Intent

Students will follow their initial forays into the behavior of a pendulum by testing the effects of several variables on the period of a pendulum.

Mathematics

To answer the unit question, students will have to understand what variables affect the swing of a pendulum and how they affect it. In other words, they will be searching for functional relationships between independent variables, such as the pendulum’s length, the angle of swing, and the weight of the bob, and the dependent variable, the period. To do this, they will perform a series of controlled experiments. In this early activity, they will compile a list of variables they think might affect the period and then each test one of these variables.

Progression

The activity begins with a discussion of variables that might affect a pendulum’s period. Students then work in groups to test one of the variables, using methods of their own design. Finally, they report what they did and what they learned.

Approximate Time

35 minutes for activity

30 minutes for discussion

Classroom Organization

Groups

Materials

Unwaxed dental floss or fishing line

Rulers or metersticks

Paper clips

Masking tape

Heavy washers (all the same size and shape)

Stopwatches

Protractors

Scissors

Doing the Activity

Remind students that to answer the initial question, Does the story’s hero really have time to carry out his escape plan?, they must consider the narrower question that was posted yesterday, How long would it take for Poe’s pendulum to make 12 swings?

Explain that, to answer this revised question, students will follow this general plan of investigation.

Post these steps under the revised question for students to refer to throughout the unit.

Ask groups to now consider this question:What might affect the period of a pendulum?Have groups make lists of potentially relevant variables, that is, of all the things they think might influence the period of a pendulum.

Then work together to make a class list of things that might influence the period of a pendulum. You can introduce the term bob for the weight at the end of the pendulum. Here are some variables students might propose.

Because this is simply a brainstorming process, use whatever ideas students present. For example, they might more naturally think about the distancethe bob is pulled back than the angle of the pendulum with respect to the vertical. In this activity,it is fine if they use as their variable the horizontal distance the bob is pulled from its resting vertical position, or the curved distance through which the bob is pulled, instead of the angle of amplitude. Whatever measurement they use, though, be sure they define it precisely.

The general concept of angle, and the specific notion of angle of amplitude for a pendulum, will be introduced in The Standard Pendulum and related activities found in Pendulum Variations.

Students will conduct today’s experiments in their groups. With this in mind, you may want to give some attention to this question: How would you judge a group member’s contribution? To emphasize issues of group cooperation, you might ask the class to create a list of criteria on which this group work should be judged, such as the following.

You might post this list of “criteria for a successful group” for students to refer to. Once discussion of the activity is complete, you might return to these criteria as a follow-up. (Another opportunity for work on this area of learning is suggested for Pendulum Conclusions, in which students assign grades to themselves and to their group members based on their contributions to group work.)

In this activity, each group is to focus on a single variable. Assign a variable to each group, or let each group choose a variable from the list they generated. You may want to ensure that at least one group looks at each of the key variables of weight, length, and amplitude.

Provide an assortment of materials (whatever you have readily available) from which groups can choose. The activity is not intended to produce definitive results; instead, students should have the freedom to experiment and to make mistakes. In later activities—The Standard Pendulum, Pendulum Variations, and An Important Function—they will be performing other pendulum experiments with a better understanding of the process of experimentation.

As groups work, be sure they are recording their findings and planning how they will report their procedures as well as their data. Students will vary in their efficiency at completing their experiments, so allow enough time that all groups can compile at least some results. Encourage groups to explore other variables if they have time.

Discussing and Debriefing the Activity

As groups share their results, follow up on the earlier discussion of experimentation. Whenever possible, point out the difficulty in making a decision about “what matters” without keeping all variables constant except the one being studied. Some groups may have done fairly controlled experiments, changing just one variable. They may state, for example, that they changed the weight of the bob and got a different period. (This idea of a controlled experiment will be formally introduced in the next activity, Close to the Law.)

You can ask groups about their confidence in their results. How certain are you that weight makes a difference? Are you 90% sure? Are you absolutely certain? Not at all certain?

If the opportunity arises, ask whether groups ever measured the period of the same pendulum more than once and, if so, whether they got exactly same result. This discussion can be an introduction to the idea of measurement variation, a topic that will arise in a later activity.

Inform students that these initial experiments are not the last they will perform. However, before they conduct additional experiments, they need to study more about how to tell whether a variable “makes a difference” in the period of a pendulum’s swing.

Key Questions

What variable did you measure?

What did you do to measure this variable’s effect on the period of the pendulum?

How long do you think it will take a 30-foot pendulum to make 12 swings?

How certain are you that your variable affects the period?

Did you ever get different periods for the same pendulum?

Supplemental Activity

Height and Weight (reinforcement or extension) asks students to explore whether the weight of something is correlated with its height (in a context of the students’ own choosing). This activity relates to today’s discussion about what variables are related to the period of a pendulum’s swing.