Newton's Second Law in 2-D

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Students will be able to apply Newton's Second Law to 2-dimensional motions.

Big Idea

Today students identify how an object's acceleration changes when horizontal and vertical forces are present.


In yesterday's lesson, students were introduced to Newton's Second Law and became familiar with solving F=ma problems. Today, the goal is to take that knowledge and apply it to situations with forces in the x and y directions (HS-PS2-1). I try to offer a variety of strategies to accomplish our goal, so the lesson starts with a one-minute refresh essay followed by some brief notes on the application process (SP5). Finally, students get to apply their new knowledge towards the end of class with collaborative problem solving (SP6).

One-Minute Refresh Essay

10 minutes

To start class today, students come into the room and take out a blank sheet of notebook paper. On the board I've written "In your own words, describe Newton's Second Law."

This is a 1-minute refresh essay, where students get only 1 minute to individually respond to the prompt. The goal is to get students thinking about what they learned during the previous lesson, since they need to have F=ma at the forefront of their minds for today's lesson. I do actually use a stopwatch, but because some of my students need a little time to process, I usually give them about 90 seconds.

After their time is complete, I randomly select a student to share his or her essay and then we continue around the room until everyone has shared. I try to only be a facilitator during this process and let students consider each essay shared by their peers. For example, if a student makes an assumption that is not valid, I let another student speak up and question the invalid statement. I also encourage students to write down any valid ideas that they had forgotten to include. This is also an opportunity for me to informally observe my students and get a sense of how well they know Newton's Second Law.

Notes on Newton's Second Law

15 minutes

It's time for students to take out their notebooks to copy down some helpful tips in solving 2-D force situations. My students are operating under the expectation that they must write down key points from the presentation. This expectation of how to take notes has been outlined and ingrained in their learning since freshman year. Because these are AP students, how they organize their notes (notebook, binder, etc.) is a decision the individual student gets to make. I assume at this point in their high school careers they have an established system to stay organized.  

I display the Second Law in 2-D presentation (also available in pdf format) to help the students understand what they need to write down. I have a hard copy of the slides in my hands as I circulate throughout the room, which includes notes (viewable when the file is downloaded). These notes help me to stay focused and ensure I mention the highlights as we progress through each slide. I usually have a lot of interaction with my students throughout the presentation. The students will ask questions, participate in solving any examples, and connect to real-world situations to stay engaged the entire time.

The specific goal of these notes are to show students that forces, which are a vector, can exist in more than 1 dimension. In fact, the application of Newton's Second Law in 2-dimensional problems is often much more useful than looking at F=ma in only 1 dimension. So, I start by showing students the steps to solve for these problems. The students can then apply these steps as we look at a qualitative and quantitative example. Before I provide the solution to the final slide (the answer is only visible when downloaded), I give students several minutes to read and think about the problem (individually or with those seated near them). Then, I ask students to contribute information as I walk them through the solution.

Collaborative Problem Solving

25 minutes

Students get themselves into groups of 6, and since they are mature and able, I let students choose their own groupings. Usually we have groups of 2, 3, or 4, so today is definitely an opportunity for students to work with someone new. Once students are in their groups, they are instructed to pick one person for each homework problem assigned. As they are deciding who is which number, I go around and pass out today's practice problems and encourage students to write their name and number at the top. 

Once students are organized, I direct students to solve the problem that corresponds to the number they've chosen. For example, if Sonya is number 5, she's in charge of doing only number 5 on her problem set. If students have done this properly, each group will have 1 student doing each problem. The purpose of this strategy is to get students practicing what they've just learned before they share their answers.

The students get about 10 minutes to solve their individual problems, although they should use their peers as a resource if needed. I am also walking around the room with the answer key to answer questions and provide students hints as needed. At the end of the work time, I ask all of the students who had the first problem to share their answers. Each person from each group will share, and then I reveal the correct answer. The students that did not work on the first problem should write down the correct answer. The process continues with groups 2 through 6 so everyone has a chance to share and record the correct answers.

With any remaining time before the end of class, students debrief in their groups and discuss their work and the solutions just presented. I walk around and encourage students to ask each other questions, so students might ask a peer "Why did you use cosine with that angle?" or "Did you round that part of your answer to get the final solution?" This type of closure to the lesson is very informal, but it gives me an opportunity to talk with a variety of students in small groups while checking for understanding. The collaborative conversations between students, with or without me present, continues until the end of the class.