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# Plan a Trip to the Asteroid Belt

Lesson 6 of 11

## Objective: Students use Newton's Second Law and kinematic equations to determine the time it would take various rockets to go from Earth to the asteroid belt beyond Mars.

## Big Idea: Kinematics equations and Newton's 2nd Law allow us to better understand the universe around us and to make predictions about an object's motion.

*50 minutes*

For this lesson, students determine the time it takes a spaceship to reach the asteroid belt starting from Earth. Students are given the force of the spaceships thrust and its mass and from that determine the ship's acceleration. The students apply the kinematic equations to determine the time it takes to make the trip. This is done as a way to unify the major topics learned: the equations of motion and Newton's Laws of motion. It is important to do this because to fully understand how the universe operates, students need to know that all of the topics in physics are connected and interdependent. Students work in co-operative groups as this gives them a chance to bounce ideas off of each other as they work through solving the multi-step problem.

This lesson involves the NGSS Performance Standard HS-PS2-1, the mathematical relationship between the net force acting on an object and its acceleration. Through out this lesson students will use mathematics and computational thinking, which is Science Practice 5 and engage in argument from evidence, which is Science Practice 7. Math Practice 2: Reason abstractly and quantitatively as is also a part of the activity as they problem solve real-life situations using the kinematic equations and Newton's 2nd Law.

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As students come into class, displayed on the board is the instruction to take the Socrative quiz on Newton's 2nd Law (SOC #: 13851027), which I start right before class. Most students use their smart phones, but there are laptops available for the few who don't have a smart phone. It is a four question quiz whose purpose is to give a snap-shot of what students know about net force and the application of Newton's 2nd Law. This quiz is set so that Socrative.com reveals student's names and their responses as they give them (only I can see the results). I know within the first few minutes of class if there are misunderstandings that need to be addressed. If more than 7 or 8 students make mistakes, then I review the concepts with the whole class before we move on. Otherwise, I work one-on-one or one-on-two with those few students as the rest of the class works on the space trip assignment.

The purpose of the quiz is to check students understanding and completion of the homework. If students complete the homework sheet, then they are likely to ace this mini-quiz. While students are taking this quiz, I circle the classroom checking to see if their homework is complete. I don't collect it as we are going to review it together as a class, but I do expect students to attempt all problems. If they are not, students lose points.

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#### Correct F=ma Homework

*15 min*

While I walk around the classroom and check for completion of Newtons 2nd Law Practice worksheet, I look for exemplary work. When I find it, I ask that student if I can use their sheet as an example for the rest of the class. Usually, they agree. As I walk away, the student has a big grin on their face and they sit a little taller in their seat. I try to chose a student who is typically not one of the top performers because everyone needs recognition for excellence in their work.

Using a document camera, I display the Student Work Exemplar on the projector. Should there be a mistake on the sheet, I gently correct it and ask how many other students made the same mistake. I make it clear that students should correct any mistakes they have on this sheet so that they learn from those mistakes. Here is a sample sheet that shows a student who corrected their mistakes: Student Work. The only requirement for their corrections is that they make them with a different colored pen or pencil, so that when students look back at their work, they see the mistakes to avoid.

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#### Plan a Space Trip Activity

*30 min*

For this Space Trip Activity, students have information on three types of spaceship propulsion systems: conventional chemical rocket, ion drive and solar sail. Their goal is to determine the time it takes one type of spaceship to reach the asteroid belt starting from Earth. Students need to choose what type of propulsion they would use and why. This requires that they make an argument and support it with some facts which is Science Practice 7: Engaging in argument from evidence. Most of the information that students need are on the sheet. However, they do need to use a smart phone or computer to do a quick internet search to get a basic idea of what the different types of propulsion system are and what they look like.

This assignment combines the newly learned Newton's 2nd Law so that they can calculate the ships acceleration, then the students have to use the kinematics equations in order to calculate the time for the trip. Two of the ships (space sail and ion drive) have a constant acceleration for the entire trip. These student work samples are great examples of how to do this assignment: ion drive and space sail. However, the conventional rocket only fires for 30 minutes, then has a constant velocity for the remainder of the trip. This MS-Excel document shows the Ship Project Solutions for each type of drive. The spreadsheet is set up so that I can change initial conditions (spaceship mass, thrust force, distances) and it recalculates the time and final velocity.

Students work cooperatively, which gives them a chance to talk through the assignment and to help each other. I have students work in groups of two to increases the chance of all students making significant contributions to the assignment. To mix things up, I instruct the students to work with someone in the class with whom they have never worked with before. If students work with the same people they can develop bad patterns where one or two usually do the work of the group. While students work on this assignment, I circulate the room and provide support where needed and ensure students are on task.

I collect the student work at the end of the period and share with the students that they are on their way to becoming great space scientists!

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- LESSON 1: Inertia is Latin for "Lazy"
- LESSON 2: Something About Sigma: Calculating Net Force
- LESSON 3: Manipulating Forces
- LESSON 4: Discovering Newton's 2nd Law
- LESSON 5: Applying Newton's Second Law Quantitatively
- LESSON 6: Plan a Trip to the Asteroid Belt
- LESSON 7: Combining Newton's Second Law and Kinematics
- LESSON 8: Friction Is Not Fiction!
- LESSON 9: Pushing the Pathfinder
- LESSON 10: Self-Assessment on Forces
- LESSON 11: Quiz on Newton's Laws