AP Physics 1: Newton's Third Law Deep Dive

Newton’s Third Law is deceptively simple to state but consistently challenging to apply correctly. Mastering it is not about memorizing "for every action there is an equal and opposite reaction"; it's about developing the analytical skill to dissect complex force interactions, which is fundamental to solving a wide range of AP Physics 1 problems, from two-block systems to rocket propulsion. This deep dive will move you beyond the slogan to a functional, problem-solving understanding of action-reaction pairs.

The Core Definition and Identifying True Pairs

Newton’s Third Law states: If object A exerts a force on object B, then object B simultaneously exerts a force on object A that is equal in magnitude and opposite in direction. These two forces are an action-reaction pair.

The critical, non-negotiable features of a true third law pair are:

1. The forces are of the same type (e.g., both gravitational, both normal, both tension).
2. They act on two different objects.
3. They are always equal in magnitude and opposite in direction.

Consider a book resting on a table. The Earth pulls down on the book with the force of gravity ($F_{g,book}$). The true third law partner to this force is not the table pushing up on the book. Instead, it is the book pulling up on the Earth ($F_{g,Earth}$). Both are gravitational forces, and they act on different objects (book and Earth).

The second pair in the table—the contact force between the book and table—is also a valid Newton’s Third Law pair. Confusing the upward normal force on the book with the reaction to gravity is one of the most common conceptual errors.

Why Action-Reaction Pairs Never Cancel Each Other

A fundamental consequence of the third law is that the two forces in a pair never act on the same object. Since they act on different objects, they cannot cancel each other out in a force analysis. Cancellation of forces only occurs within a free-body diagram (FBD), which analyzes the net force on a single object.

Let’s return to the book on the table. In the book’s FBD, there are two forces: gravity (down) and the normal force from the table (up). If the book is at rest, these forces are equal and opposite on the book, so they cancel, resulting in zero net force and no acceleration. These are not a third law pair; they are two different forces (gravitational and normal) acting on the same object (the book). Their balance is a consequence of Newton’s First or Second Law (ΣF = 0 for equilibrium).

The third law pair partners to these forces—the book pulling on the Earth and the table pushing on the book—are completely absent from the book’s FBD because they act on the Earth and the table, respectively. Keeping the "different objects" rule clear in your mind is the key to avoiding cancellation confusion.

Analyzing Contact Forces Between Objects

Complex problems often involve multiple objects in contact, like two blocks being pushed along a frictionless surface. Newton’s Third Law is the essential tool for analyzing the forces at the interface.

Imagine Block A (2 kg) and Block B (3 kg) on a frictionless table. You push on Block A with a 10 N force to the right. To find the acceleration of the system and the contact force between the blocks, you must employ a disciplined method:

1. Define the action-reaction pair at the contact. Block A pushes on Block B with a force $F_{AonB}$ to the right. Therefore, by Newton’s Third Law, Block B pushes on Block A with a force $F_{BonA}$ of equal magnitude to the left.
2. Draw separate FBDs for each object.

• For Block A: Forces include the applied 10 N force (right), $F_{BonA}$ (left), and gravity/normal forces (which cancel vertically).
• For Block B: The only horizontal force is $F_{AonB}$ (right).

1. Apply Newton’s Second Law (ΣF = ma) to each FBD.

• System: Treating both blocks as one object (5 kg), the only external horizontal force is the 10 N push. Thus, $a_{system}=10N/5kg=2m/s^2$.
• Block B: $F_{AonB}=m_B\ast a=(3kg)(2m/s^2)=6N$.
• By the third law, $F_{BonA}$ is also 6 N.
• Check Block A: ΣF = 10 N (right) - 6 N (left) = 4 N. $m_A\ast a=(2kg)(2m/s^2)=4N$. It checks out.

This process shows how the internal contact forces (the third law pair) are determined by the motion of the objects and the external forces applied.

Applying the Law to Pushing and Pulling Scenarios

Pushing and pulling scenarios often involve ropes, strings, or direct contact, and they test your understanding of how forces transmit through agents. A classic puzzle question highlights a key principle: A rope under tension pulls with equal magnitude on the objects at both ends.

Consider you (70 kg) and a friend (50 kg) on frictionless ice. You pull on a light rope connecting you both with a force of 60 N.

• Third Law Pairs: Your hand pulls on the rope (action); the rope pulls on your hand (reaction, 60 N leftward on you). At the other end, the rope pulls on your friend (action, 60 N rightward on them); your friend’s hand pulls on the rope (reaction).
• Analysis: The rope’s tension is 60 N throughout. The net external force on the you-rope-friend system is zero. Therefore, the center of mass does not accelerate. However, internal forces cause each of you to accelerate toward each other.
• Your acceleration: $a_{you}=F_{net}/m=60N/70kg\approx 0.86m/s^2$ (leftward).
• Friend’s acceleration: $a_{friend}=60N/50kg=1.2m/s^2$ (rightward).

The forces on you and your friend are a third law pair via the rope, so they are equal. The difference in acceleration is due solely to the difference in mass.

Common Pitfalls

Pitfall 1: Confusing "balanced forces" with "third law pairs."

• Mistake: Saying the upward normal force on a stationary object is the reaction to the downward gravitational force.
• Correction: Check the "two different objects" rule. For forces to be balanced on a single object (ΣF=0), they must act on that same object. A third law pair always acts on two different objects and therefore never appears together on a single FBD to be "balanced."

Pitfall 2: Assuming the weaker object exerts a weaker force.

• Mistake: In a collision between a truck and a car, believing the truck exerts a larger force on the car than the car exerts on the truck.
• Correction: The third law is absolute. The forces are always equal in magnitude. The dramatic difference in outcome is due to the difference in mass and resulting acceleration (Newton’s Second Law: $a=F/m$), not a difference in the contact force magnitude.

Pitfall 3: Misidentifying the agent and receiver of a force.

• Mistake: Stating "the force of the hand" without specifying what the hand is acting on and what is acting on the hand.
• Correction: Always phrase forces explicitly: "The hand exerts a force on the box." This discipline makes identifying the corresponding reaction force ("The box exerts a force on the hand") straightforward.

Pitfall 4: Thinking tension in a rope is "used up" or differs if masses differ.

• Mistake: In the ice-pulling example, thinking you pull on your friend with 60 N but they pull back on you with less force because they are lighter.
• Correction: For a massless rope (a standard AP assumption), tension is transmitted undiminished. The third-law pair of forces at each end of the rope segment are equal, making the tension constant.

Summary

• A true Newton’s Third Law pair consists of two forces that are always the same type, equal in magnitude, opposite in direction, and act on two different objects. The mantra "same type, different objects" is your best guide.
• Action-reaction forces never cancel each other out because they act on different objects. Cancellation only happens within the free-body diagram of a single object when forces are balanced.
• To analyze contact forces, define the third-law pair at the interface, draw separate free-body diagrams, and apply Newton’s Second Law to each object systematically.
• In pulling/pushing scenarios with ropes, tension pulls equally on both attached objects. Different accelerations result from different masses, not different magnitudes of force.
• Consistently ask "What is the agent? What is the object acted upon?" This discipline prevents most misidentifications of force pairs.