# Confusion regarding Newton's Third Law of Motion

1. ### jysim

7
I'm just a humble human being here, so if my question comes across as stupid, please forgive me! :)

Newton's Third Law of Motion states that for every action there is an equal (in magnitude) but opposite (in direction) reaction. One of my A-level revision guidebooks state that the attraction forces between the Earth and the Moon is an example of an action-reaction pair. However, isn't the Earth's gravitational force greater than that of the Moon? Does Newton's Third Law of Motion apply to every situation, if so, why does resultant force still exist since every force produced will definitely bring about a reaction which is equal in magnitude and opposite in direction?

2. ### andresordonez

68
The forces between moon and earth are equal in magnitude and opposite in direction. What may be confusing you is that the gravitational fields are different.

The magnitude of the gravitational field of the earth is
$$g_E = \frac{G M_E}{r^2}$$
where r is the distance to the center of the Earth, and G is the gravitational constant

The magnitude of the gravitational field of the moon is
$$g_M = \frac{G M_M}{r^2}$$
where r is the distance to the center of the moon

The magnitude of the force an object with mass m is subjected to when it is in a gravitational field g is
$$F = g m$$

The force the Earth is subjected to by the gravitational field of the moon is
$$F_1 = \frac{G M_M}{r^2} M_E$$
where r is the distance between the moon and the earth.

The force the Moon is subjected to by the gravitational field of the earth is
$$F_2 = \frac{G M_E}{r^2} M_M$$

Note that
$$F_1 = F_2$$

And thus the magnitude of the two forces is the same. The direction of the forces is obviously opposite to each other.

Newton's third law doesn't always apply. Consider for example two charges moving in perpendicular directions. However it is valid for gravitational interactions, and "mechanical interactions" (i.e. when two objects interact by contact).

The resultant force appears because the action force is on one object and the reaction is on the other object (they're not on the same object!). Think of an ice skater that pushes another skater, the resultant force on each of them (same magnitude and opposite direction) will accelerate them and move them apart.

3. ### AlephZero

7,298
You may be getting confused by the force of gravity on an object on the surface of the moon or the surface of the earth, and the force between the moon and the earth.

You are right the weight of the same object (e.g. the astronaut Neil Armstrong) is smaller on the surface of the moon than on the surface of the earth, but in that case the equal and opposite forces are between Armstrong and the earth, or between Armstrong and the moon.

4. ### jysim

7
Thanks andresodonez and AlephZero for clearing things up for me regarding the Earth and Moon issue :)

However, I still don't quite comprehend Newton's Third Law.
Say I push a block on the floor, when I push the block with my hand, there is a reaction force by the block on my hand. But why isn't my hand pushed away by the block as a result? (Since my push on the box causes the box to move)

Sorry for being so dense hahaha! I just have to clear things up for an upcoming test!

5. ### cepheid

5,190
Staff Emeritus
The block does push back on your hand with equal force. If you drew free body diagram for just your hand (nothing else), then you'd have two horizontal forces acting on it. The first force is the reaction force from the block, and the second force is the force on your hand from the part of your arm that it is connected to. Since your hand is accelerating forwards along with the block, Newton's second law says that there must be a NET Force on your hand. In other words, the force from your arm (which is in the direction of motion) must be greater than the force from the block (which is opposite to the direction of motion).

6. ### PeterO

2,319
I use the following situation to try to explain Newton's Third law to my students.

The scenario is a student attempting a standing jump from the floor onto a chair which has a cane seat.
The student sort of succeeds, except that having landed on the chair, the cane which makes up the seat is unable to support the student and he breaks through the seat of the chair.
The following statements have to be assessed as True or False.
#1: In order to jump from the floor, the student pushes on the floor with a force greater than the floor pushes on the student.
#2: Having left the floor the student is travelling up but slowing, so the Earth is pulling more strongly on the student than the student is pulling on the Earth.
#3: When the student lands on the chair, the student should find the chair pushes more strongly on the student than the student pushes on the chair, thus stopping the student.
#4: The chair actually breaks - showing that the student pushed more strongly on the chair than the chair pushes on the student.

NOTE: Each of the statements is False.
#1: The student pushes on the floor with a force greater than the student's weight.
#2: Since the pull of he Earth was the only force acting on the student, the student slowed down.
#3: The student hoped the chair would push with a force greater than his weight, thus stopping his downward motion, not merely ensuring constant velocity.
#4: The student pushes with a force less than his weight [because the chair was reacting with a force less than his weight].

7. ### Michael C

132
The block does indeed push against you as hard as you push against it. Which one of you actually moves depends on friction with the floor. If the block has a smooth surface, and is also much lighter than you, then there will be much more friction between you and the floor than there is between the block and the floor. Because of this, it's the block that moves and not you.

Now let's make that floor very, very slippery, so there's practically no friction. This time, when you push against the block, both you and the block will move. The magnitude of the force on both you and the block is the same, but the block will move more than you do because it has less mass. (You can try this out on an ice rink).

Now we keep the floor slippery but we nail down the block so it can't move. This time, when you push against the block, only you move.

8. ### Ken G

3,601
Here is also a list of key things to bear in mind whenever you think about the third law:
1) action/reaction pairs never act on the same object, they are a relationship between two objects. Thus they never cancel out, unless you group both objects into the same system and call the pair a set of internal forces, akin to internal pressure, that do not affect the motion of the center of mass of the united system as a whole.
2) Since the forces don't act on the same object, we generally do not consider both of them when we consider the motion of the object. Instead, we look at all the forces on the object, each of which is a single member of some action/reation pair.
3) The forces in an action/reaction pair are always of the same type-- whether gravity, or contact forces, or electric forces, or whatever. A force is of a given kind, and expresses a relationship between two objects, and that relationship is actually a pair of forces.
4) Action/reaction pairs are not the only time you find two equal and opposite forces, so the presence of balancing forces does not mean you have an action/reaction pair. Indeed, since action/reaction pairs usually do not cancel each other because they act on different objects, when you do find two forces that balance on one object you are not talking about an action/reaction pair. Note also that balancing forces on a single object (like a standing person experiences a gravity downward and a force from the ground upward) are generally not of the same type of force, so again they are not an action/reaction pair. This all means that we do not use action/reaction pairs to infer the motion of a single object, we only use them to understand how two objects move in response to their mutual interaction. In most cases, you never invoke Newton's third law at all, but it is quite useful in proving that internal forces cannot move the center of mass of a united system.

9. ### technician

Imagine the floor you are standing on is an ice rink, If you push against the block it will move away from you but won't you move away from the block, across the ice because of the push on you.

10. ### harrylin

Can you elaborate on that? It appears to me that conservation of momentum implies the third law of Newton, however also accounting for the inertia of field energy.

11. ### nDever

68
You are firmly seated in a rolling office chair and you push yourself from the table. The table doesn't move but you do. The table has returned the force that you gave it. The table didn't move because it was firmly planted on a rug (frictional forces).

When you pushed your block, it pushed you too but you didn't go anywhere because the force it gave you wasn't enough to overcome the frictional forces.