#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

markdown-image

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.

markdown-image

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!).

markdown-image

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:

markdown-image

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.

markdown-image

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

markdown-image

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

markdown-image

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

markdown-image

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

markdown-image

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! 🌟

#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

markdown-image

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.

markdown-image

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!).

markdown-image

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:

markdown-image

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.

markdown-image

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

markdown-image

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

markdown-image

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

markdown-image

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

markdown-image

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

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

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

#Key Concepts:

#Visualizing Force Pairs

#Identifying Force Pairs

#Common Force Pairs:

#Atwood Machines: A Classic Example

#What is an Atwood Machine?

#Deriving the Acceleration Formula

#Step-by-Step Derivation:

#Common Mistakes and Misconceptions

#Final Exam Focus

#Common Question Types:

#Last-Minute Tips:

#Practice Questions

#Multiple Choice Question 1

#Multiple Choice Question 2

#Free Response Question

#Free Response Question 2

Explore more resources

How are we doing?

Newton's Laws of Motion: Third Law

John Smith

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

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

#Key Concepts:

#Visualizing Force Pairs

#Identifying Force Pairs

#Common Force Pairs:

#Atwood Machines: A Classic Example

#What is an Atwood Machine?

#Deriving the Acceleration Formula

#Step-by-Step Derivation:

#Common Mistakes and Misconceptions

#Final Exam Focus

#Common Question Types:

#Last-Minute Tips:

#Practice Questions

#Multiple Choice Question 1

#Multiple Choice Question 2

#Free Response Question

#Free Response Question 2

Explore more resources

How are we doing?