What Is the Reaction Force to Earth's Gravitational Pull on a Book?

[Saitama]

Homework Statement

A book is at rest on a table. What is the "reaction" force according to Newton's third law to the gravitational force by the Earth on the book?

(1)the normal force exerted by the table on the book
(2)the normal force exerted by the table on the ground
(3)the normal force exerted by the ground on the table
(4)the gravitational force exerted on the Earth by the book

Homework Equations

The Attempt at a Solution

Analysing the FBD of book, the forces acting on it are its own weight and the normal reaction from the table. So the answer should be 1 but the answer key states 4. I understand that weight is the "gravitational force" exerted on the book by the earth. I don't see how 4 is the answer.

Any help is appreciated. Thanks!

 

[phinds]

I'm with you. Don't see what we could be missing that would allow #4 to the right answer.

 

[WannabeNewton]

This is a very common misconception that arises. Newton's 3rd law for the given scenario says that since the Earth exerts a gravitational force on the book, the book exerts an equal and opposite gravitational force on the Earth. This is the reaction force; the force pairs in Newton's 3rd law act on two distinct interacting bodies, not the same body. The normal force from the table on the book is of an entirely different physical origin not to mention it acts on the book itself so there is no way it can be the 3rd law reaction force due to the gravitational force exerted by the Earth on the book.

 

[Saitama]

This is the reaction force; the force pairs in Newton's 3rd law act on two distinct interacting bodies, not the same body.

Completely missed it, thanks! :)

So that would mean that if I suspend the book in the air, the answer still remains the same?

 

[voko]

To supplement Newton on Newton.

Note that the question is formulated very precisely: it is talking about the reaction force to the gravitational force by the Earth on the book, NOT to the weight.

Why?

Because "the gravitational force by the Earth on the book" is applied to the book. This is commonly known as "weight", but "weight" has a couple of conflicting definitions, one of which is "the gravitational force by the earth", and the other is whatever is felt by the support of the object with the weight. The normal force of the table is the reaction to this "whatever is felt by the support", which is a different force; suffice it to say it acts on the table, not on the book.

 

[WannabeNewton]

So that would mean that if I suspend the book in the air, the answer still remains the same?

Yes the 3rd law reaction force due to the gravitational force of the Earth on the book is always the gravitational force of the book on the Earth.

That's a great point Voko. The various connotations of the term "weight" is certainly something to keep in mind if the term shows up in some context.

 

[Saitama]

Note that the question is formulated very precisely: it is talking about the reaction force to the gravitational force by the Earth on the book, NOT to the weight.

Why?

Because "the gravitational force by the Earth on the book" is applied to the book. This is commonly known as "weight", but "weight" has a couple of conflicting definitions, one of which is "the gravitational force by the earth", and the other is whatever is felt by the support of the object with the weight. The normal force of the table is the reaction to this "whatever is felt by the support", which is a different force; suffice it to say it acts on the table, not on the book.

Thanks voko!

In this case, is it correct to say that "whatever is felt by the support" is equal to the "gravitational force by the Earth on the book" in magnitude? I guess that would be incorrect, there are two normal forces acting on the legs of the table. So for equilibrium, $Mg+N=N_1+N_2$ where M is mass of table and N1 and N2 are the normal forces on the legs. N is the force due to the book on the table. Correct?

 

[voko]

In this case, is it correct to say that "whatever is felt by the support" is equal to the "gravitational force by the Earth on the book" in magnitude? I guess that would be incorrect, there are two normal forces acting on the legs of the table.

That's my mistake. I should have said "whatever is felt by the support of an object from the object".

The book feels two forces: the pull of gravity and the normal force from the table. Because it is stationary, these must be equal in magnitude and opposite in direction. By Newton's third law, then, the table must feel (from the book) a force equal in magnitude and opposite in direction to the force it exerts on the book, which, in the stationary case, is thus equal to the force of gravity felt by the book.

In a non-stationary case this force may be different from the force due to gravity!

 

[technician]

Where did this question come from?
Is it a published exam question?

 

[Saitama]

That's my mistake. I should have said "whatever is felt by the support of an object from the object".

The book feels two forces: the pull of gravity and the normal force from the table. Because it is stationary, these must be equal in magnitude and opposite in direction. By Newton's third law, then, the table must feel (from the book) a force equal in magnitude and opposite in direction to the force it exerts on the book, which, in the stationary case, is thus equal to the force of gravity felt by the book.

In a non-stationary case this force may be different from the force due to gravity!

Thanks voko!

Where did this question come from?
Is it a published exam question?

I copied this question from a practice sheet, well, kind of hard to explain but I hope you get an idea. Why would you like to know that anyways? ;)

 

[technician]

As a teacher it is always interesting where questions come from, not all questions are good questions!
This is a very straight forward question and, unfortunately, some of the responses are misleading.
I agree that 4 is the correct answer.

 

[Enigman]

Thanks voko!
I copied this question from a practice sheet, well, kind of hard to explain but I hope you get an idea. Why would you like to know that anyways? ;)

An I.I.T. D.P.P. or is it N.E.E.T. ?

 

[D H]

As a teacher it is always interesting where questions come from, not all questions are good questions!
This is a very straight forward question and, unfortunately, some of the responses are misleading.

While we see a lot of bad questions coming from India, this isn't one of them. This is a very good, straightforward, unambiguous question with only one possible correct answer, which is #4. That one of the choices is a bit misleading (#1) is intentional. That the correct answer should be #1 is a very common misconception amongst students, so it's best to address this misconception head on. You teachers should check for this misconception, and that's exactly what this question is doing.

The third law reaction to the downward gravity force by the Earth on the book is *not* the upward normal force by the table on the book. It can't be, for three reasons.

• Test #1: Are the forces equal but opposite?
  Poke a tiny bit deeper and one can see that the downward gravitational force on the book and the upward normal force on the book are not equal but opposite forces. The net force on the book is not zero. It can't be because the book is undergoing uniform circular motion about the Earth's rotational axis. There are also other forces acting on the book such as buoyancy from the air and tidal forces from the Sun and Moon. Newton's third law doesn't ask say that third law force pairs are approximately equal but opposite. It is an exact law.
  
  However, one doesn't need to go to this depth of analysis to eliminate option #1 as a possibility. There are two simpler tests that let's one say that option #1 is incorrect.
• Test #2: Are the two forces acting on two different bodies?
  With answer #1, both forces act on the book, the normal force on the book and the gravitational force on the book. These two forces cannot form a third law force pair per this test. The third law reaction of some force F imposed by body A on body B is the force -F imposed by body B on body A.
• Test #3: Are the two forces two different aspects of the same force?
  With answer #1, one of the forces is gravitation, the other, the normal force. Third body force pairs must necessarily be different aspects of the same force. The reaction to gravitation is gravitation, the reaction to the normal force is the normal force. The reaction to gravitation cannot be the normal force.

 

[Saitama]

Those three tests do look useful, thanks a lot D H! :)

 

[technician]

While we see a lot of bad questions coming from India, this isn't one of them. This is a very good, straightforward, unambiguous question with only one possible correct answer, which is #4. That one of the choices is a bit misleading (#1) is intentional. That the correct answer should be #1 is a very common misconception amongst students, so it's best to address this misconception head on. You teachers should check for this misconception, and that's exactly what this question is doing.

I completely agree with you, it is a straight forward good question.
I think you misunderstood my reference to 'responses' !
It is not the response in the question that I was referring to !
Us teachers look at student responses and if there is any pattern of misunderstanding we would then look at the question in more detail. Examiners reports regarding exams pick up these issues regarding questions.
If the responses (in the question) were in a different order the proportion of correct answers from students could be different. I have been aware of this in my teaching.