Determine g from a pendulum by linearizing the data
Three steps, the way the exam actually works: work through the lab, write down your own measurements, then answer a 6-point free response. What you recorded goes to the grader with your writing, so a conclusion that does not follow from your own numbers will cost you the point — exactly as it would with a real reader.
Run the investigation
- 1Make sure the lab is set to Earth, and keep the amplitude small (under about 15°).
- 2Set the pendulum length to 0.50 m and record the period the lab reports for one full swing.
- 3Repeat at lengths of 1.00 m, 1.50 m, and 2.50 m, recording the period each time.
- 4Square each of your four periods — you will need those values to find a slope.
- 5Return to 1.00 m, change the bob mass, and record the period again for part (d).
Booting the lab…
Record what you measured
These are your numbers, not ours. The grader sees them, so your conclusions have to follow from what you actually recorded.
| Period at L = 0.50 m | s |
|---|---|
| Period at L = 1.00 m | s |
| Period at L = 1.50 m | s |
| Period at L = 2.50 m | s |
| Period at L = 1.00 m after changing the bob mass | s |
Answer the free response
You are asked to determine the local gravitational field strength from pendulum measurements. (a) This simulation reports the period exactly, but in a real laboratory you would start a stopwatch and time ten oscillations rather than one. Explain why, and identify which type of experimental error that technique reduces. (b) A classmate plots period against length and gets a curve. Explain what you should plot instead to obtain a straight line, and derive the expression for the slope of that line. (c) Using your data, calculate a value for g. Show your work and give appropriate units. (d) Using your mass measurement, state whether the period depends on the mass of the bob and justify your answer with both your data and the governing equation.
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