong(Unless relativity comes in ,in which 3rd law is not valid) and what we are doing is basically missing something. The book gave the example of a horsecart case(Which is very famous among beginners). Study about it and you will understand what I want to say.