# Measurement Error

## Procedure

• Measure the diameter of the first cylinder using the Vernier caliper. Follow the link to see an image of the Vernier caliper and instructions on its use. Remember to include units and an error estimate. Do this several times (Why?) -- you decide how many.
• Think of a method to measure the circumference of the first cylinder precisely using the tools provided. (This was part of the prelab assignment.) Perform this measurement several times. (Why?)
• Repeat for the other four cylinders.

Your report in the notebook should include:

• ### An abstract

• What measurements will you take?
• What tools will you use? Include the procedures in sufficient detail that another student could repeat your work.
• Why are you performing this experiment? What do you hope to learn?
• ### Data

A neat table in pen of all measurements with units and with estimated measurement errors. Record the raw data, before reduction (that is, before performing any mathematical operations on them).
• ### Error analysis

• Record the average diameter of each cylinder as dbest ± dbest, where dbest is the "error on the mean".
• Record the average circumference of each cylinder as Cbest ± Cbest.
• For each cylinder, determine the best value of the ratio = circumference/diameter with propagated error: Rbest ± Rbest.
• Graph the best straight line through the circumference (vertical axis) vs. diameter (horizontal axis) data and record the slope and the y-intercept. Plot by hand or with Mathematica. (Mathematica might save some time here.) What numerical value should the slope approximate?
• Identify at least two sources of statistical error.
• Identify at least two sources of systematic error.
• ### A conclusion

Explain what you learned (not what you did).

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