O Botafumeiro - SHM on a grand scale
The Cathedral of Santiago de Compostela (St James of the Field of Stars) in northwest Spain has been a pilgrimage site for centuries. One of its famous sights is that of the Botafumeiro: an enormous thurible (incense-burner) which is swung at great speed at the end of major services, covering almost the entire span of the north and south transepts. If you've never seen it before, have a look at this before going further (the swinging starts at 1:10).
It makes a good attention-grabber for a lesson, but then there are also some interesting bits of Physics you can pull out of it:
1) On a simpler level, you could calculate the length of the rope it's being swung on based on the time period of the swings. The tirabolieros (the people pulling on the rope) leave it swinging freely from about 2:30 in the video and I measure the time period just after that point as about 9.5 seconds. Using the usual school-level equation for the time period of a simple pendulum gives a value for l of about 22m. However, the Botafumeiro is swinging through a very large angle at this point - I would estimate at least 70°. This means the more accurate formula needs to be used, in which case I get l to be more like 19 metres, which is closer to the value given in Baker & Blackburn (2005, p28). This is a nice example of needing a more accurate formula once the assumptions inherent in an approximated formula don't apply.
Remember also that l is not just the length of the rope, but the distance from the point of suspension to the centre of mass of the whole system. Since the rope used is rather substantial, the centre of mass of the whole system will be quite a bit higher even than the centre of the Botafumeiro.
2) The tirabolieros use an ingenious method to increase the amplitude of the swinging. The loaded botafumeiro is clearly heavy, judging by the size of the initial swing (1:13 on the video) - estimates vary, but more than 50kg seems reasonable. Pushing it whilst it's swinging, in the manner of a child on a playground swing, would be neither practical nor safe so instead they do something which might initially look peculiar, but has some ingenious physics behind it. They:
- pull hard on the rope at the midpoint of each swing to decrease its length and then
- let it go back to its original length just before the botafumeiro reaches the extreme of each swing.
The decrease in length does Work on the botafumeiro which increases its GPE. This is then transferred to KE when the rope is returned to its original length, thus increasing the speed and, hence, the amplitude of the swing.
You can model this quite easily in a lab by looping a long string over a smooth support with a pendulum bob on the other end, giving it a small swing and trying to increase its amplitude without extra pushing. Once you get the hang of the tiraboleiros' technique, it's strikingly effective. Here's a video I made to show how it can be done.
Baker G and Blackburn J (2005). The Pendulum: A Case Study in Physics. Oxford: OUP.