Would air resistance be an issue in the Cavendish experiment or are the velocities so low as to be irrelevant? Could it cause the experiment to fail?
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$\begingroup$ The final result is a slightly twisted torsion rod at rest. Any damping on how it gets there is irrelevant to the final result, yet wanted so the rod settles in the final state faster. $\endgroup$– Jon CusterCommented Sep 2, 2023 at 14:00
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$\begingroup$ ... but determining the torsion coefficient of the wire attached to the torsion rod requires measuring its natural oscillation period, which could be affected by air resistance. $\endgroup$– gandalf61Commented Sep 2, 2023 at 14:45
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$\begingroup$ The variation done at my school was in a vacuum chamber, so it can be a problem (it's a question of how much if it's in air). $\endgroup$– MaximusIdealCommented Sep 2, 2023 at 17:01
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$\begingroup$ @JonCuster Cavendish’s mass were never static when he took readings. He measured three successive maxima and from those readings he was able to estimate the position a suspended mass would have had if it had came to rest. $\endgroup$– FarcherCommented Sep 2, 2023 at 20:15
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2 Answers
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The speed with which the masses move through the air in the cavendish experiment are extremely low. Air movement caused by people breathing on the apparatus will be orders of magnitude bigger in comparison. The apparatus needs to be well-shielded for this reason.
answered Sep 2, 2023 at 16:06
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For his first few experiments Cavendish used a torsion wire arrangement which had a period of about $800$ seconds and then introduced a stiffer wire which had a period of about $400$ seconds.
The amplitude of motion was around $5\,\rm mm$ thus the speed of the smaller lead balls was of the order of $10\,\rm \mu m/s$ meaning that air resistance did nit play a significant part in the experiment.
Cavendish found it took too long (hours) for the smaller lead masses to stop oscillating so to find the position of rest Cavendish too three successive readings of the maximum deflections (either way), $x_1,\,x_2$ and $x_3$ and then the position of rest was $\frac 12 \left((x_1+x_3)/2 +x_2 \right)$ which helped make a correction for the damping that w3as present.
The smaller lead balls arrangement and the torsion wire were contained in a Mahogany box to reduce air currents and the whole apparatus was in a room about $3\,\rm m$ cube to guard against temperature variations.
All manipulation of the apparatus, eg moving the larger balls was done from outside the room and observations of the scales were also taken from outside the room using telescopes as can be seen in the illustrations shown in the Wikipedia article cited by the OP and the illustrations on the last couple of pages of Cavendish's Royal Society paper.
