EK Physics question - Newton's third law

[pine138]

EK Physics Item 21:

Newton's Third Law states that for every action there exists an equal and opposite reaction. What is the force that acts in reaction to the force of Earth's gravity on an object on its surface?

A) The normal force that the object exerts on the Earth
B) The force of gravity that the object exerts on the Earth
C) The normal force that the Earth exerts on the object
D) The force of gravity that the Earth exerts on the object

Answer

Spoiler

B is correct. Newton's Third Law refers to the same type of force acting between two objects. In this case the Earth exerts a force of gravity on an object and the object exerts an equal and opposite force on the Earth. Choice A is incorrect because the normal force is not always equal in magnitude to the force of gravity; for example, the normal force on an inclined plane. Choices C and D are incorrect because the reaction force would be exerted by the object on the Earth. Choice D also restates the same force that is acting in the question stem.

I do not understand the rationale for the answer. I had chosen C because the normal force is the reactionary force to the force of gravity.

Thanks!

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[aldol16]

The normal force is not the opposite force of gravity. The normal force is just a force perpendicular to whatever surface the object is on that keeps it from "falling" through the surface. In other words, it's the force of the surface on the object, not of the Earth on the object. To see this in a concrete example, think about resting a book on a table. The book isn't falling through the table so there must be a force preventing it from doing so. The table is exerting a force on the book that is equal to the force exerted by the book on the table. If the table was inclined, it would still exert a force on the book that is perpendicular to its surface so that the book doesn't fall through the surface. But since it's inclined now and there's no force preventing the book from sliding down the (frictionless) table, the book will do so due to gravity.

Newton's third law simply states that any force that object A exerts on object B, object B exerts an equal but opposite force on object A. Keep your objects straight. If object A = Earth and object B = book, then book exerts an equal but opposite force on object A. The reason the Earth doesn't appreciably accelerate towards the book is because the Earth is so massive that any acceleration is minuscule.

 

[Asteri]

Hey pine,

Newton's third law is used in situations with object pairs. Whenever one object acts upon the other via any type of force, the second object acts equally and in an opposite fashion to the first force. In this case, the first force (the Earth acting upon an object via gravity) is the Earth acting upon the object. Thus, the equal and opposite force must come from the object acting upon the Earth. This is the rationale why C and D are wrong choices, as the equal and opposite force cannot be the Earth acting upon the object again - it must be the object acting upon the Earth.

My guess is that you were thinking of the force diagram of an object sitting flat on the Earth (no ramps - we will discuss that below). Gravity pulls the object down, and the normal force pushes up. However, in Newton's third law we have to look at the forces acting upon the Earth to find the equal and opposite reaction - not continuing to look at the force diagram of the object.

While A represents a force of the object acting upon the Earth, it still is not correct. The reason given by EK is that normal force is not always equal to gravity - they use the example of a ramp, where friction is partly used to counteract gravity. Thus, gravity and the normal force are not always equal (or opposite for that matter), and thus this answer does not fulfill Newton's third law. Personally I don't think this explanation is very intuitive (I wouldn't have thought of ramps first), so I will explain other reasons why A is wrong below.

Generally* in force pairs like this, the forces are the same type of force. So for example, when the Sun acts upon the Earth via gravity the Earth acts equally and oppositely upon the Sun via gravity. When two magnets interact with each other, they both exert magnetic forces in an equal and opposite manner. When two objects touch, they exert equal and opposite normal forces upon each other. That is another reason why A and C are wrong - normal forces are not part of the force pair in objects as described in this system. They may happen to be equal magnitude or opposite direction in some cases, but it is not guaranteed (thus it cannot be part of Newton's third law). But in this case, when the Earth exerts gravity upon an object there must exist a gravitational force from the object upon the Earth, and this must have the same magnitude (remember, F = G*m1*m2/r^2 will be the same in both cases - m1,m2, and r will be the same in each direction) and opposite direction (i.e. the object pulls the Earth towards the object, the Earth pulls the object towards the Earth).


Hopefully that helped you understand why A, C, D are wrong, and why B is correct. If it didn't, please ask for further clarification!

*I cannot think of any counterexample and doubt there are any

 

[pine138]

Thank you both!
This really helped clear it up.

Just a quick followup question: Is there a force pair for normal force?

 

[Asteri]

Yes, there is. For example, in this system the normal force exerted by the Earth is what keeps the object from accelerating inside of the Earth. Likewise, there is a normal force exerted by the object onto the Earth to keep the Earth from accelerating into the object - recall that otherwise, due to the force of gravity from the object pulling the Earth, there would be acceleration of the Earth towards the object (i.e. an unbalanced force leading to acceleration).

Note that you can also see this in collisions - when one object impacts another, an equal an opposite force (basically a normal force) is exerted on each object in the duration of the collision.

 

[aldol16]

Just a quick followup question: Is there a force pair for normal force?

The normal force is really a simplification of the electromagnetic repulsion felt between moving atoms close together, at the microscopic level. The sum of all those repulsive forces at surface-object interfaces gives you the normal force. So at the microscopic level, the atoms in the object repel the atoms in the surface, which gives rise to the normal force. Therefore, the atoms in the object are exerting a repulsive force on the atoms in the surface. The atoms in the surface are exerting an equal but opposite force on the atoms in the object.

At the macroscopic level, the normal force is exerted by surfaces on objects. So the opposite force to the normal force of the surface on an object is the force of the object on the surface.