The Problem of the Dangling Magnet

Here’s a variation on a physics problem we discussed in my first-ever Skills in Physics Tutorial at the University of Sussex. I hadn’t realized that solutions were provided for Tutors so had to exercise my enfeebled brain in finding a solution. You’ll probably find it a lot easier…

A rectangular bar magnet hangs vertically from a pivot at one of its ends. When gently displaced the magnet undergoes small oscillations either side of the vertical with a period of one second.  A horizontal magnetic field is then applied so that the equilibrium orientation of the magnet is  45° to the vertical. If the magnet is gently displaced from this new position, what is the new period of oscillation?

Comment: you do not need any further information about the size, shape or mass of the magnet in order to solve this problem.

14 Responses to “The Problem of the Dangling Magnet”

  1. 0.84089641525371454303 seconds?

    • I don’t think all your figures are significant…

      • Yes, it’s just the default precision of my ‘SpeedCrunch’ calculator :o)
        But I would disagree with your statement. At first, we don’t know the precision of the measurement (it says mysteriously: ‘one second’) and second (another second this time, oh Lord), as far as I know there is still a bit of a discussion about the numbers of figures one should show for a single particular measurement, since for the error we have only an estimate…

      • “One” has only one significant figure

      • “One” has only one significant figure
        With this poor resolution they would get a new period of 1 second again. But I don’t want to bother you anymore with this staff. Sorry, the answer should be 2^{-1/4}s.

      • …with this staff …with this stuff I meant.

      • ““One” has only one significant figure”
        I would think that “one” can have any number of significant figures. It could mean 1 or 1.00 or 1.00000000000. If it only has one significant figure then my answer to the question is also 1(1sf), otherwise I agree with 2^{-1/4} 😉

      • telescoper Says:

        Indeed you’re probably right I think “1” and “one” both imply an exact integer whereas 1.0 would imply some rounding….

  2. Inverse fourth root of two?

  3. Peter Thomas Says:

    As the person who set this problem, I would accept the answer 2^{-1/4}s ~= 1s, but not 1s! I hope that you enjoyed it. Please if you have any similar problems, send them my way. Thinking up interesting but accessible problems is really hard.
    Prof. P.

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