Measurement Error
Goal
- To determine the ratio of a cylinder's circumference to its diameter.
Equipment
- Digital caliper. Follow the
link to see an image of the Digital caliper and instructions on its use.
- Ruler
- Four cylinders of varying sizes.
Procedure
- Measure the diameter of the first cylinder using the
Digital caliper.
Remember to include units and an error
estimate. Do this several times (Why?) -- you decide how many, (no less
than 4 or more than 10).
- Each cylinder should have a radius marked on its end. Position this mark
vertically against the scale, aligned with the zero. Now roll
the cylinder along the edge of the scale five complete rotations until this
mark returns to the vertical position. The distance along the scale between
the zero position and the vertical radius mark is precisely is five circumferences.
Perform this measurement several times. (Why?)
- Repeat for the other three cylinders.
Complete your lab report in the jupyter notebook and include:
Title Block
- Date:
- Group Number:
- Author:
- Partner 1:
- Partner 2:
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 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).
It is acceptable practice to include calculated values here with their
associated uncertainties that are documented in the Analysis section of the
lab report.
Analysis
- Record the average diameter of each cylinder as
dbest ± Δdbest,
where Δdbest is the "error on the mean".
- Record the average circumference of each cylinder as
Cbest ± ΔCbest.
- For each cylinder, determine the best value of the ratio =
circumference/diameter with propagated error:
Rbest ± ΔRbest.
- 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 use Mathematica or a spreadsheet.
(Mathematica or spreadsheet might save some time here.) What numerical value
should the slope approximate?
Sources of Error
- Identify at least two sources of statistical error with explanations.
- Identify at least two sources of systematic error with explanations.
Conclusion
Explain what you learned (not what you did).
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