Manual digital timing devices such as stopwatches are ubiquitous in the education sector for experimental work where automated electronic timing is unavailable or impractical. The disadvantage of manual timing is that the experimenter introduces an additional systematic error and random uncertainty to a measurement that hitherto could only be approximated and which masks useful information on uncertainty due to variations in the physical conditions of the experiment. A model for the reaction time of a timekeeper using a stopwatch for a single anticipated visual stimulus of the type encountered in physics experiments is obtained from a set of 4304 reaction times from timekeepers at swimming competitions. The reaction time is found to be well modelled by the normal distribution N(ϵ, σ2) = N(0.11, 0.072) in units of seconds where ϵ and σ2 are the systematic error and variance for a single time measurement. Consistency between timekeepers is shown to be very good. The reaction time for a stopwatch-operated start and stop experiment can therefore be modelled by N(0, 0.102), assuming that the average reaction time is the same in both cases. This makes a significant contribution to the uncertainty of most manually timed measurements. This timing uncertainty can be subtracted out of the variation observed in repeat measurements in the real experiment to reveal the uncertainty solely associated with fluctuations in the physical conditions of the experiment.
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For example, an image suggests a new asteroid has a diameter of d = 2r = 0.5 km with an uncertainty of 0.2 km. What is its volume? V = 4πr3/3 so that δV = 4πr2δr yielding V = 0.065 ± 0.079 km3.
