Length Measurement

Challenge:  To design a length measurement device or set of devices to allow you to find the length or circumference of regular objects as precisely and accurately as possible.

Parameters:  The measuring device must be able to measure length and circumference. The unknown objects will be rectangular prisms and cylinders. The smallest measurement expected may be a centimetre while the largest may be up to a meter. You will be given the unknown objects and will have 10 minutes to use your device(s) to get as precise a measurement of the dimensions as possible. You will report your measurements with appropriate precision and specify your absolute and relative uncertainty. You will then be shown how to calculate the volume of the objects and how to show your calculations properly.

Scoring:  Your effort will be scored based on the accuracy of your measurements and your estimate of your uncertainty, as follows:

| % differences | summed  + Confidence Penalty*

* Confidence Penalty:  The absolute value logarithm of the ratio between your total relative uncertainty and your actual percent differences.

Rank will be based on score, with lowest score earning highest rank.

Physics:  A measuring device can only be as accurate as the standard from which it is copied. Its precision depends on the fine-ness of its markings and your ability to interpolate between those marks. Another factor is the material properties of the device. Most materials expand and contract with temperature changes or rough use.

Extensions:  Practice makes perfect. Make sure you can reliably use your measuring device. Find out how averaging multiple measurements of the same dimension can be used to reduce uncertainty.

Help/Hints:  Have each member of the group try to independently find the measurements of an object, then compare within the group. What factors can cause disagreement? What does that tell you about uncertainty?

Quiz Topics:  Measurement, Uncertainty, Scientific communication

Online Text:  chapter 1