# Springing into Hooke's Law

## Objective

Students describe, measure, and analyze the applied force and stretch distance of a spring.

#### Big Idea

Today is all about stretching students' knowledge of Hooke's Law by exploring the relationships between forces, mass, and displacement.

## Context & Equipment Needs

Today's lesson includes an activity that acts as one of the seven inquiry labs needed for AP Physics 1, and it fits into Big Idea 3 (interactions of an object with other objects can be described by forces) of the AP Physics 1 Curriculum Framework. Hooke's Law makes for a great guided inquiry topic since students have some background knowledge about springs from the previous lesson (HS-PS2-1). The lesson starts with a rubber band demonstration before students get right into the lab (SP3, SP4, & SP5). As a fun closure activity, each student shares an "ah ha moment" that they experienced during the lab activity or demonstration portion of the class.

Materials required for the demonstration include a ring stand, clamp, rubber band, and hanging mass.

For the inquiry activity, each group needs a meter stick, various hanging masses, a pair of scissors, various springs, a ring stand, and a timer.

## Hooke's Law Demo

10 minutes

I start engaging students' minds by showing them a simple example of Simple Harmonic Motion. I have one Rubber Band Strand System already together in the front of the class when the students walk in. Once the bell rings, I pull the hanging mass straight down a short distance (a few centimeters are adequate depending on the band's elasticity) and then release it. It's important to pull the mass straight down and get the system to equalize a bit before collecting any data. To keep my class active and while the rubber band system is adjusting, I usually invite two sleepy-looking students up to the front of the room and have one count the oscillations that occur while the second student times a pre-established time interval (10 seconds usually works well). The student that is counting oscillations keeps track with tallies on the front board and the student that is timing can use a classroom stopwatch or her cell phone. The student that is timing records the total oscillations on the front board and then we repeat the process a few more times to get a variety of results. Each time we repeat the process I choose different students to participate, trying to get as many students up and moving as possible. The hope of the demo is to get students focused on the day's activity and engage as much of the class as possible.

With everyone sitting back in their seats, I ask students to volunteer why the results vary, sources of error, and ways to improve our demonstration of Simple Harmonic Motion. If a student does not get the chance to participate in some part of the demo, I make sure they contribute to our whole-class discussion. I moderate the whole-class discussion by waiting for students to raise their hands and selecting students who are either extremely eager or rarely willing to participate (those who rarely participate always get to go first). I then let other students respond to points that the first student made, with questions such as "Jimmy, do you agree with what Joy said?" The point of our discussion is to get my students to recognize that rubber bands are not a great example of Hooke's Law and that a spring would provide much better results. Since the rest of the class time is spent with students working in pairs, I find it important to ensure we (as a class) are on the same page and have an opportunity for a rich discussion.

## Hooke's Law Inquiry Lab

35 minutes

I hand out the lab sheet (which includes a materials list) to each student and give them a few minutes to read and digest the activity individually. This gives the students a chance to think about a plan in a quiet, contemplative atmosphere. I then make sure everyone is comfortable with the vocabulary and handout by asking students to show me hand signals about how they are feeling. A thumb's-up indicates that the students are comfortable, a side-to-side thumb indicates the student feels some apprehension about the activity, and a thumb's-down tells me I need to address a concern with that student. When a student shows a thumb's-down, I find the next available opportunity to go over to that student and have a conversation about his worries. If a large portion of the class is not showing a thumb's-up signal, I stop immediately and answer questions.

I allow students to choose a partner and then a comfortable work area for this lab since there are fewer safety concerns than normal. Most students choose to work at their lab tables/desks, but the floor or front counter is also an option. Because of the inquiry format, I have springs, masses, meter sticks, scissors, ring stands and timers grouped at the front of the room. The pairs decide which materials they want to include in their design and experiment, and how they combine the materials to effectively answer the guiding questions.

The purpose of this lab is to get students thinking about Hooke's Law. Specifically, I want students to explain how concepts of simple harmonic motion can be applied to calculate and compare various spring constants. Students get the opportunity to experiment with both rubber bands (the same type that were used in the demo) and various springs. My hope is that students are able to apply their understanding of Newton's Second Law and Hooke's Law to calculate a variety of spring constants.

The timing of this lab is limited by the time of a class period, so I provide students reminders of how much time is left in the class. As students finish collecting data, I encourage them to take pictures of the apparatus so they can describe it in the lab write-up. Once data collection and pictures are complete, students are expected to put the lab materials back at the front of the room.

Each lab group is expected to write their own complete lab on a separate sheet of paper. Their write-ups act as a summative assessment, so they must include a question, a procedure, data, graphs, a conclusion with evidence, and an error analysis. Ideally this complete lab write-up would be due at the end of class, however all pairs work at different paces and I never want students to feel rushed. Since they are designing and carrying out the experiment as a pair, and since the students have chosen their own lab partners, the completion of this lab outside of the classroom (if needed) should not pose a problem.

## Hooke's Law "Ah Ha!" Closure

5 minutes

As a nice closure activity when time is short, I keep students at their lab areas and ask them to share one "ah ha" moment they had during the lab activity. Once an idea is shared with the class, it cannot be repeated to keep the process authentic. The entire sharing process should be continuous with one student sharing immediately after the next, and little pause in-between. Depending on time, I may elect to have the students do this individually or share a group "ah ha." While the students are sharing, I take short notes in my plan book or on my computer so that I can use these students' "ah ha" moments during the next class period. Keeping a few of these front and center in my mind really helps remind me that I can connect to prior knowledge on a personal level. For example, if a student shares that he finally sees why mass isn't included in Hooke's Law, I make sure to mention the irrelevant nature of mass during the next class. Also, I find that if the students are still standing while sharing "ah ha" moments, they literally have to demonstrate their learning by thinking on their feet!

## Stretching it Further (Extension)

15 minutes

I sometimes incorporate technology in this lab by including a force sensor with the original materials. As colleges and universities move towards more technologically-based labs, I find it's important to familiarize students with different probes and methods of doing the lab. Here is a comparison of the traditional set-up with a one that includes a Dual-Range Force Sensor made by Vernier.

This year, I have some time on a short-schedule day to allow students to repeat the lab with a force sensor. I find that students really enjoy comparing their calculated force results with those put out by Vernier's Logger Pro software. The software also allows students to see a graphical representation of the data, so they have another opportunity for comparison between their work and the probe's measurements. Students often like to compete to see who can put a greater force on the spring, which leads to some fun interactions between students that don't normally work together.

Setting up this equipment, or allowing students to put together the equipment is not difficult. They arrange the materials as described above, but include a force sensor as the connection piece between the spring and the ring stand.