# Decoding Newton's Second Law

## Objective

Students will examine their virtual data and uncover the relationships between force, mass, and acceleration.

#### Big Idea

Acceleration is the result of unbalanced forces acting on an object.

## Graphical Warmup: Sorting Motion Graphs

15 minutes

After a week-long absence from class, I return with an important goal: to take the virtual data assembled by students last week and use it to formally introduce Newton's Second Law. This is, naturally, one of the high points of physics history. It is also an essential Performance Expectation (HS-PS2-1) of the NGSS.

Before getting underway with that goal, however, I ask students to engage in a sorting activity involving sets of position, velocity, and accelerations graphs. I reveal a prompt on the board while showing a package of cards in my hand. I spend a few minutes ensuring that students understand the task of grouping the graphs into sets of position, velocity, and acceleration functions that go together and describe the same object in motion.

I count off students, from 1 to 5, and create 5 randomized groups. Each team receives a set of the graphs and they immediately begin to sort them. Students need to recognize the possible scenarios and discuss with one another how the graphs should be grouped. Here is a brief snippet of that kind of work:

This exercise takes about 3 minutes to explain, about 5 minutes to implement, and another 5 minutes to debrief and discuss solutions. A solution is shown just below and the position, velocity, and acceleration graphs are shared as resources as well. Doing this work allows us to refer back to our most recent unit and to keep those lessons fresh and relevant.

## Activity A: Crowdsourcing Data with a Single Force

20 minutes

During the previous class, students accessed a website and collected virtual data regarding forces, masses, and accelerations. The work clearly aligns with NGSS Performance Expectation HS-PS2-1 (Newton's Second Law). Today, I want to leverage their individual data sets (four points each) into a larger data set by "crowdsourcing" the data and drawing conclusions from the larger set of data. The task students worked on was broken up into two parts - first, they explored a friction-free environment, then they folded in the complication of friction as a competing force. To start, we gather the data for the friction-free environment.

I create a Google spreadsheet and quickly share it with 4-5 students who have their personal computers with them. These students become the portals through which others can contribute their data. In order for the conclusion to be more apparent, I create the spreadsheet with the forces as the y-axis and the accelerations as the x-axis. This is a bit counter-intuitive; during the simulations, students chose forces and observed the resulting accelerations so the graph we make today somewhat subverts the traditional independent and dependent variable roles.

The data columns fill up quickly. From the data, it is a simple task to create a graph, showing the relationship between the forces and accelerations. Interestingly, students saw data points that were clear outliers, disrupting the linearity of the data, and are sufficiently motivated to revisit their notes. Several transcription errors are corrected before moving forward.

We calculate a slope that is just a touch greater than 10; the mass under test was a 10-kg mass. This is close enough for us to propose that, without friction, the acceleration equals the ratio of applied force to mass.

## Activity B: Crowdsourcing Data with Multiple Forces

20 minutes

We turn out attention to the second activity which incorporates friction as a force that competes with the applied force. Using the same spreadsheet as before, I create a few more columns for students to populate with their data from the second activity.

As soon as the data sets are entered, I create a graph showing the applied force versus acceleration. The data are very linear, which is satisfying.

Again, the slope appears to be just about 10, matching the mass of the object under test. What's hidden, however, is the impact of the frictional force; the applied forces available in the simulation are quite large and the small (~ 20 newtons) frictional force is obscured by that scale. In order to draw this idea out, I show the ratio of applied force to acceleration on the spreadsheet:

As all of these ratios are greater than 10, we recognize that, though the slope is 10, there must be an intercept and that the applied force is not the best y-axis to use. Students review their work and nominate the idea that the difference between the applied and frictional forces is proportional to the acceleration, and the proportional factor is the mass. In other words:

Fnet = m * a

We use this insight to end the day with a set of formalized notes about Newton's Second Law.

## Formalizing Newton's Second Law

20 minutes

We end the day by recapping the insights made from the virtual data collection activities. First, I summarize, with a simple diagram, the results without friction. Then, I add in the frictional force and show the final, more universal result from that exploration.

I take some time to get students to think of Newton's Second Law as a corollary to his First Law: The Law of Inertia. Students have a sing-song understanding of it from elementary school and from middle school Physical Science: They can recite it but really have no true understanding of it. The idea that an object will keep moving without forces acting on it is counter-intuitive mostly due to the fact that, in our experience, there are always forces, like friction or gravity, acting on objects. I share some thoughts with students about travelling in space and the consequence of Newton's First Law: with zero friction, we can turn off engines and coast great distances without ever using any fuel. We end the day with a free-form discussion about Newton's First and Second Laws.