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G5-3. Using Newton's 3rd Law

The purposes of this guide are to identify the characteristics of action and reaction forces. We'll start with a statement of Newton's 3rd Law that is phrased differently than the one in the text but says the same things.

Newton's 3rd Law: For every force that acts on an object--we'll call this force an action force--there is a reaction force with these characteristics:

• the reaction force acts on a different object than the action force,
• the action and reaction forces have the same magnitude,
• the action and reaction forces have opposite directions.

Note in particular something that makes the 3rd Law fundamentally different from the 2nd Law. The 2nd Law deals with net force and the the acceleration of one object. In order to determine the acceleration of an object using the 2nd Law, you have find the vector sum of all the forces acting on that one object. The emphasis here is on one object. The 3rd Law always deals with the forces on two objects. These two forces, termed action and reaction, have nothing to do with the object's state of motion. So, for example, you couldn't use an action-reaction pair to determine what an object's acceleration is. By the way, the determination of which force of the pair is the action and which is the reaction is arbitrary. One just makes a choice and sticks with it for a particular problem situation.

Given a physical situation, you need to be able to identify action-reaction force pairs. This is easy to do if you apply the three bullets above. Here are some examples.

Example 1:  An apple falls toward the Earth in a vacuum chamber. What is the action-reaction force pair and its characteristics?

Solution: In order to help see how to answer, we prepare a table with two sets of four columns, one set for the action force and one for the reaction force. Note the following:

• The force type is the same for both action and reaction. This will always be true for an action-reaction pair.
• The roles of the objects, Earth and apple in this case, are reversed for the reaction compared to the action force.
• The directions of the forces are opposite for the action-reaction pair.
 Action Reaction force (type) exerted by acts on in what direction force (type) exerted by acts on in what direction gravitation Earth apple down gravitation apple Earth up

Now we translate this information into a sentence as follows.

The gravitational force of the Earth acting on the apple downward is equal in magnitude to the gravitational force of the apple acting on the Earth upward.

That single sentence is the solution to the problem and is sufficient to answer the original question. Note that applying the 3rd law helps us to identify the fact that the apple exerts a gravitational force on the Earth. Perhaps that was a surprise to you. In fact, all objects exert gravitational forces on each other. Since the magnitudes of the gravitational forces exerted by the apple and Earth are the same, you may wonder why the Earth doesn't fall up to meet the apple at the same rate that the apple falls down to meet the Earth. The answer involves application of the 2nd Law. Since the magnitudes of the forces are the same, the acceleration of either object is inversely-proportional to its mass. The Earth has much greater mass than the apple and therefore has a much smaller acceleration. The Earth's acceleration is, in fact, too small to be noticeable.

Example 2: Let's take the situation further. Suppose that air friction is present; that is, we take the apple out of the vacuum chamber. What are the action-reaction force pairs and their characteristics now?

Solution: We still have the gravitational forces. We add the friction forces to the table.

 Action Reaction force (type) exerted by acts on in what direction force (type) exerted by acts on in what direction gravitation Earth apple down gravitation apple Earth up friction air apple up friction apple air down

Translated into a sentence:

The friction force of the air acting on the apple upward is equal in magnitude to the friction force of the apple acting on the air downward.

To help make sense of this, on a molecular level, molecules in the air collide with the apple. In each collision of the apple with a molecule, the apple and molecule exert equal and opposite forces on each other.

Now we'll consider a situation that is a bit more troublesome but can be sorted out quickly by using a table for organization.

Example 3. A book rests on a table. Identify the action-reaction force pairs and their characteristics.

Solution: There are two types of forces acting; these are normal and gravitation. There is an action-reaction pair for each type.

 Action Reaction force (type) exerted by acts on in what direction force (type) exerted by acts on in what direction gravitation Earth book down gravitation book Earth up normal table book up normal book table down

Now in sentence form:

The gravitational force of the Earth acting on the book downward is equal in magnitude to the gravitational force of the book acting on the Earth upward.

The normal force of the table acting on the book upward is equal in magnitude to the normal force of the book acting on the table downward.

The fact that the book and the table each exert a normal force says that each supports the other. That may seem like an odd thing to say, but application of the 3rd Law predicts that fact.