Gravitational Acceleration

Goal: To measure gravitational acceleration near the earth's surface

Materials:

• Several masses (you could use coins, which makes it easy to double or triple masses).
• Strong string or nylon fishing line, able to support your weight without breaking.
• Hook on which to tie pendulum; should be fastened to make the pendulum as long as possible (I used the ceiling hook for a hanging plant).
• Stopwatch or watch with second hand.

Procedure

1. Weigh your masses.
2. Tie them to the end of the string.
3. Tie the string to your hook.
4. Measure as accurately as possible the distance between the hook and the center of the masses; this is your pendulum length L.
5. Displace the pendulum (measure the horizontal distance x of the displacement of the pendulum from its rest position.)
6. Measure the length of time required for the pendulum to make 10 complete back-and-forth swings (10 periods). Determine the value of T.
7. Repeat at least twice.
8. Repeat your experiment, varying the mass by at least 25%.
9. Repeat your experiment, varying the length of the string by at least 25%.

Data Handling

1. Does the period change when you changed the mass? How will this affect your calculation for the gravitational acceleration?
2. Does the period change when you changed the length? How will this affect your calculation for gravitational acceleration?
3. Average your values for T.
4. Using the average value, determine the acceleration due to gravity for all masses and lengths you used. [As we see in chapter 11, the formula for the period of a pendulum is T = 2π √(L/g).]
5. Average your results.
6. Compare your average with the accepted value (9.8 meters/second²) and explain any differences.

Report

1. Describe your materials, equipment, an dprocedures in sufficient detail that your fellow students could repeat your experiment.
2. Report your data. Be sure to indicate the amount of error in your measurements. For example, if you can only measure a mass of 25 gms within 1 gm, your error would be 25 ± 1, or 1/25 = 4%.
3. Present your data in an organized form, preferably in a table, in such a way it is easy to compare results as you repeate trials or vary a specific contributing factor.
4. Show a sample calculation, if you have calculated values.
5. If you did a series of experiments, varying something by increasing or decreasing a factor, try to plot your data (y-axis) as a function of the factor (x-axis).
6. You may use a spreadsheet to calculate your information and create your table.
7. Summarize your results.
8. Draw conclusions about what is happening.
9. Suggest at least one way to improve your experiment.

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