Newton's laws multiple choice question

[mcdavid&goliath]

Homework Statement

A book of mass m is sitting on a table of mass M. Which of the following statements regarding Newton's Laws of motion is true?

(a) Newton's Third Law says that the magnitude of the normal force from the table on the book is equal to mg.
(b) Newton's Second Law says that the normal force from the ground on the table is equal to Mg.
(c) Newton's Third Law says that the normal force from the ground on the table is equal and opposite the normal force from the book on the table.
(d) Newton's Second Law says that the magnitude of the gravitational force on the book from the Earth is equal and opposite the gravitational force on the Earth from the book.
(e) Newton's Third Law says that the normal force on the table from the ground is equal and opposite the normal force on the ground from the table.

Homework Equations

F_net = ma
F_{A on B} = -F_{B on A}

The Attempt at a Solution

I was thinking that the answer is (e) since it's a statement of Newton's third law (the two normal forces are force pairs), but the answer key has (a) as the answer. Can anyone help me out?

 

[haruspex]

I was thinking that the answer is (e) since it's a statement of Newton's third law (the two normal forces are force pairs), but the answer key has (a) as the answer.

I'm with you. (a) is also true, and also requires Newton's 3rd law, but it also requires other laws. It is only the combination of those laws that leads to (a).

 

[J Hann]

The force of the table on the ground is the weight of the table (plus book).
The normal force is the reaction force due to that weight.
The normal force is generally a reaction force to forces that you can describe using
the laws of physics and is perpendicular to the surface upon which it is acting.
That leaves out (e) because you know the force on the ground from the table.

 

[mcdavid&goliath]

Since the table is in contact with the ground, it must exert a normal force on the ground right?

 

[haruspex]

The force of the table on the ground is the weight of the table (plus book).
The normal force is the reaction force due to that weight.
The normal force is generally a reaction force to forces that you can describe using
the laws of physics and is perpendicular to the surface upon which it is acting.
That leaves out (e) because you know the force on the ground from the table.

Not sure what you are concluding there. Do you agree e is a valid answer or not? If not, on what grounds?

 

[J Hann]

Not sure what you are concluding there. Do you agree e is a valid answer or not? If not, on what grounds?

I would have to accept (e) as a correct answer in addition to (a).
It just seems that one would diagram the forces with the weight of the table (and book) acting
on the ground and the normal force would act in the opposite direction.
So if one wants to describe the normal force as any perpendicular force acting between
two objects in contact then (e) has to be acceptable.

 

[jbriggs444]

I'm with you. (a) is also true, and also requires Newton's 3rd law, but it also requires other laws. It is only the combination of those laws that leads to (a).

a is NOT true. You are misreading the answer.

(a) Newton's Third Law says that the magnitude of the normal force from the table on the book is equal to mg.

A) is not a statement about what the normal force is. It is a statement about what Newton's Third Law says.

It is indeed correct that for a book just sitting there (not accelerating) that the normal force will be equal to mg. But that is not a direct consequence of Newton's third law. That is a consequence of Newton's third law in conjunction with Newton's second law and the law of gravity [and the fact that nobody has their hands on the book].

As such, a) is not a correct statement.

 

[haruspex]

a is NOT true. You are misreading the answer.

no, I read it OK, but was careless in my phrasing. I meant that the last part of the sentence in (a) is true, but that it can only be derived from N3 by combining it with other laws. Thanks for picking that up.

 

[jbriggs444]

I apologize for the accusation. Thank you for accepting it gracefully.

 

[haruspex]

I apologize for the accusation. Thank you for accepting it gracefully.

No apology necessary. It is important to challenge statements that may tend to confuse students.

 

[Mister T]

(a) Newton's Third Law says that the magnitude of the normal force from the table on the book is equal to mg.

Newton's Third Law implies that the magnitude of the normal force from the table on the book is equal to the magnitude of the normal force from the book on the table. That magnitude is mg but you need Newton's Second Law to draw that conclusion.

(e) Newton's Third Law says that the normal force on the table from the ground is equal and opposite the normal force on the ground from the table.

Yes. I agree.

If you changed "Newton's Third Law" to "Newton's Second Law" in both those statements that would make (a) true and (e) false.

 

[mcdavid&goliath]

Thanks everyone!

 

[Mister T]

Okay, now that the OP is done, can I ask you what makes you think (a) has anything to do with Newton's Third Law?

(a) Newton's Third Law says that the magnitude of the normal force from the table on the book is equal to mg.

The net force on the book in the vertical direction must be zero. There's a downward force of magnitude mg and an upward normal force, both exerted on the book.

Now, if they said the magnitude of the normal force from the book on the table equals mg, I'd agree that you need both N2 and N3.