Bagel Swinger

Essential Question
How does a pendulum work? How do you find the period of a swing?

Objectives

 * Collect data and construct a graph to find a relationship between the length of the period and another variable.
 * Explain the relationship between the physical characteristics of the pendulum and its period.

Introduction & Student Background
Almost anyone asked about a pendulum knows the type of motion. Good examples include old cuckoo clocks, a grandfather clock, swings, and anything dangling on a length of string. Pendulums also come into play every time you walk or run. Your arms and legs swing at a natural frequency depending on their lengths and weight distributions.

Ask the students what determines the period of the pendulum. You will get several answers including mass and length.

So long as the mass is concentrated at the end of the pendulum, the length is the only variable of importance. This is called the simple pendulum or point-mass limit. Once the mass is spread along the length then it becomes more complicated and is called a physical pendulum.

Vocabulary

 * period, periodic
 * length
 * repeated
 * mass, weight
 * cycle, cyclic

Materials

 * bagels
 * string
 * dowel rods 1/4 inch, 1 foot long.
 * duct tape

PREP

 * 1) Attach the two rods to the edge of the table with duct tape. They must be far enough apart to let a bagel swing on each one without hitting each other.

ACTIVITY

 * 1) Give each group two pre-cut strings of different length. They will each tie the bagel on differently, but the lengths will vary.
 * 2) Hang the bagels off the ends of the rods.
 * 3) Start both bagels swinging together. They should move apart as they swing. They will get out of phase with each other.
 * 4) Reduce the mass of the bagel by taking a bite out of it.
 * 5) Swing the bagel again and compare the period each time you take a bite. Make the bites big, about 1/4 of the bagel.
 * 6) Discuss the size of the variations. Ask students which bagel had the longer period.

How it fits to Standard

 * Forces on objects make them move. Changes in forces will cause changes in the motion.
 * Forces and motions can be measured.

Follow Up
Create a graph or scatterplot with all the data of the students. The horizontal axis should be the length of the string & pendulum, while the vertical axis would be the length of the period.