Newton's Third Law (College Board AP® Physics 1: Algebra-Based)

It is a common error to misidentify the forces acting in a third law situation. You may have identified the force acting on the ground as weight. The magnitude of the normal contact force of the foot acting on the ground is equal to the person's weight (assuming only one foot is on the ground) which is where the confusion arises. 

Remember that for a third law pair of forces, they must be the same type of force. So if you are considering the weight of the person, you actually mean the gravitational pull of the Earth on the person. Therefore, the third law pair would be the gravitational pull of the person on the Earth.

It can be very helpful to simplify the language when you deal with third law pairs and just describe the force as a push or a pull to start with.

A good framework for this is a 3 part label: Object A pushes/pulls on Object B, and Object B pushes/pulls on Object A.

From here you can see if you are dealing with a third law pair and add in the extra detail from there.

A physics textbook is at rest on a lab bench. Student A draws a free-body force diagram for the book and labels the forces acting on it.

Student A says the diagram is an example of Newton's third law of motion. Student B disagrees and says the diagram is an example of Newton's first law of motion.

Indicate which student is correct and justify your reasoning.

Answer:

Step 1: State Newton's first law of motion

• Objects will remain at rest or move with a constant velocity unless acted on by a resultant force

Step 2: State Newton's third law of motion

• If Object A exerts a force on Object B, then Object B will exert a force on Object A which is equal in magnitude but opposite in direction

Step 3: Check if the diagram satisfies the conditions for identifying Newton's third law

• A Newton's third law force pair must be:

  • The same type of force 

  • The same magnitude

  • Opposite in direction

  • Acting on different objects

• The forces acting on the book are not the same type

  • The forces acting on the book are weight and normal contact force

• The forces are not acting on different objects

  • Both forces are acting on the book

• Therefore, this is not an example of Newton's third law

  • This is an example of Newton's first law

Step 4: Indicate which person is correct

• Student B is correct

Step 5: Justify your reasoning

• The clue is the free-body force diagram; these only apply to multiple forces acting on one object

• The forces acting on the book are of equal magnitude and in opposite directions, so there is zero resultant force acting on the book and it remains at rest on the lab bench

• To apply Newton's third law to this situation, the interaction between two objects must be considered

  • The book pushes on the table and the table pushes back on the book

    • These are both normal contact forces of equal magnitude and opposite direction

  • The book pulls on the Earth, the Earth pulls on the book

    • These are both weight forces (the gravitational pull of the Earth on the book, and the gravitational pull of the book on the Earth) of equal magnitude and opposite direction

Just because you see two forces of equal magnitude acting in opposite directions doesn't mean they are a Newton's third law force pair! The confusion often arises in the book example because the normal contact force of the book on the table is equal in magnitude and opposite in direction to its weight.

You must remember to apply the specific criteria; a Newton's third law pair must meet all of the criteria.