## 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. 2^{-1/4}s ?

3. Inverse fourth root of two?

4. 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.