Summary
Students are introduced to Newton's second law of motion: force = mass x acceleration. After a review of force, types of forces and Newton's first law, Newton's second law of motion is presented. Both the mathematical equation and physical examples are discussed, including Atwood's Machine to illustrate the principle. Students come to understand that an object's acceleration depends on its mass and the strength of the unbalanced force acting upon it. They also learn that Newton's second law is commonly used by engineers as they design machines, structures and products, everything from towers and bridges to bicycles, cribs and pinball machines. This lesson is the second in a series of three lessons that are intended to be taught as a unit.Engineering Connection
Newton's second law of motion provides the foundation for much of the mathematics in engineering mechanics. In the study of dynamics, engineers apply Newton's second law to predict the motion of an object experiencing a net force. Using the equation F = ma, engineers can model the position, velocity and acceleration of an object, or they can measure these values to learn about the forces acting on the object. In the field of statics, engineers use Newton's second law to calculate forces acting upon stationary objects. Because a nonmoving object's acceleration is zero, the forces acting on the object must sum to zero. For example, in designing structures, engineers apply Newton's second law in calculating the forces acting on joints in the framework of buildings and bridges.
PreReq Knowledge
Students should be familiar with the concepts of mass, properties of matter (weight, density, volume), and basic algebraic equations.
Learning Objectives
After this lesson, students should be able to:
 State Newton's second law and explain what it means.
 Explain that force is measured in Newtons, and that mass is measured in kilograms.
 Distinguish between mass and weight.
 Use Newton's second law to compare the amount of force required to move objects of varying masses.
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Educational Standards
Each TeachEngineering lesson or activity is correlated to one or more K12 science,
technology, engineering or math (STEM) educational standards.
All 100,000+ K12 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.
Each TeachEngineering lesson or activity is correlated to one or more K12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K12 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.
NGSS: Next Generation Science Standards  Science

Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object.
(Grades 6  8 )
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Do you agree with this alignment?
This Performance Expectation focuses on the following Three Dimensional Learning aspects of NGSS:Science & Engineering Practices Disciplinary Core Ideas Crosscutting Concepts Plan an investigation individually and collaboratively, and in the design: identify independent and dependent variables and controls, what tools are needed to do the gathering, how measurements will be recorded, and how many data are needed to support a claim. Alignment agreement:
Science knowledge is based upon logical and conceptual connections between evidence and explanations.Alignment agreement:
The motion of an object is determined by the sum of the forces acting on it; if the total force on the object is not zero, its motion will change. The greater the mass of the object, the greater the force needed to achieve the same change in motion. For any given object, a larger force causes a larger change in motion. Alignment agreement:
All positions of objects and the directions of forces and motions must be described in an arbitrarily chosen reference frame and arbitrarily chosen units of size. In order to share information with other people, these choices must also be shared.Alignment agreement:
Explanations of stability and change in natural or designed systems can be constructed by examining the changes over time and forces at different scales. Alignment agreement:

Construct, use, and present arguments to support the claim that when the kinetic energy of an object changes, energy is transferred to or from the object.
(Grades 6  8 )
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This Performance Expectation focuses on the following Three Dimensional Learning aspects of NGSS:Science & Engineering Practices Disciplinary Core Ideas Crosscutting Concepts Construct, use, and present oral and written arguments supported by empirical evidence and scientific reasoning to support or refute an explanation or a model for a phenomenon. Alignment agreement:
Science knowledge is based upon logical and conceptual connections between evidence and explanations.Alignment agreement:
When the motion energy of an object changes, there is inevitably some other change in energy at the same time. Alignment agreement:
Energy may take different forms (e.g. energy in fields, thermal energy, energy of motion). Alignment agreement:

Analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.
(Grades 9  12 )
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Do you agree with this alignment?
This Performance Expectation focuses on the following Three Dimensional Learning aspects of NGSS:Science & Engineering Practices Disciplinary Core Ideas Crosscutting Concepts Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims or determine an optimal design solution. Alignment agreement:
Theories and laws provide explanations in science.Alignment agreement:
Laws are statements or descriptions of the relationships among observable phenomena.Alignment agreement:
Newton's second law accurately predicts changes in the motion of macroscopic objects. Alignment agreement:
Attraction and repulsion between electric charges at the atomic scale explain the structure, properties, and transformations of matter, as well as the contact forces between material objects.Alignment agreement:
Empirical evidence is required to differentiate between cause and correlation and make claims about specific causes and effects. Alignment agreement:
International Technology and Engineering Educators Association  Technology

Compare, contrast, and classify collected information in order to identify patterns.
(Grades 3  5 )
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State Standards
California  Science

Construct, use, and present arguments to support the claim that when the kinetic energy of an object changes, energy is transferred to or from the object.
(Grades
6 
8 )
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Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object.
(Grades
6 
8 )
More Details
Do you agree with this alignment?

Analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.
(Grades
9 
12 )
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Indiana  Science

Cite specific textual evidence to support analysis of science texts.
(Grades
6 
8 )
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Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions.
(Grades
6 
8 )
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Introduction/Motivation
Newton's second law of motion builds on the first law of motion, which states that objects remain at rest or in constant motion unless a forces act upon them. The second law extends this concept and describes the change in motion with a mathematical equation. This equation is commonly written as F=ma, where F is the magnitude of the unbalanced force, m is the mass of the object and a is the resulting acceleration.
Let's talk through an example, qualitatively, such as the pulling of a wagon. If a wagon weighs 10 kg and you pull it with a given force, it accelerates forward. If you pull it with twice as much force, it accelerates twice as much. If you exert the same force on an identical wagon that weighs 20 kg, it accelerates half as much.
(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 Second Law Presentation (a 16slide PowerPoint® presentation) to teach the lesson.
 (optional) Build or procure an Atwood machine to use for a class demonstration. An Atwood machine is simply a rope strung through an elevated pulley holding equal weights at each rope end; see slide 15 for a diagram. This is relatively easy to build with a pulley, string and two water bottles containing equal amounts of water. Alternatively, find an online Atwood Machine simulation.
 In advance, make copies of Newton's First and Second Law Homework (one per student).
 At some point during the presentation, perhaps when talking about some examples (slides 37), go over how to draw (conceptual) freebody diagram vectors (arrows) of force, velocity and acceleration, which students will be asked to do as part of the homework assignment.
Background Concepts
Newton's second law can be used to describe the acceleration of an object based on total force applied and the mass of the object. The equation is commonly written as F=ma. Simply put, the more force applied to an object, the faster it will accelerate. Similarly, if the same force is applied to two objects of different mass, the object with the higher mass will accelerate less quickly.
Newton's Second Law of Motion Presentation Outline (slides 116)
Open the Forces and Newton's Second 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 understand that the acceleration of an object depends on both the mass of the object and the strength of the force acting on it.
(slide 2) Briefly review what student should know about forces, as covered in the previous lesson in the unit, What Is Newton's First Law? Ask students: What is a force? What are the two categories of forces? What are seven specific types of forces?
(slides 36) These slides show pictures to prompt students to think of the types of forces that were introduced on Day 1. For each slide, describe the situation shown and ask students to identify what force is illustrated and whether it is a contact or a noncontact force.
(slide 7) As students look at a diagram that shows people standing at various places on the planet Earth, introduce an additional type of contact force called the normal force. When you are standing on the ground, your weight is a force acting in the downward direction, and the normal force is what we call the force of the ground pushing back up on you. Because the force of gravity and the normal force are balanced, your motion does not change.
This may be a good time to review how to draw (conceptual) freebody diagram vectors (arrows) of force, velocity and acceleration.
(slide 8) Expect students to recognize this slide as very similar to one in the previous lesson. Briefly review the types of forces introduced in that lesson, pointing out the addition of the normal force to the listing.
(slide 9) Review the definition of a force. Relate it back to Newton's first law by reminding students that applying a force changes the velocity of an object. Expand further by asking students: What unit is used to measure force? In SI units, force is measured in Newtons (N).
(slide 10) Continue reviewing Newton's first law and acceleration. Ask students: What is Newton's first law? What are some examples? What is the definition of acceleration? Acceleration is a change in velocity. Expect students to already know that a force can cause a change in velocity. Lead students to make the connection that acceleration is caused by a force (acceleration is the change in velocity).
(slide 11) Introduce Newton's second law: An object's acceleration depends on the strength of the unbalanced force acting on it, and the mass of the object. This is also commonly written as F=ma (force equals mass times acceleration).
(slide 12) If I apply the same force to two objects, the object with less mass experiences greater acceleration and the more massive object experiences less acceleration.
Thinking of the wagon example from earlier, if we apply the same force to both wagons. The wagon with the smaller mass experiences a greater acceleration, while the wagon with the larger mass experiences a lesser acceleration.
As another example, think of a tugboat. How is the magnitude of a tugboat's acceleration different when it is pulling a big barge compared to when it is pulling nothing?
(slides 1314) What is mass? Mass is the amount of matter an object contains. Then introduce weight as a gravitational force. Weight is a measure of how strong gravity pulls on an object. An object's weight depends on the strength of gravity. The official way to write this is force = mass x acceleration. This is equivalent to force equals mass x gravitational acceleration (gravity), as it is more accessible to students who may not make the direct connection between acceleration and gravity. Tell students: The acceleration is a result of the gravitational field. On the Earth, the force due to gravity is mediumsized, on the moon it is teenytiny, and on Jupiter it is really huge! Notice that on each planet the force changes as does the acceleration due to gravity (it depends on its mass and radius [squared]). In this were a story, the mass is like Goldilocks, it does not change size, only the surroundings (the environment) change.
(slide 15) Present a demo using an Atwood machine. Start by holding equal masses at different positions and have students predict what will happen when you let go. Add a small amount of weight so students can observe the two masses accelerate. When the masses are equal, they do not move because gravitational forces are equal. When masses are different enough to overcome friction, an acceleration of the masses can be observed. Emphasize that the different masses must have different gravitational forces for them to move. This leads into Newton's second law, as reinforcement of the concept.
(slide 16) Review the concepts from the day's lesson. Conclude the presentation with a quick review of the key concepts, as listed on the slide, with blanks for students to supply the answers. At this point, expect students to understand that an object's acceleration depends on its mass and the strength of the unbalanced force acting upon it. Newton's second law is among the most commonly used equations in engineering. This simple equation has empowered engineers to design even the most complicated machines. It is something engineers take into account and exploit as they design everything from towers and bridges to bicycles, cribs and pin ball machines. Engineers use the second law equation to predict the motion of objects and to model the motion of objects receiving forces in order to determine the net force. They also use the equation to calculate the forces acting upon stationary objects—we want the forces acting on some nonmoving objects, such as buildings and bridges, to sum to zero.
Conclude the lesson by administering the homework assignment, as described in the Assessment section.
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
velocity: The speed and direction of an object.
Worksheets and Attachments
Assessment
PreLesson Assessment
Review: Review the main points from the previous lesson, What Is Newton's First Law? Ask students to answer the review questions on slides 37, 910 of the Forces and Newton's Second Law Presentation. Student answers reveal their base knowledge of the concepts.
Lesson Summary Assessment
Concept Review: At lesson end, ask students the three review questions on slide 16. Ask them to supply the answers for the blanks in the sentences. Student answers reveal their comprehension of the concepts presented.
Homework
Homework: At lesson end, distribute Newton's First and Second Laws Homework for completion as an assessment for this lesson and the previous lesson in the unit. This requires students to draw (conceptual) freebody diagram vectors (arrows) of force, velocity and acceleration. Review students' answers to gauge their individual depth of comprehension of the concepts presented.
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
Contributors
Elizabeth Anthony, Scott Strobel, Jacob TeterCopyright
© 2014 by Regents of the University of Colorado; original © 2013 University of California DavisSupporting Program
RESOURCE GK12 Program, College of Engineering, University of California DavisAcknowledgements
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 GK12 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: July 20, 2017
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