A first-year report on the Chapter 4 pendulum experiment is submitted for checking

PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Records, communication and the epistemology of evidence

Measurement and Method, Ch Writing the result, and the integrity of the data behind it

Problem

A first-year report on the Chapter 4 pendulum experiment is submitted for checking. It reads, in part: "Fifty timings of ten swings of a

1.000\,\mathrm{m}

pendulum give

g = 9.81304 \pm 0.023199\,\mathrm{m\,s^{-2}}

. The timing table's second column is headed 'Time (s)

\pm 0.01

'. The graph plots the fifty timings against reading number, without error bars, captioned only 'Graph of results'. We thank our supervisor for laboratory space. This experiment proves Newton's law of gravity; the small difference from the standard value of

9.81\,\mathrm{m\,s^{-2}}

is attributed to human error." The report never states the pendulum's release amplitude, although the quoted

g

already includes the correction for it,

\phi_0 = 3.0^\circ \pm 1.0^\circ

, a factor of

1+\phi_0^2/16

on the period. The laboratory notebook, kept throughout, also records a second run of fifty timings of the same pendulum, taken a week later by a labmate with the same stopwatch: a mean period of

(2.0048 \pm 0.0018)\,\mathrm{s}

from all fifty timings, of which timing

37

, at

19.44\,\mathrm{s}

, fails Chauvenet's criterion for this run (Chapter 7), leaving

(2.0060 \pm 0.0013)\,\mathrm{s}

from the remaining forty-nine, both standard uncertainties. The other five rows of the first run's budget apply to the second run unchanged and together contribute

0.0150\,\mathrm{m\,s^{-2}}

u_{\rm c}(g)

. The report makes no mention of this second run and does not acknowledge the labmate who carried it out. (a) Find at least seven faults in the submitted report. For each, name the rule it breaks, the chapter that established that rule, and say whether it is a matter of integrity or of presentation and reasoning. (b) Rewrite the quoted result of the first run correctly, with its coverage factor

k=1

. (c) Using the same amplitude correction as the first run, compute the value of

g

the second run gives, with its combined standard uncertainty, first from all fifty timings and then with timing

37

excluded, and compare each with the first run's corrected result and with the local value

g_{\rm loc} = 9.8118\,\mathrm{m\,s^{-2}}

(Chapter 4). (d) Write a repaired concluding paragraph: state both runs' results side by side, never merged into one quoted value, the coverage factor, the comparison with

g_{\rm loc}

, the amplitude correction actually applied, and the scope of the result.

Browse the problem library