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# Deriving Universal Gravitation

Lesson 5 of 8

## Objective: Students will be able to derive the universal gravitation constant.

## Big Idea: Students think like Newton and use a computer simulation to explore the law of universal gravitation.

*50 minutes*

At this point in the rotational motion unit, students have a strong knowledge of angular quantities, angular kinematics, and centripetal force, so today's goal is to explore Newton's Law of Universal Gravitation (HS-PS2-4). Students begin by watching a video clip from PBS on gravity and then use a simulation to identify and apply Newton's Law of Universal Gravitation (SP2, SP5, & SP8). The simulation gives students (working in pairs) an opportunity to relate gravitational force to mass, before determining the universal gravitation constant. Finally, the lesson ends with students participating in an analogy prompt closure that allows them to creatively express what they've learned.

#### Resources

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Because there are so many resources out there and my students will be active for the rest of the lesson, I decide to use this NOVA video to introduce Newtonian Gravitation. It is the goal of this video introduction to provide students with a concise and straight-forward look at the concepts and history of the law of universal gravitation. My students are quite interested in modern physics (as I've noticed through side conversations in my classroom), so the video immediately captures their attention with the reference to Einstein's Theory of Relativity. Also, when I use a NOVA video I remind my students that this is a great resource to supplement what we do in class.

Before I start the video I make sure my expectations are clear. Students need to be sitting quietly, listening and watching the video, and taking notes on meaningful material. To me, meaningful material includes any reference to previously learned concepts, equations, vocabulary, and examples. While I do not collect their notes, they are an essential resource as students work through the simulation. I am telling my students these expectations as I'm on my way to start the video.

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After we've finished watching the video, students use a computer simulation that allows them to be more active in their learning. The simulation allows students to visualize how force changes as mass and distance change. Specifically, students start by changing the mass of and distance between the two interacting objects. Then, students use the given force on the simulation to calculate the gravitation constant. Finally, students answer conclusion questions that apply the law of universal gravitation to situations involving satellites and planetary interactions.

Before we start the activity, I assign partners using the random student generator that already has my students' names loaded. By displaying the random generator on the front board, there is an element of suspense as the partners are assigned. Partners work best for this activity so that each student can be actively engaged throughout the work time. Because this activity does not need to be completed outside of class, I feel comfortable in choosing the pairings for my students.

We use MacBook Pro's in my district, so my students are familiar with how the computer and cart organization works. After each pair has been assigned, the students move to sit near each other, push their desks together, and grab a computer. As the computers are booting I pass out the Newtonian Gravitation PhET Lab so that each student receives a copy. This document directs them to PhET where they will be using the gravity force lab. The activity sheet is also meant to direct the students in their learning so that they are confident in what material needs to be understood. However, the values in the data table and answers to the questions need to be completed on a separate sheet of paper.

While students are working, I walk around to ensure they are actively engaged in the learning process. This means that they are on the proper website, reading or discussing some component of the simulation, and writing down appropriate information from the simulation. When I walk around, I'm spot checking their written work and engaging students in questions such as "What is the highest value of mass you've used so far?" or "What happens when the two masses are touching?"

The students' written answers are the most important part of this activity, so I ensure they are thinking through how they prove any claims they make. I do a lot of walking and questioning throughout their work time to ensure they can justify anything that they have written. The AP Physics 1 exam places a lot of emphasis on justifying thought processes, so my goal in our dialogue is to practice with students how to justify their arguments.

When there is approximately 10 minutes prior to the end of class (5 minutes left of the time I've allowed for this activity), I ask students to put the computers back on the cart and return to their seats. I also tell them at this point that the lab is due at the start of the next class meeting. Once everyone is back in their seats, we are ready to move into the closure activity for our lesson.

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With about five minutes left of class, I ask the students to stop working and focus on me for a moment. I remind students that the purposes of today's activities were to define and explore Newton's Law of Universal Gravitation. As I'm talking, I give each student a small, blank notecard.

Once everyone has a notecard, I ask students to respond to an analogy prompt that is on the front board. I've put the prompt on the board while the students were working on the simulation, and it's been hidden from their view so they aren't able to think too deeply about their responses. As I reveal the prompt to the students, they must write the prompt and their responses on the index card. For this particular activity, the prompt is "This gravity simulation was like _________ because _______."

This is their "exit ticket," meaning that they can't leave until they've handed me their card. To avoid anyone sneaking out of the room, I stand at the door and collect the cards on their way out. Once I've collected all of the cards, I read and use them to adjust my teaching practices. For example, if a student says "This gravity simulation was like a marathon because it was way too long." I might take a question off the activity before doing it again the following year. It's always fun to read some of their creative responses!

#### Resources

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- LESSON 1: Introduction to Angular Motion
- LESSON 2: Constant Angular Acceleration
- LESSON 3: Rotation of a Ladybug
- LESSON 4: Uncorking Centripetal Force
- LESSON 5: Deriving Universal Gravitation
- LESSON 6: Exploring Kepler's Three Laws
- LESSON 7: Reviewing Rotational Motion
- LESSON 8: Rotational Motion Test