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Summary Students are introduced to Newton's third law of motion: For every action, there is an equal and opposite reaction. They practice identifying action-reaction force pairs for a variety of real-world examples, and draw and explain simplified free-body diagram vectors (arrows) of force, velocity and acceleration for them. They also learn that engineers apply Newton's third law and an understanding of reaction forces when designing a wide range of creations, from rockets and aircraft to door knobs, rifles and medicine delivery systems. This lesson is the third in a series of three lessons intended to be taught prior to a culminating associated activity to complete the unit.
This engineering curriculum aligns to Next Generation Science Standards (NGSS).

Engineering Connection

Consider the apple, which according to folklore, fell on Isaac Newton's head and sparked his thoughts on gravity and motion. Gravity applies a downward force on the apple's stem, and the stem applies an equal and opposite force upwards to keep the apple suspended. When the stem became too weak to apply an equally strong reaction force, the apple plunged downward toward his head.

Examples of Newton's third law of motion are ubiquitous in everyday life. For example, when you jump, your legs apply a force to the ground, and the ground applies and equal and opposite reaction force that propels you into the air. Engineers apply Newton's third law when designing rockets and other projectile devices. During launch, the burning fuel exerts a downward force, and the reaction force pushes the rocket into the air. In space, the rocket applies its rear thrusters to move forward, which provides another example of how engineers take advantage of reaction forces in their designs.

Learning Objectives

After this lesson, students should be able to:

Identify action-reaction force pairs.

Draw and explain simplified free-body diagrams showing action-reaction pairs.

State and explain Newton's third law.

Educational Standards

Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.

Suggest an alignment not listed above

Worksheets and Attachments
Visit [www.teachengineering.org/lessons/view/ucd_newton_lesson03] to print or download.

Pre-Req Knowledge

Students should be familiar with the concepts of mass, properties of matter (weight, density, volume), and basic algebraic equations.

Introduction/Motivation

Newton's third law of motion builds further on the first and second laws of motion. The third law of motion states that for every action, there is an equal and opposite reaction. This can be observed both in objects at rest and those that are accelerating. For example, a resting box pushes down on the ground due to a gravitational force. In reaction to this, the ground presses back up, what we call a "normal force," at an equal magnitude. These forces balance so no acceleration of the box occurs.

Newton's third law can also be observed in rockets and other projectiles. To launch, a large force is exerted from the engines of a rocket on the space behind it. In reaction to this force, the air pushes back with an equal magnitude, propelling the rocket forward. What other examples can you think of?

(Continue by showing the presentation and delivering the content in the Lesson Background section.)

Lesson Background and Concepts for Teachers

Teacher Preparation

Be ready to show students the Forces and Newton's Third Law Presentation (a seven-slide PowerPoint® presentation) to teach the lesson.

For the Hero's Engine demonstration, have handy a soda can, nail, piece of string and water. Use a nail to poke four holes around the base of an empty soda can. When the nail is in each hole, push the nail to the left or the right to angle the hole so the water will stream out on a tangent to produce thrust; do the same for each hole. Tie a string to the tab. For the demonstration, fill the can with water and lift it with the string over a sink or tub (or outside) so students can observe the rotational movement of the can spinning as water flows out of the holes. Refer to slide 2 and NASA Pop Can "Hero Engine" for instructions.

In advance, make copies of Newton's Final Quiz (one per student).

At some point during the presentation, perhaps when talking about some action-reaction examples (slides 3-6), go over how to draw the (conceptual) free-body diagram vectors (arrows) of force, velocity and acceleration, which students will be asked to do as part of the homework assignment.

Newton's Third Law of Motion Presentation Outline (slides 1-7)

Open the Forces and Newton's Third Law Presentation for all students to view and present the lesson content, guided by the script below and text in the slide notes. The slides are animated so clicking brings up the next text/image/answer.

Objective: To be able to identify action-reaction force pairs.

( slide 2) Introduce Newton's third law of motion: for every action, there is an equal and opposite reaction. Ask students: Have you heard this before? What do you think it means?

Then demonstrate the third law by showing students a modern version of Hero's Engine, which takes just a few minutes. Hero of Alexandria was an ancient Greek mathematician and experimentalist who lived in Egypt. His original engine was steam-powered, but the soda can version works well to demonstrate the same concept. For the demo, fill the prepared can with water and lift it with the string over a sink or tub (or outside) so students can observe the rotational movement as water flows out of the holes and the can spins. The can spins due to the reaction force associated with the flow of water.

Alternatively, demonstrate the third law by having one student sit on a scooter with a basketball and then throw the ball to another student. The reaction force from the throw is evident when the throwing student is propelled backward on the scooter.

( slide 3) Tell students that forces come in what are called "action-reaction force pairs." This slide shows a stack of concrete blocks resting on the ground. Identify the action-reaction pair for the class: the block's weight pushes on the ground and the ground pushes back up on the block.

( slide 4) Next, ask students to identify the action-reaction pair in the photograph of a firing cannon. The cannon exerts a force on the cannon ball, and the cannon ball exerts an equal and opposite force on the cannon. Point out that Newton's third law explains the recoil of projectile weapons such as cannons and guns. Students who have seen Wall-E may recall a scene in which the robot uses the fire extinguisher as a propulsion system (the reaction force causes the robot to move). Another good third law/recoil example is a garden hose dancing around the yard, moving because of the force of water running through it.

( slide 5) Ask students to identify the action-reaction force pairs in the photograph of a space shuttle launch. The space shuttle exerts a downward force, and the reaction force pushes it upwards.

( slide 6) Challenge students to identify all the action-reaction force pairs in this photograph of two football players. Examples: hand-helmet, hand-shoulder, ball-hand, shoe-ground.

This may be a good time to review how to draw (conceptual) free-body diagram vectors (arrows) of force, velocity and acceleration.

( slide 7) Review the concepts from all three lessons in this unit. Conclude the presentation with a review of the key concepts, as listed on the slide, with blanks for students to supply the answers. Through these three lessons, expect students to have developed an understanding of Isaac Newton's three laws of motion. These fundamental laws of physics describe how forces impact the motion of objects. Without forces, no changes in motion can occur. Understanding forces can be a very powerful thing! Because engineers understand how forces cause objects to slow down, speed up and turn, they are able to design complicated mechanical systems ranging from airplanes to door knobs to delicate drug delivery systems.

Next, conduct the associated activity, Sliding Textbooks, followed by the final quiz, as described in the Assessment section.

Associated Activities

Sliding Textbooks - In a two-part experiment using a table, textbook, string and water bottle, student teams investigate how forces, such as applied force and friction, affect the acceleration of an object. They graph and analyze their results, consider applications for high- and low-friction surfaces, and see how forces play a role in engineering design.

Vocabulary/Definitions

acceleration: The amount of change in an object's velocity.

force: A push, pull or twist of an object.

inertia: An object's resistance to changing its motion.

Newton's first law: Unless an unbalanced force acts on an object, an object at rest stays at rest and an object in motion stays in motion.

Newton's second law: Force = mass x acceleration aka F=ma

Newton's third law: For every action, there is an equal and opposite reaction.

velocity: The speed and direction of an object.

Assessment

Pre-Lesson Assessment

Homework Review: Review students' answers to Newton's First and Second Laws Homework, which was assigned at the close of the previous lesson, What is Newton's Second Law? Verify that students are confident with Newton's first and second laws before continuing with Newton's third law.

Post-Introduction Assessment

Questions: As an embedded assessment, gauge student understanding of Newton's third law based on their responses to the questions on slides 4, 5 and 6 of the Forces and Newton's Third Law Presentation. Use the questions on slide 7 as a review prior to administering the final quiz.

Lesson Summary Assessment

Unit Quiz: After reviewing the questions on slide 7, answering any remaining student questions and conducting the associated activity, Sliding Textbooks, administer Newton's Laws Final Quiz as an assessment that covers the material in all three lessons in the unit. This requires students to draw (conceptual) free-body diagram vectors (arrows) of force, velocity and acceleration. Alternatively, administer the quiz after this lesson (before conducting the associated activity).

References

Louviere, Georgia. "Newton's Laws of Motion." 2006. Rice University. Accessed April 1, 2014. http://teachertech.rice.edu/Participants/louviere/Newton/index.html

"Newton's Laws." 2014. Physics Tutorial, The Physics Classroom. Accessed April 1, 2014. http://www.physicsclassroom.com/class/newtlaws

Copyright © 2014 by Regents of the University of Colorado; original © 2013 University of California Davis

Contributors Elizabeth Anthony; Scott Strobel; Jacob Teter

Supporting Program RESOURCE GK-12 Program, College of Engineering, University of California Davis

Acknowledgements

The contents of this digital library curriculum were developed by the Renewable Energy Systems Opportunity for Unified Research Collaboration and Education (RESOURCE) project in the College of Engineering under National Science Foundation GK-12 grant no. DGE 0948021. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: January 20, 2021

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Students are introduced to Newton's third law of motion: For every action, there is an equal and opposite reaction. They practice identifying action-reaction force pairs for a variety of real-world examples, and draw and explain simplified free-body diagram vectors (arrows) of force, velocity and acceleration for them.

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in nature there is an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal and opposite force on object A. Notice that the forces are exerted on different objects.

Newton's third law states that when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction. The third law is also known as the law of action and reaction.

when you jump, your legs apply a force to the ground, and the ground applies and equal and opposite reaction force that propels you into the air. Engineers apply Newton's third law when designing rockets and other projectile devices.

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What is Newton's Second Law of Motion?

Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.

Newton's second law of motion, unlike the first law of motion pertains to the behavior of objects for which all existing forces are unbalanced. The second law of motion is more quantitative and is used extensively to calculate what happens in situations involving a force.

Defining Newton's Second Law of Motion

Newton's second law states that the acceleration of an object depends upon two variables - the net force acting on the object and the mass of the object. The acceleration of the body is directly proportional to the net force acting on the body and inversely proportional to the mass of the body. This means that as the force acting upon an object is increased, the acceleration of the object is increased. Likewise, as the mass of an object is increased, the acceleration of the object is decreased.

Newton's second law can be formally stated as,

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

This statement is expressed in equation form as,
\(a=\frac{F_{net}}{m}\)
The above equation can be rearranged to a familiar form as \(F=ma\)
Since force is a vector, Newton's second law can be written as \(\vec{F}=m\vec{a}\)
The equation shows that the direction of the total acceleration vector points in the same direction as the net force vector.
Deriving Newton's Second Law

For Changing Mass

Let us assume that we have a car at a point (0) defined by location X ₀ and time t ₀. The car has a mass m ₀ and travels with a velocity v ₀. After being subjected to a force F, the car moves to point 1 which is defined by location X ₁ and time t ₁. The mass and velocity of the car change during the travel to values m ₁ and v ₁. Newton's second law helps us determine the new values of m ₁ and v ₁ if we know the value of the acting force.

Taking the difference between point 1 and point 0, we get an equation for the force acting on the car as follows:
\(F=\frac{m_1v_1-m_0v_0}{t_1-t_0}\)
Let us assume the mass to be constant. This assumption is good for a car because the only change in mass would be the fuel burned between point "1" and point "0". The weight of the fuel is probably small relative to the weight of the rest of the car, especially if we only look at small changes in time. Meanwhile, if we were discussing the flight of a bottle rocket, then the mass does not remain constant and we can only look at changes in momentum.

For Constant Mass

For a constant mass, Newton's second law can be equated as follows:
\(F=m\frac{v_1-v_0}{t_1-t_0}\)
We know that acceleration is defined as the change in velocity divided by the change in time.
The second law then reduces to a more familiar form as follows: \(F=ma\)
The above equation tells us that an object will accelerate if it is subjected to an external force and the amount of force is directly proportional to the acceleration and inversely proportional to the mass of the object.

What is a Net Force?

A net force ΣF is the sum of all forces acting on a body. More precisely, it is the vector sum of all forces acting on a body.

Consider two forces of magnitude 30 N and 20 N that is exerted to the right and left respectively on the horse shown in the picture. If we assume the rightward direction as positive, then the net force on the horse can be calculated as follows:\(\sum F=30\,N-20\,N=10\,N\)\(\sum F=10\,N\,to \,the\, right\)

Application of Second Law

The application of the second law of motion can be seen in identifying the amount of force needed to make an object move or to make it stop. Following are a few examples that we have listed to help you understand this point:

Kicking a ball

When we kick a ball we exert force in a specific direction, which is the direction in which it will travel. In addition, the stronger the ball is kicked, the stronger the force we put on it and the further away it will travel.

Pushing a cart

It is easier to push an empty cart in a supermarket than it is to push a loaded one. More mass requires more force to accelerate.

Two people walking

Among the two people walking, if one is heavier than the other then the one weighing heavier will walk slower because the acceleration of the person weighing lighter is greater.
Get a glimpse of Newton's second law of motion being taught in BYJU'S classes.
Newton's Second Law Solved Examples

Example 1:
If there is a block of mass 2kg, and a force of 5N is acting on it in the positive x-direction, and a force of 3N in the negative x-direction, then what would be its acceleration?
To calculate its acceleration, we first have to calculate the net force acting on it.

\(F_{net}\) = 5N - 3N = 2N

Mass = 2kg

∴ Acceleration = \( \frac 22 \) = 1 m/\(s^2\)

Example 2:

How much horizontal net force is required to accelerate a 1000 kg car at 4 m/s²?
Solution:
Newton's 2nd Law relates an object's mass, the net force on it, and its acceleration:
Therefore, we can find the force as follows:

Substituting the values, we get
1000 kg × 4 m/s ² = 4000 N
Therefore, the horizontal net force is required to accelerate a 1000 kg car at 4 m/s ₂ is 4000 N.

Newton's second law is applied in daily life to a great extent. For instance, in Formula One racing, the engineers try to keep the mass of cars as low as possible. Low mass will imply more acceleration, and the more the acceleration, the chances to win the race are higher.

Stay tuned to BYJU'S and KEEP FALLING IN LOVE WITH LEARNING

Frequently Asked Questions - FAQs

How does Newton's second law of motion apply to rockets?

We know that according to Newton's second law of motion, force is a product of mass and acceleration. When a force is applied on the rocket, the force is termed as thrust. Greater the thrust, greater will be the acceleration. Acceleration is also dependent on the mass of the rocket. Lighter the rocket faster is the acceleration.

How does Newton's second law apply to a car crash?

According to the definition of Newton's second law of motion, force is the dot product of mass and acceleration. The force in a car crash is dependent either on the or the acceleration of the car. As the acceleration or mass of the car increases, the force with which car crash takes place will also increase.

What are Newton's second law examples in everyday life?

Following are Newton's second law examples in everyday life:

Pushing a car is easier than pushing a truck with the same amount of force as the mass of the car is lesser than the mass of the truck.

In golf game, acceleration of the golf ball is directly proportional to the force with which it is hit by the golf stick. Also, the force applied is inversely proportional to the mass of the ball.

What is the other name for Newton's second law?

The other name for Newton's second law is a law of force and acceleration.

What are some daily life examples of Newton's second law of motion?

Newton's second law of motion explains how force can change the acceleration of the object and how acceleration and mass of the same object are related. Therefore, in daily life, if there is any change in the acceleration of the object due to the applied force, then they are the examples of Newton's second law.

Acceleration of the rocket is due to the force applied known as thrust and is an example of Newton's second law of motion.

Another example of Newton's second law is when an object falls down from a certain height, the acceleration increases because of the gravitational force.

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Newton's Second Law Of Motion - Derivation, Applications, Solved Examples

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Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration. Newton's second law of motion, unlike the first law of motion pertains to the behavior of objects for which all existing forces are unbalanced.

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F = ma, or force is equal to mass times acceleration. Learn how to use the formula to calculate acceleration.

The law of Force and Acceleration, a force upon an object causes it to accelerate according to the formula net force = mass x acceleration. So the acceleration of the object is directly proportional to the force and inversely proportional to the mass.

Pushing a car is easier than pushing a truck with the same amount of force as the mass of the car is lesser than the mass of the truck.

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What is Newton's first law? (article) | Khan Academy

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Also called the law of inertia, this is the most important thing to realize about motion.

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relations between the forces acting on a body and the motion of the body, first formulated by English physicist and mathematician

The property of a body to remain at rest or to remain in motion with constant velocity is called inertia. Newton's first law is often called the law of inertia.