The Arizona STEM Acceleration Project

An Inquiry Approach to Newton’s 2nd Law

An Inquiry Approach to Newton’s 2nd Law

An 9th-12th grade STEM lesson

Jeff Steinert

3/10/2023

Notes for teachers

• This lesson takes place in a classroom for about two hours. It extensively employs elements of Modeling Instruction.
• Students should work in small groups of 2-4.
• An emphasis on experimental design, precise measurement, and careful analysis of graphical results, with an end goal of development of a simple mathematical model.
• Facilitate student reflection on their analysis of the graphical results as they work in small groups.
• Engage the whole class in coming to consensus on a mathematical model via post-analysis “board meeting”.

List of Materials

• Lab Apparatus for demonstration and data collection.
• Student access to a device with the Vernier Graphical Analysis application installed (free in Basic version)
• 24” by 32” dry erase whiteboards and markers for student groups to display their data and analysis of the results.
• Reading: Birth of a Masterpiece - Newton’s Principia

Science Standards:

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HS.P3U1.6: Collect, analyze, and interpret data regarding the change in motion of an object or system in one dimension, to construct an explanation using Newton’s Laws.

Science and Engineering Practices:

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• ask questions and define problems
• develop and use models
• plan and carry out investigations
• analyze and interpret data
• use mathematical and computational thinking
• construct explanations and design solutions
• engage in argument from evidence
• obtain, evaluate and communicate information

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Arizona Science Standards

Arizona ELA Standards

9-10.RI.1 Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

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9-10.RI.2 Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.

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11-12.RI.4 Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze how an author uses and refines the meaning of a key term or terms over the course of a text.

9-10.RI.8 Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning.

Objectives:

Today we will design an experiment to investigate how forces cause objects to accelerate.

Today we will collaborate to collect and analyze data to determine the physical law governing forces and acceleration.

Today we will share our understanding of forces and accelerations with others using graphical and mathematical representations.

Today we will explore the application of this physical law to changing the motion of objects.

Agenda (60 minutes per day)

Day 1:

Force and acceleration experiment design using available equipment

Use Graphical Analysis to collect and plot data and find a mathematical relationship

Prepare small whiteboards for sharing

Hold “board meeting” to reach preliminary consensus and discuss next steps

Assign Principia Reading as homework

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Day 2:

Complete analysis in small groups and share in whole-class discussion

Reach final consensus on a physical law governing forces and acceleration

Discuss Principia Reading and Edmund Halley’s role as the instigator, editor, and publisher of Newton’s great work

Complete examples demonstrating the application of Newton’s 2nd Law

Why do objects accelerate? How can we change the acceleration?

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What have we already learned about forces that can help us answer these questions?

What can we measure to understand?

Let’s investigate further!

Hands-on Activity Instructions

• In a group of 2-4, collect data using the equipment demonstrated by your teacher.
• Your teacher will assign you an amount of extra mass to add to your cart as you accelerate it in your experiment. Measure and record the total mass of everything you are accelerating in kg.
• In Vernier Graphical Analysis or Logger Pro, graph Force on the vertical axis and Acceleration on the horizontal axis.
• Collect data as you accelerate your cart and added mass.
• Inspect your graph to make sure no stray outliers appear. If they do, collect your data again until they are no longer present.
• Inspect your Fnet vs. a graph and make any necessary adjustments to linearize the plot.
• Find the slope and intercept of your linearized plot using a linear fit. Write the equation you find relating Net Force (Fnet ) and Acceleration (a), including units for all numerical quantities.
• On your group whiteboard, sketch your graph and write your equation. Include your total mass, so other groups understand what you did.
• What do you think the slope of your linear graph tells you? Is your intercept significant? What does it tell you? Does this make sense?

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Collecting Data:

Analyzing Results:

Assessment

Data Collection and Graphing: What does your Fnet vs a graph tell you? Does it need to be modified to create a linear relationship, or can you write a mathematical relationship? What is your slope? Your intercept? Share your group’s results on your group whiteboard and in the class results table on the board.

Compare and Contrast: How do your results compare to your classmates? What is the same and what is different? Is there a pattern you can see in the class results? If so, what is it?

Complete PostLab and/or Lab Report: Document what you have learned and share with others.

Reading: What spurred Newton to document what he had learned and to share it with the world?

Differentiation

Circulating as groups work on their data collection and analysis of their results will allow the teacher to provide additional assistance to groups that may need it. This might include inspecting graphs of Fnet vs a to make sure data quality will yield good results and that students have provided all necessary information and representations easily visible on their small whiteboards.

For issues that perplex multiple groups, a whole-class discussion can help, especially if suggestions for solutions come from the other groups in the classroom instead of the teacher.

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Remediation

Extension/Enrichment

Groups that complete their analysis quickly can be enlisted to assist those that might be struggling, especially with the nuts and bolts of collecting and plotting data in Graphical Analysis. Teaching others is always the best way to become expert in something new.

The Reading (Birth of a Masterpiece - Newton’s Principia) provided can be given to students who have completed their analysis quickly, but should also be assigned to all students to complete before Day 2. It is evident that Newton’s solitary and reclusive existence prior to Halley’s visit would likely have continued had the younger man not provided the stimulus for writing, his skills as an editor, and the funding to publish the Principia.