A stopwatch used to time a pendulum runs fast

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Measurement and Method, Ch Repeated readings: scatter, the mean and the standard error

Problem

A stopwatch used to time a pendulum runs

1.0\,\%

fast, so every measured swing time is measured

1.0\,\%

longer than the true time. The operator's hand-timing also scatters, with sample standard deviation

s = 0.15\,\mathrm{s}

per single-swing timing, found from ten readings. ((a)) Classify the

1.0\,\%

rate error and the

0.15\,\mathrm{s}

scatter as random or systematic, and give the test that decides it. ((b)) The operator increases the number of timings from

10

1000

. Predict what happens to (i) the standard error of the mean and (ii) the size of the rate error.

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