Physics Core/AP 1 and 2

Physics Lab

# Lab: Pendulum Motion 2

## Goal: To determine the dependence of the pendulum period on mass, string length.

NOTE: This lab is similar, but different in goal from the Pendulum Lab Part 1. In that lab, we took the formula T = 2π √ (L/g) as a given; here we will try to understand how it was derived.

#### Materials:

• At least 3 different masses (you could use coins, which makes it easy to double or triple masses). Masses should vary by at least 25%.
• A least 3 lengths of strong string or nylon fishing line, able to support your weight without breaking. String lengths should vary by at least 25%.
• 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 the least massive to the end of the shortest string length you have.
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 for each mass, but the same string length.
9. Repeat your experiment for each mass, for the next string length, until you have done a complete sequence (all available masses for all available string lengths) at least three times each.

#### Data Handling

1. Present your data in an organized tabular form.
2. Plot your data in a reasonable fashion: for example, plot the variation in period as a function of mass for each individual string length, then plot the period (separately) for each string length and mass.
3. Does the period change when you changed the mass? How might this affect your previous lab calculation for the gravitational acceleration?
4. Does the period change when you changed the length? How might this affect your previous lab calculation for gravitational acceleration?
5. Show how your results support or contradict the formula used to determine gravitational acceleration in the previous lab by solving T = 2π √ (L/g) for g.

#### 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 for your calculated values.
5. Show your graphs of period vs. mass and period vs. string length.
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.

Upload your report to the Moodle Lab Assignment for this Lab.