Newton's Third Law & Action-Reaction Pairs: Videos & Practice Problems

Newton's third law, known as the law of action-reaction, states that for every action force, there is an equal and opposite reaction force. This means that when one object exerts a force on another, the second object exerts a force of equal magnitude but in the opposite direction. For example, if a person pushes a block with a force of 20 newtons, the block pushes back with a force of -20 newtons. Understanding these force pairs is crucial for analyzing motion and calculating acceleration using the equation F = m × a.

Newton's Third Law & Action-Reaction Pairs

Newton's third law, known as the law of action and reaction, states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another, the second object exerts a force of equal magnitude but in the opposite direction back on the first object. For example, if person A pushes block B with a force of 50 newtons (denoted as \( F_{AB} = 50 \, \text{N} \)), block B exerts a force back on person A, represented as \( F_{BA} = -50 \, \text{N} \). It is crucial to understand that these forces act on different objects, preventing them from canceling each other out and allowing for movement.

In practical terms, consider the normal force, which is the force exerted by a surface to support the weight of an object resting on it. If block A exerts a downward force due to its weight, the floor exerts an equal upward normal force in response. Another example is gravitational force; while the Earth pulls you down with a force of \( mg \) (where \( m \) is mass and \( g \) is the acceleration due to gravity), you also pull on the Earth with an equal force, though the Earth's massive size results in negligible acceleration.

To illustrate these concepts, consider a scenario where an 80 kg person (A) stands on a frozen lake and pushes a 40 kg ice block (B) with a force of 20 newtons. The force exerted by the person on the block is \( F_{AB} = 20 \, \text{N} \). According to Newton's third law, the block exerts an equal and opposite force on the person, \( F_{BA} = -20 \, \text{N} \). To analyze the motion, free body diagrams for both objects must be drawn, identifying all forces acting on them.

For block B, the only horizontal force is \( F_{AB} \), while for person A, the only horizontal force is the reaction force \( F_{BA} \). Using the equation \( F = ma \), we can calculate the acceleration of each object. For block B, the equation becomes:

\[ F_{AB} = m_B \cdot a_B \Rightarrow 20 \, \text{N} = 40 \, \text{kg} \cdot a_B \Rightarrow a_B = 0.5 \, \text{m/s}^2 \]

For person A, the equation is:

\[ -F_{BA} = m_A \cdot a_A \Rightarrow -20 \, \text{N} = 80 \, \text{kg} \cdot a_A \Rightarrow a_A = -0.25 \, \text{m/s}^2 \]

This example highlights that even though the forces are equal, the resulting accelerations differ due to the mass of each object. The acceleration is inversely proportional to mass, meaning that objects with different masses will accelerate differently when subjected to the same force.

Which of the options is NOT an action-reaction pair in the following situation? A book slides across the floor, slowing down due to friction.

• A. Friction on the book from the floor & friction on the floor from the book
• B. Weight of the book from the Earth & gravitational force on the Earth from the book
• C. Weight of the book & normal force on the book
• D. Normal force on the book from the floor & normal force on the floor from the book

Answer: (C)

Here’s what students ask on this topic:

What is Newton's third law of motion?

Newton's third law of motion, also known as the law of action-reaction, states that for every action force, there is an equal and opposite reaction force. This means that if one object exerts a force on another object, the second object exerts a force of equal magnitude but in the opposite direction on the first object. Mathematically, this can be expressed as:

$F_{\mathrm{AB}}=-F_{\mathrm{BA}}$

where $F_{\mathrm{AB}}$ is the force exerted by object A on object B, and $F_{\mathrm{BA}}$ is the force exerted by object B on object A.

Can you give an example of Newton's third law in everyday life?

A common example of Newton's third law in everyday life is the interaction between a person and the ground when walking. When you push your foot backward against the ground, the ground pushes your foot forward with an equal and opposite force. This reaction force propels you forward, allowing you to walk. Another example is the normal force: when you place a book on a table, the book exerts a downward force due to gravity, and the table exerts an equal and opposite upward force, preventing the book from falling.

How does Newton's third law apply to rocket propulsion?

Newton's third law is fundamental to rocket propulsion. When a rocket engine expels gas molecules at high speed in one direction (action force), the rocket itself is pushed in the opposite direction (reaction force). This can be expressed as:

$F_{\mathrm{rocket}}=-F_{\mathrm{gas}}$

where $F_{\mathrm{rocket}}$ is the force on the rocket and $F_{\mathrm{gas}}$ is the force on the expelled gas. This principle allows rockets to move in the vacuum of space where there is no air to push against.

Why don't action and reaction forces cancel each other out?

Action and reaction forces do not cancel each other out because they act on different objects. According to Newton's third law, if object A exerts a force on object B, object B exerts an equal and opposite force on object A. Since these forces are applied to different objects, they do not cancel out but instead result in changes in motion for each object. For example, when you push a block, you exert a force on the block, and the block exerts an equal and opposite force on you, causing both you and the block to accelerate in opposite directions.

How do you calculate the acceleration of an object using Newton's third law?

To calculate the acceleration of an object using Newton's third law, you first identify the action-reaction force pair. Then, use Newton's second law, $F=ma$, to find the acceleration. For example, if a person pushes a block with a force of 20 N, and the block has a mass of 40 kg, the acceleration of the block is:

$a=\frac{F}{m}=\frac{20}{40}=0.5 m/s^2$

Similarly, the reaction force on the person can be used to calculate their acceleration.