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:
Your name
Your lab partner's name
Your lab station number
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
d_{best} ±
d_{best},
where d_{best} is the "error on the mean".
- Record the average circumference of each cylinder as
C_{best} ±
C_{best}.
- For each cylinder, determine the best value of the ratio =
circumference/diameter with propagated error:
R_{best} ±
R_{best}.
- 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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