Isaac Newton’s Laws of Motion form the foundation of AP® Physics 1, shaping how we analyze forces and motion. While all three laws are essential, Newton’s Third Law of Motion—which states that every action has an equal and opposite reaction—is particularly important for solving force-related problems on the AP® exam. Mastering this law helps explain real-world phenomena like normal forces, tension, and propulsion, from walking to the mechanics of rocket launches.

What is Newton’s Third Law of Motion?

Newton’s Third Law of Motion states: “For every action, there is an equal and opposite reaction.” This means when an object exerts a force on another object, the second object exerts a force back that is equal in size but opposite in direction. This can be expressed mathematically as F_{A \text{ on } B} = -F_{B \text{ on } A}.

• Action and Reaction Forces: These forces come in pairs known as interaction pairs. They act on two different objects and are always equal in magnitude but opposite in direction.
• Recognizing Interaction Pairs: This understanding helps in solving physics problems as they allow us to categorize forces effectively.

Force Pairs

Forces always occur in pairs, known as interaction pairs. A common mistake students make is thinking that action-reaction forces cancel out, but they do not because they act on different objects. If object A pushes on object B, then object B pushes back on object A with equal force. The forces are always of equal magnitude and in opposite directions, but they act on two distinct objects.

For example, when a swimmer pushes backward on the water, the water pushes forward on the swimmer. Another example is a book resting on a table. The book pushes down on the table due to gravity, and the table pushes up on the book with an equal normal force.

Recognizing True Interaction Pairs in AP® Physics 1

When solving physics problems, correctly identifying interaction pairs is crucial. A common pitfall is confusing Newton’s Third Law forces with forces acting on a single object.

Incorrect Thinking:

• A book on a table experiences gravity downward and a normal force upward. Since these forces cancel, they must be an action-reaction pair. ❌ (Wrong: These forces act on the same object, not two different objects.)

Correct Thinking:

• The book pulls down on the Earth with a gravitational force, and the Earth pulls up on the book with an equal and opposite gravitational force. ✅ (Correct: These forces involve two objects—Earth and the book.)

By keeping this distinction clear, AP® Physics 1 students can avoid common mistakes and confidently apply Newton’s Third Law in force-related problems!

Real-World Examples of Newton’s Third Law

Walking

To fully analyze walking through the lens of Newton’s Third Law, let’s break it down into key steps:

Step 1: Identify the Action Force

When a person steps forward, their foot applies a force on the ground in the backward direction.

Step 2: Recognize the Reaction Force

In response, the ground exerts an equal and opposite force forward on the foot. This force is what propels the person forward.

Step 3: Apply Newton’s Third Law Mathematically

Using Newton’s Third Law, we can express this force interaction as:

F_{\text{foot on ground}} = -F_{\text{ground on foot}}

…where:

• F_{\text{foot on ground}} is the force exerted by the foot on the ground (backward).
• F_{\text{ground on foot}}​ is the equal and opposite force exerted by the ground (forward).

This reaction force overcomes inertia and accelerates the person forward. The greater the force applied backward, the greater the forward acceleration—this is why running requires pushing harder against the ground.

Understanding Internal and External Forces

In physics, forces can be classified as internal or external, depending on whether they originate within or outside a system.

Internal forces are exerted by objects within a system on each other and do not change the motion of the system’s center of mass. For example, the forces between atoms in a solid or the tension within a rope are internal because they do not influence the system’s overall movement.

External forces, on the other hand, come from outside the system and can change its center of mass motion. A classic example is a car’s engine: while its parts exert internal forces on each other, the vehicle will not move forward unless an external force—such as the friction between the tires and the road—acts on it.

Tension in Systems: An Application of Newton’s Third Law

Tension is the force that is transmitted through a string, rope, or cable when it is pulled tight by forces acting from opposite ends. It plays a crucial role in AP® Physics 1, particularly in problems involving pulleys, elevators, and hanging masses. Since tension is a force, it follows Newton’s Laws, meaning it can be analyzed using free-body diagrams and force equations.

In many physics problems, we assume ideal strings, which means they have zero mass and do not stretch or compress. This simplifies calculations because the tension is the same at all points along the string. In reality, ropes and cables do have mass and elasticity, but for introductory physics problems, this assumption makes problem-solving more manageable.

Example Analysis: Equilibrium in a Pulley System

Consider a system where a pulley is used to lift a mass, and the system is in equilibrium (no acceleration). To determine the tension in the string, follow these steps:

• Step 1: Analyze Forces on Each Mass and String Segment
  • Draw a free-body diagram for each mass in the system.
  • Identify forces acting on the masses: gravity and tension.
  • If the system includes a pulley, recognize that tension acts throughout the entire string, assuming it is ideal.
• Step 2: Apply Newton’s Third Law to Tension Forces
  • Since the string is continuous and massless, the tension force is equal and opposite at both ends: F_{\text{tension on mass A}} = -F_{\text{tension on mass B}}
  • This equality holds in equilibrium, meaning neither mass is accelerating.
• Step 3: Solve for Tension Using Force Balance Equations
  • In equilibrium, the sum of all forces must be zero (\sum F = 0).
  • If the system is not in equilibrium, use Newton’s Second Law (\sum F = ma) to find acceleration and then determine the tension.

Understanding how to analyze tension forces is essential for solving pulley and string problems efficiently. Mastering these steps will help with AP® Physics 1 free-response and multiple-choice questions, particularly those involving force interactions and equilibrium conditions.

Non-Ideal Strings

Unlike ideal strings, non-ideal strings have mass, which affects tension along their length. In such cases, tension is not uniform because different sections of the string must support not only the attached object but also the weight of the string itself. This becomes especially important in problems involving long or heavy cables, such as elevator cables or suspension bridges.

Practical Problem-Solving Using Newton’s Third Law

Example 1: Calculating Forces on a Rope

Problem: A person pulls on a rope attached to a wall. If the person pulls with a force of 100 N, what is the force exerted by the wall?

Solution:

• Step 1: Action force: pulling force by person, F_{\text{person on rope}} = 100 \text{ N}.
• Step 2: Reaction force: force by wall, F_{\text{rope on wall}} = 100 \text{ N}.

Example 2: Two-Mass Pulley System

Problem: Two masses, 5 kg and 10 kg, are connected by a string over a pulley. What is the tension in the string?

Solution:

• Step 1: Calculate Net Force and Acceleration Using Newton’s Second Law:
  • (m_1 + m_2)a = (m_2 - m_1) g
  • Substituting values:
  • (5 + 10)a = (10 - 5)(10)
  • 15a = 50
  • a = 3.3 \text{ m/s}^2
• Step 2: Determine Tension
  • For the 5 kg mass:
    • F_T - m_1 g = m_1 a
    • F_T - (5)(10) = (5)(3.3)
    • F_T - 50 = 16.5
    • F_T = 67 \text{ N}
  • For the 10 kg mass:
    • m_2 g - F_T = m_2 a
    • (10)(10) - F_T = (10)(3.3)
    • 100- F_T = 33
    • F_T = 67 \text{ N}
• Final Answer: The tension in the string is approximately 67 N.

Summary and Key Takeaways: Newton’s Third Law of Motion

Newton’s Third Law of Motion explains that forces always come in equal and opposite pairs. Recognizing action-reaction pairs is pivotal in solving motion-related problems. Remember that internal forces cancel within a system, whereas external forces cause motion. Practicing these concepts solidifies understanding.

Newton’s Third Law is foundational for mastering physics. Its principles apply widely across various scenarios. Confidence in this law enables tackling both academic and real-world challenges, equipping students with essential physics problem-solving skills.

Term	Definition
Newton’s Third Law of Motion	For every action, there is an equal and opposite reaction.
Interaction Pairs	Pairs of forces acting on two separate objects, equal in magnitude and opposite in direction.
Internal Forces	Forces exchanged by objects within a system, not affecting the overall motion of the system’s center of mass.
External Forces	Forces acting on a system from external sources, impacting the motion of the system’s center of mass.
Tension	The pulling force transmitted along a flexible medium, such as a string or cable when it is subjected to forces at each end.

Sharpen Your Skills for AP® Physics 1

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