Chapter 7 Newton’s Third Law

A photograph of a hammer striking a nail.

The hammer and nail are interacting. The forces of the hammer on the nail and the nail on the hammer are an action/reaction pair of forces.

In This Chapter, you will use Newton’s third law to understand how objects interact.

What is an interaction?

All forces are interactions in which objects exert forces on each other. If A pushes on B, then B pushes back on A. These two forces form an action/reaction pair of forces. One can’t exist without the other.

《 LOOKING BACK Section 5.5 Forces, interactions, and Newton’s second law

The figure illustrates an action reaction pair using the objects "A" and B.

What is an interaction diagram?

We will often analyze a problem by defining a system—the objects of interest—and the larger environment that acts on the system. An interaction diagram is a key visual tool for identifying action/reaction forces of interaction inside the system and external forces from agents in the environment.

The figure illustrates the System and interaction between the two objects depicted within a box surrounded by the Environment.

How do we model ropes and pulleys?

A common way that two objects interact is to be connected via a rope or cable or string. Pulleys change the direction of the tension forces. We will often model

  • Ropes and strings as massless;

  • Pulleys as massless and frictionless.

The objects’ accelerations are constrained to have the same magnitude.

The figure illustrates two blocks labeled "A" and B connected by a rope.

What is Newton’s third law?

Newton’s third law governs interactions:

  • Every force is a member of an action/reaction pair.

  • The two members of a pair act on different objects.

  • The two members of a pair are equal in magnitude but opposite in direction.

The figure illustrates a rocket accelerating upward. Two equal and opposite force vector arrows point upward and downward from the rocket thrusters.

How is Newton’s third law used?

The dynamics problem-solving strategy of Chapter 6 is still our primary tool.

  • Draw a free-body diagram for each object.

  • Identify and show action/reaction pairs.

  • Use Newton’s second law for each object.

  • Relate forces with Newton’s third law.

《 LOOKING BACK Section 6.2 Problem-Solving Strategy 6.1

The figure illustrates two free body diagrams for an action reaction pair R and C on the x y coordinate plane.

Why is Newton’s third law important?

We started our study of dynamics with only the first two of Newton’s laws in order to practice identifying and using forces. But objects in the real world don’t exist in isolation—they interact with each other. Newton’s third law gives us a much more complete view of mechanics. The third law is also an essential tool in the practical application of physics to problems in engineering and technology.

Learning Objectives

After studying this chapter, you should be able to

  1. 7.1 Represent interactions with an interaction diagram.

  2. 7.2 Solve interaction problems using Newton’s third law.

  3. 7.3 Apply acceleration constraints.

  4. 7.4 Solve problems that include ropes and pulleys.