# Newton's Third Law Pairs

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#### suomi24

##### Full Member
5+ Year Member
I'm Reviewing NS Exam 1 right now, and have a question about #27 on the physics section.

Question: "A book rests horizontally on a table. The book experiences a gravitational force of mg due to the earth’s gravity. According to Newton’s third law:"

The correct answer is "the earth experiences a gravitational force of mg from the book"

I answered that the normal force would oppose Fg. "the book experiences a normal force of mg pushing up due to the table."

I understand the reasoning behind the correct answer, my question is if Force of gravity exerted on an object by the earth and vice versa constitutes a Newton's Third Law Pair, then what is the "equal and opposite reaction" to the normal force? We all learned to to draw free body diagrams with force of gravity being opposed by the normal force, so if that isn't Newton's third law where does it come from?

Hi, suomi24--

The book and table are in contact, so they must have equal and opposite forces. The book pushes down on the table, and the table pushes back on the book. The table's force on the book is the normal force. A free body diagram does not show Newton's third law pair because, by definition, the pair of forces must act on different objects--the two forces cannot act on the same object. The earth and book paired forces are done through gravitational forces. So the free body diagram you are drawing has the two forces done on the book--the earth's gravitational force downward called the weight force, and the book's contact force upward called the normal force. They are equal because the book is in static equilibrium; if it was free-falling, it would have no normal force.

If you drew a free body diagram of the table, you would have three forces acting on it: the earth's gravitational force downward + the earth's gravitational force on the book downward (the mass of the book puts extra force down on the table) = the earth's contact force pushing up on the table (the normal force).

Of course, the book pushes down on the table with the same value as the earth's gravitational pull puts on the book (the earth is the source of the force, after all). If you push down on the book with your hand, the normal force will increase, but the weight force of the book does not change (mass of the book is constant); we simply add a third force in this case.

I hope that helps.

Good luck studying!

Thanks!

Hi, suomi24--

The book and table are in contact, so they must have equal and opposite forces. The book pushes down on the table, and the table pushes back on the book. The table's force on the book is the normal force. A free body diagram does not show Newton's third law pair because, by definition, the pair of forces must act on different objects--the two forces cannot act on the same object. The earth and book paired forces are done through gravitational forces. So the free body diagram you are drawing has the two forces done on the book--the earth's gravitational force downward called the weight force, and the book's contact force upward called the normal force. They are equal because the book is in static equilibrium; if it was free-falling, it would have no normal force.

If you drew a free body diagram of the table, you would have three forces acting on it: the earth's gravitational force downward + the earth's gravitational force on the book downward (the mass of the book puts extra force down on the table) = the earth's contact force pushing up on the table (the normal force).

Of course, the book pushes down on the table with the same value as the earth's gravitational pull puts on the book (the earth is the source of the force, after all). If you push down on the book with your hand, the normal force will increase, but the weight force of the book does not change (mass of the book is constant); we simply add a third force in this case.

I hope that helps.

Good luck studying!