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# Forces as Vectors

Lesson 2 of 16

## Objective: Students will come to understand the vector nature of forces.

*50 minutes*

During the previous lesson, students defined force and explored the different types of force. The goal for today's lesson is then to apply that knowledge of forces (HS-PS2-1) in an activity. Specifically, students will use spring scales to explore the vector nature of forces (SP3 & SP5). I start the class with a pop quiz before moving into the actual lab activity. Today's lesson ends with a hand signals closure.

This lab activity requires the following supplies per group: 1 blank sheet of 8.5" x 11" paper, 3 strings (each of varying lengths from 6" - 11"), and 3 spring scales.

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#### A Pop Quiz Introduction

*15 min*

As the closure of my previous lesson, I asked students to use hand signals as an indication of how they felt about defining force. Almost all of my students felt confident that they could define force, so today I start by giving students a pop quiz.

This short quiz is meant to formally assess if students can define force, differentiate between contact and action-at-a-distance forces, and describe at least two individual forces. After students have had approximately ten minutes to complete this quiz, I collect their papers by lab table. Collecting the papers this way allows me to then pass the quizzes back out so that nobody receives their own quiz and we can informally grade the quizzes as a class.

When we grade quizzes as a class, I ask students to give each question an upward, downward, or leftward vector. An upward vector tells me that the student grading the quiz is 90% confident that the answer is correct, a downward vector tells me the grader is 90% sure the answer is incorrect, and a leftward vector tells me that the grader is unsure of the answer's correctness. I read the answers aloud from the answer key, allow students to make their vectors, and then recollect the quizzes. This informal grading opportunity allows students to get a general idea of how they did on the quiz since they'll need to apply the vector knowledge in today's activity.

These quizzes offer not only offer me information on how well my students are able to define and describe force, but they also allow me to segue into today's activity. As part of the definition of force, students should have mentioned that forces are vectors and that vector nature is the focus for the rest of the class hour. After class is over, I do go through and regrade these quizzes to better provide feedback for each individual student.

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#### Forces as Vectors Activity

*30 min*

At this point in the year my students have formed deep relationships with each other, so I allow them freedom in choosing lab partners. Groups of four seem to work best for the lab so three students can be operating spring scales while the fourth student records data. After they've chosen their groups, someone from each group needs to get a copy of the lab, three pieces of string, three spring scales, and a blank sheet of computer paper.

The purpose of this lab activity is to get students to see that forces are a vector quantity. Students construct a coordinate plane on their blank sheet of computer paper and tie the three pieces of strings together (forming a knot). Attached to each string is a spring scale, which displays the magnitude of force on each string. Using the origin to align the knot of the 3 strings, students then measure the angles that correspond to each force and calculate the resultant force. Because the knot is stationary at the origin, its net force should be zero.

The procedure in the lab document is straight-forward, but I still make sure to circulate throughout the room and check-in with each group. I'm offering feedback on how they attach the string to the scales, ensuring they are setting up the coordinates properly, and generally building rapport through informal conversations. Students understand the expectation that once they have completed collecting the data it's time to move into the data analysis section.

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 everything back the way they found it 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. Since each student is expected to do his own work, I encourage students to take pictures of the plotted vectors so that they can complete the assignment at home.

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#### Tug of War Exit Ticket

*5 min*

As soon as students have all their materials returned to the front of the room, I play this quick video clip of a 3-way tug of war. The video clip serves as a nice representation of what the students did during the activity, but on a much more intense scale.

After watching the video, students need to write one sentence, on a half sheet of paper, explaining the vector nature of the forces they saw. This will be the students' ticket out the door, and it's a fun way to get students thinking about how today's activity can be applied to the real world. As a teacher, it helps me informally assess if students are grasping the vector nature of forces. I can use information from my students' responses to adjust pacing and address misconceptions if needed. If student responses are accurate, then I can feel confident about moving on to the rules of free body diagrams.

#### Resources

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- LESSON 1: Defining Force
- LESSON 2: Forces as Vectors
- LESSON 3: An Introduction to Free Body Diagrams
- LESSON 4: Newton's First Law
- LESSON 5: Newton's Second Law in 1-D
- LESSON 6: Newton's Second Law in 2-D
- LESSON 7: Ramping up Forces
- LESSON 8: Practicing Newton's Second Law
- LESSON 9: Tensions, Pulleys, & Elevators - Oh My!
- LESSON 10: Tension Lab
- LESSON 11: Figuring out Friction
- LESSON 12: Newton's Third Law
- LESSON 13: An Atwood's Machine Inquiry Lab
- LESSON 14: Newton's Laws AP Practice
- LESSON 15: Newton's Laws Review
- LESSON 16: Forces Unit Test