g: a pendulum

Students will time the periods of pendulums to determine if length or mass affects them. Students can then use a pendulum to calculate the acceleration of gravity.

A lesson plan for grades 9–12 Science

By Bill Sowell

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Learning outcomes

Students will learn:

• whether the length of a pendulum affects its period
• whether the mass of a pendulum affects its period

Teacher planning

Time required for lesson

55 minutes

Materials/resources

For each 2–3 students:

• tables or place to attach pendulum
• meter stick
• scissors
• tape
• string
• two different masses
• stopwatch

Pre-activities

Definitions of:

• pendulum
• period of a pendulum (T)
• length of a pendulum (L)
• g (acceleration of gravity)
• accepted value for acceleration of gravity on earth 9.8 m/s/s

Activities

Part I

Does mass affect the period of a pendulum?

Procedure:

Part IA

1. Put the meter stick between two tables (about one foot apart). Tape the ends of the meter stick in place. Measure enough string to just about reach the floor.
2. Tie the smaller of the two masses to the string and tie the string to the meter stick. Measure the distance from the center of the mass to the meter stick for future reference. This is the length of the pendulum (L).
3. Use your stopwatch to time five back and forth swings (periods) of the pendulum. It is important that the angle you pull the pendulum back is no more than 20–30 degrees from vertical. Record your time for five periods.
4. Find the length of one period by division. Record your time for one period.
5. Repeat three times and take the average of the three periods. Record your average period.

Part IB

6. Attach the larger of the two masses to the string and tie the string to the meter stick. Make sure the distance from the center of the mass to the meter stick (L) is the same as with the smaller mass.
7. Use your stopwatch to time five back and forth swings (periods) of the pendulum. It is important that the angle you pull the pendulum back is no more than 20—30 degrees from vertical. Record your time for five periods.
8. Find the length of one period by division. Record your period.
9. Repeat three times and take the average of the three periods.
10. Compare the two periods from parts IA and IB. Does the mass of a pendulum affect the period?

Part II

Does the length of the period affect the period of a pendulum?

Procedure:

Part IIA

1. Put the meter stick between two tables and measure the string so that it just reaches the floor.
2. Attach one of the two masses to the string and tie the string to the meter stick. Record the mass and length of the pendulum (L).
3. Use your stopwatch to time five back and forth swings (periods) of the pendulum. It is important that the angle you pull the pendulum back is no more than 20–30 degrees from vertical. Record your data for five periods.
4. Find the length of one period by division. Record your period (T).
5. Repeat three times and take the average of the three periods. Record your average period.

Part IIB

6. Now using the same mass, shorten the string significantly. Make it ¹/₂–²/₃ of its original length. Record the mass and length of the pendulum (L).
7. Use your stopwatch to time five back and forth swings (periods) of the pendulum. It is important that the angle you pull the pendulum back is no more than 20–30 degrees from vertical. Record your data for five periods.
8. Find the length of one period by division. Record your period.
9. Repeat three times and take the average of the three periods. Record your average period.
10. Compare the two periods. Does the length of a pendulum affect the period?

Part III (optional)

Calculate the constant g using from the period T and the length of the pendulum L, using the instructions: RTF | WPS.

Assessment

Student sketches of pendulum along with data they collect.

Optional: Calculated value for “g” along with relative error. Value of “g” and relative error to the accepted value.

Supplemental information

As a follow-up to this activity, I have had my students model it on a program we have called Interactive Physics. If you have this program at your school you might use it, as they enjoyed seeing the computer get similar results to theirs.

There are copies of the activity in RTF and works formats.