#AP Physics C: Mechanics - Newton's Third Law Study Guide 🚀

Hey there, future physics champ! Let's break down Newton's Third Law and make sure you're totally ready to ace that exam. This guide is designed to be your go-to resource, especially the night before the test. Let's get started!

#Newton's Third Law of Motion: Action-Reaction Pairs

For every action, there is an equal and opposite reaction.

It's more than just a catchy phrase; it's a fundamental principle! Let's make sure you understand it inside and out.

Key Concept

Newton's Third Law is all about force pairs. These forces are:

Always between two interacting objects.
Always the same type of force (e.g., both are tension, both are gravitational).
Always equal in magnitude but opposite in direction.

#Key Concepts:

Action-Reaction: If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.
Simultaneous Forces: These forces occur at the same time; one doesn't cause the other.
Universal Application: This law applies to all forces: gravity, electromagnetism, etc.

Memory Aid

Think of it like a handshake: When you push on someone's hand, they push back on yours with the same force, but in the opposite direction.

#Visualizing Force Pairs

A visual representation of Newton's Third Law. The force exerted by the hand on the wall is equal and opposite to the force exerted by the wall on the hand.

Another example of action-reaction pairs. The force of the foot on the ball is paired with the force of the ball on the foot.

#Identifying Force Pairs

Identify the interacting objects: Who is pushing on whom?
Determine the force type: Is it tension, friction, gravity, etc.?
Visualize the direction: Are the forces acting in opposite directions?

Exam Tip

When drawing free-body diagrams, use the same color or circle force pairs to help visualize them. This can prevent errors when setting up equations!

#Common Force Pairs:

Friction between two surfaces
Tension in a rope or cable
Air resistance on a moving object
Gravity between two objects
Magnetic force between two magnets

#Atwood Machines: A Classic Example

Atwood machines are a favorite on the AP exam because they combine Newton's Second and Third Laws. Let's get comfortable with them!

#What is an Atwood Machine?

Two masses connected by a string over a pulley.
Used to demonstrate the relationship between force, mass, and acceleration.
Assumptions: massless string, frictionless pulley (usually!).

A typical Atwood Machine setup with two masses connected by a string over a pulley.

#Deriving the Acceleration Formula

Free Body Diagrams: Draw them for each mass, showing tension (T) and weight (mg).
Newton's Second Law: Apply ΣF = ma to each mass.
- For m1: T - m1g = m1a
- For m2: m2g - T = m2a
Combine Equations: Eliminate T (tension) to solve for acceleration (a).

$a = \frac{m_2 - m_1}{m_1 + m_2}g$

Quick Fact

The acceleration of an Atwood machine is determined by the difference in the masses divided by the sum of the masses, all multiplied by g.

#Step-by-Step Derivation:

Free body diagrams for each mass in the Atwood machine.

$T - m_1g = m_1a$

$m_2g - T = m_2a$

Adding the two equations:

$-m_1g + m_2g = m_1a + m_2a$

Factor out g and a:

$(m_2 - m_1)g = (m_1 + m_2)a$

Isolate a:

$a = \frac{m_2 - m_1}{m_1 + m_2}g$

Common Mistake

Don't forget the signs! Make sure you assign positive and negative directions consistently. Usually, the direction of motion is considered positive.

#Common Mistakes and Misconceptions

Single Forces Don't Exist: Every force has a partner. A single force without a reaction is a no-go.
Gravity is a Force Pair: When you push down on Earth, it pushes back on you equally.
Action-Reaction Pairs Don't Cancel: They act on different objects, so they don't cancel out in the same free-body diagram.

The action-reaction pair is the swimmer pushing on the wall and the wall pushing back on the swimmer. These forces don't cancel because they act on different objects.

#Final Exam Focus

Alright, let's talk strategy for the big day. Here's what to focus on:

High-Priority Topics:

Newton's Third Law and identifying action-reaction pairs
Atwood Machines and related calculations
Free-body diagrams and system analysis
Combining Newton's laws with other concepts (like energy and momentum)

#Common Question Types:

Multiple Choice: Conceptual questions about force pairs, identifying forces, and applying Newton's Third Law.
Free Response: Deriving equations for systems like Atwood machines, analyzing forces in complex scenarios, and explaining the relationship between action and reaction forces.

#Last-Minute Tips:

Time Management: Don't spend too long on one question. If you're stuck, move on and come back later.
Free Body Diagrams are Key: Always start with a clear FBD. It's the foundation for solving the problem.
Read Carefully: Pay attention to the wording of the question. Identify what it's asking and what information is given.
Show Your Work: Even if you don't get the final answer, you can get partial credit for your process.
Stay Calm: Take a deep breath and approach each question with confidence. You've got this!

#Practice Questions

Let's put your knowledge to the test with some practice questions!

Practice Question

#Multiple Choice Question 1

A child on a swing is held at rest by two ropes.

Which of the following best represents the free-body diagram for the child on the swing?

A) T_L and T_R point upwards, W points downwards, T_L and T_R are larger than W B) T_L and T_R point upwards, W points downwards, T_L and T_R are smaller than W and they cancel each other C) T_L and T_R point upwards, W points downwards, T_L and T_R are larger than W and they don't cancel each other D) T_L and T_R point upwards, W points downwards, T_L and T_R are smaller than W and they don't cancel each other E) T_L and T_R point downwards, W points downwards, T_L and T_R are smaller than W and they don't cancel each other

Answer: D

#Multiple Choice Question 2

Two blocks connected by a string are being pulled by a force F.

Two blocks of masses m1 and m2 are connected by a string. A force F is applied to m1, causing both blocks to accelerate. Which of the following statements is true regarding the tension in the string?

A) The tension is equal to F B) The tension is greater than F C) The tension is less than F but greater than zero D) The tension is zero E) The tension is equal to the weight of the blocks

Answer: C

#Free Response Question

Two blocks, L and K, are connected and pushed by a force F.

Two blocks, L (5 kg) and K (9 kg), are connected by a string. A force F pushes block L, causing both blocks to move to the right with an acceleration of 2 m/s². Assume no friction.

(a) Draw free-body diagrams for each block. (b) Determine the magnitude of the force exerted by block L on block K (F_{L on K}). (c) Determine the magnitude of the applied force F.

Answer:

(a) Free-body diagrams:

Block L: Force F to the right, tension T to the left.
Block K: Tension T to the right.

(b) Since both blocks are moving together, the force exerted by block L on block K (F_{L on K}) is equal to the tension in the string. Using Newton's Second Law for block K:

<math-block>F\_{L on K} = T = m\_K a = (9 \text{ kg})(2 \text{ m/s}^2) = 18 \text{ N}</math-block>

<math-block>F - T = m\_L a</math-block>

<math-block>F = m\_L a + T = (5 \text{ kg})(2 \text{ m/s}^2) + 18 \text{ N} = 10 \text{ N} + 18 \text{ N} = 28 \text{ N}</math-block>

Therefore, the magnitude of the applied force F is 28 N.

Practice Question

#Free Response Question 2

Dave is pushing off the ground.

Dave, who weighs 589 N, pushes off the ground and accelerates at 4 m/s². By Newton's Third Law, what force does Dave exert on the ground?

Answer:

First, find Dave's mass:

$m = \frac{W}{g} = \frac{589 \text{ N}}{9.81 \text{ m/s}^2} \approx 60 \text{ kg}$

Next, find the force Dave exerts on the ground using Newton's Second Law:

$F = ma = (60 \text{ kg})(4 \text{ m/s}^2) = 240 \text{ N}$

By Newton's Third Law, Dave exerts a force of 240 N on the ground.

You've got this! Go get that 5! 🌟

Newton's Laws of Motion: Third Law

John Smith

9 min read

Next Topic - Work, Energy, and Power

Listen to this study note

Study Guide Overview

This study guide covers Newton's Third Law, focusing on action-reaction pairs, their characteristics, and identification. It explores common force pair examples like friction and tension, and uses Atwood machines as a practical application of the law. The guide also provides a derivation of the acceleration formula for Atwood machines, common mistakes, and exam tips including free-body diagrams. Finally, it includes practice multiple-choice and free-response questions for exam preparation.

#AP Physics C: Mechanics - Newton's Third Law Study Guide 🚀

#Newton's Third Law of Motion: Action-Reaction Pairs

For every action, there is an equal and opposite reaction.

It's more than just a catchy phrase; it's a fundamental principle! Let's make sure you understand it inside and out.

Key Concept

Newton's Third Law is all about force pairs. These forces are:

Always between two interacting objects.
Always the same type of force (e.g., both are tension, both are gravitational).
Always equal in magnitude but opposite in direction.

#Key Concepts:

Action-Reaction: If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.
Simultaneous Forces: These forces occur at the same time; one doesn't cause the other.
Universal Application: This law applies to all forces: gravity, electromagnetism, etc.

Memory Aid

Think of it like a handshake: When you push on someone's hand, they push back on yours with the same force, but in the opposite direction.

#Visualizing Force Pairs

A visual representation of Newton's Third Law. The force exerted by the hand on the wall is equal and opposite to the force exerted by the wall on the hand.

Another example of action-reaction pairs. The force of the foot on the ball is paired with the force of the ball on the foot.

#Identifying Force Pairs

Identify the interacting objects: Who is pushing on whom?
Determine the force type: Is it tension, friction, gravity, etc.?
Visualize the direction: Are the forces acting in opposite directions?

Exam Tip

When drawing free-body diagrams, use the same color or circle force pairs to help visualize them. This can prevent errors when setting up equations!

#Common Force Pairs:

Friction between two surfaces
Tension in a rope or cable
Air resistance on a moving object
Gravity between two objects
Magnetic force between two magnets

#Atwood Machines: A Classic Example

Atwood machines are a favorite on the AP exam because they combine Newton's Second and Third Laws. Let's get comfortable with them!

#What is an Atwood Machine?

Two masses connected by a string over a pulley.
Used to demonstrate the relationship between force, mass, and acceleration.
Assumptions: massless string, frictionless pulley (usually!).

A typical Atwood Machine setup with two masses connected by a string over a pulley.

#Deriving the Acceleration Formula

Free Body Diagrams: Draw them for each mass, showing tension (T) and weight (mg).
Newton's Second Law: Apply ΣF = ma to each mass.
- For m1: T - m1g = m1a
- For m2: m2g - T = m2a
Combine Equations: Eliminate T (tension) to solve for acceleration (a).

$a = \frac{m_2 - m_1}{m_1 + m_2}g$

Quick Fact

The acceleration of an Atwood machine is determined by the difference in the masses divided by the sum of the masses, all multiplied by g.

#Step-by-Step Derivation:

Free body diagrams for each mass in the Atwood machine.

$T - m_1g = m_1a$

$m_2g - T = m_2a$

Adding the two equations:

$-m_1g + m_2g = m_1a + m_2a$

Factor out g and a:

$(m_2 - m_1)g = (m_1 + m_2)a$

Isolate a:

$a = \frac{m_2 - m_1}{m_1 + m_2}g$

Common Mistake

Don't forget the signs! Make sure you assign positive and negative directions consistently. Usually, the direction of motion is considered positive.

#Common Mistakes and Misconceptions

Single Forces Don't Exist: Every force has a partner. A single force without a reaction is a no-go.
Gravity is a Force Pair: When you push down on Earth, it pushes back on you equally.
Action-Reaction Pairs Don't Cancel: They act on different objects, so they don't cancel out in the same free-body diagram.

The action-reaction pair is the swimmer pushing on the wall and the wall pushing back on the swimmer. These forces don't cancel because they act on different objects.

#Final Exam Focus

Alright, let's talk strategy for the big day. Here's what to focus on:

High-Priority Topics:

Newton's Third Law and identifying action-reaction pairs
Atwood Machines and related calculations
Free-body diagrams and system analysis
Combining Newton's laws with other concepts (like energy and momentum)

#Common Question Types:

Multiple Choice: Conceptual questions about force pairs, identifying forces, and applying Newton's Third Law.
Free Response: Deriving equations for systems like Atwood machines, analyzing forces in complex scenarios, and explaining the relationship between action and reaction forces.

#Last-Minute Tips:

Time Management: Don't spend too long on one question. If you're stuck, move on and come back later.
Free Body Diagrams are Key: Always start with a clear FBD. It's the foundation for solving the problem.
Read Carefully: Pay attention to the wording of the question. Identify what it's asking and what information is given.
Show Your Work: Even if you don't get the final answer, you can get partial credit for your process.
Stay Calm: Take a deep breath and approach each question with confidence. You've got this!

#Practice Questions

Let's put your knowledge to the test with some practice questions!

Practice Question

#Multiple Choice Question 1

A child on a swing is held at rest by two ropes.

Which of the following best represents the free-body diagram for the child on the swing?

Answer: D

#Multiple Choice Question 2

Two blocks connected by a string are being pulled by a force F.

Two blocks of masses m1 and m2 are connected by a string. A force F is applied to m1, causing both blocks to accelerate. Which of the following statements is true regarding the tension in the string?

A) The tension is equal to F B) The tension is greater than F C) The tension is less than F but greater than zero D) The tension is zero E) The tension is equal to the weight of the blocks

Answer: C

#Free Response Question

Two blocks, L and K, are connected and pushed by a force F.

Two blocks, L (5 kg) and K (9 kg), are connected by a string. A force F pushes block L, causing both blocks to move to the right with an acceleration of 2 m/s². Assume no friction.

(a) Draw free-body diagrams for each block. (b) Determine the magnitude of the force exerted by block L on block K (F_{L on K}). (c) Determine the magnitude of the applied force F.

Answer:

(a) Free-body diagrams:

Block L: Force F to the right, tension T to the left.
Block K: Tension T to the right.

(b) Since both blocks are moving together, the force exerted by block L on block K (F_{L on K}) is equal to the tension in the string. Using Newton's Second Law for block K:

<math-block>F\_{L on K} = T = m\_K a = (9 \text{ kg})(2 \text{ m/s}^2) = 18 \text{ N}</math-block>

<math-block>F - T = m\_L a</math-block>

<math-block>F = m\_L a + T = (5 \text{ kg})(2 \text{ m/s}^2) + 18 \text{ N} = 10 \text{ N} + 18 \text{ N} = 28 \text{ N}</math-block>

Therefore, the magnitude of the applied force F is 28 N.

Practice Question

#Free Response Question 2

Dave is pushing off the ground.

Dave, who weighs 589 N, pushes off the ground and accelerates at 4 m/s². By Newton's Third Law, what force does Dave exert on the ground?

Answer:

First, find Dave's mass:

$m = \frac{W}{g} = \frac{589 \text{ N}}{9.81 \text{ m/s}^2} \approx 60 \text{ kg}$

Next, find the force Dave exerts on the ground using Newton's Second Law:

$F = ma = (60 \text{ kg})(4 \text{ m/s}^2) = 240 \text{ N}$

By Newton's Third Law, Dave exerts a force of 240 N on the ground.

You've got this! Go get that 5! 🌟

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A book is placed on a table. What is the reaction force to the force of the book on the table? 🤔

The weight of the book

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