Friday, 31 July 2015

Analysing some knots


I've been reading more of Matt Parker's book on maths. I wasn't aware that Lord Kelvin had proposed the idea that matter consisted of knots in the ether, at a time before the existence of atoms was proven and when it was still believed that the ether permeated the whole universe. The idea was that each element was a different knot. So the study of knots was started. I've done my first, shown above. It is the simplest possible knot but not as simple as  thought when loosened slightly. It's called a trefoil knot and has 3 crossovers. More to follow!

Thursday, 30 July 2015

Amazing conglomerate rock on Rhossili Down

This rock on the top of Rhossili Down looks like concrete but it's natural. It is evidence of the recycling of rocks during the Earth's history. The rock itself is old enough to have been thrown up to make the hills overlooking the sea but the pebbles within it come from much older rocks that had been weathered and transported. They are round so they must have been carried some distance. They say that the pebbles were deposited by a river that flowed across this landscape millions of years ago.

Monday, 27 July 2015

Solving the Wobbler

Here's the solution to the Wobbler problem. It's not a universal solution because I've just used the two positions shown in yesterday's pictures. The Wobbler is made from two cardboard circles intersecting. In my solution, I have taken the slot to be a x the radius, where is a factor, a fraction of the radius.


Sunday, 26 July 2015

Making a Wobbler

I have been reading this wonderful book. Matt Parker is comedian and mathematician. I realised that given the title of the book, I should actually make the things he suggests. My problem has usually been that I have read and understood the theory but never tested it. Perhaps I'd be a real physicist if I'd tried things earlier!
 I made the Wobbler from page 65. It's two intersecting circles like this. The idea is that it rolls like a wheel because if the size of the slot is exact, then it will continue to roll like a wheel because its centre of gravity remains the same height above the ground.
 By considering the two positions shown below, I was able to prove his statement that the exact size of the slot is 29.2893% of the radius. Details to follow!


Saturday, 25 July 2015

Sand ripples on the beach at Rhossili


It was suggested to me a couple of weeks ago that the ripple marks in the altostratus clouds that have attracted my attention are formed in the same way as ripple marks in the sand. I got thinking about it again on the beach at Rhossili. First we crossed a fresh water stream flowing into the sea. The water flowed over some pebbles and then formed the characteristic ripple pattern shown in the top photograph. The sand on the bottom of the stream was likewise rippled. It occured to me that the pebbles had probably made the flow of the water turn turbulent. There is certainly turbulence in sea water - witness the white water. There are the competing flows of water in and out. But why only ripple marks in some places? An initial look at Internet sources suggests I've got some more observations to make - perhaps measuring the wavelengths of the ripples and looking at the cross-sections. My current working hypothesis for the altostratus cloud is going to be turbulent airflow.

Friday, 24 July 2015

Wind power for the Worm's Head at Rhossili

 The picture above shows Worm's Head, a tidal island at Rhossili on the Gower. The coastguard station below had a small wind turbine. The wind speed was said to be about 20mph average that day, a stiff breeze.
Conventional wisdom is to assume that the air stops dead when it hits the blades and to assume that all of the kinetic energy of the air is transferred to the blades. Let's estimate that the diameter is 50cm. 20mph = 32 km/h (5 miles is 8 km). 32 km/h = 32 x1000/3600 = 8.9 m/s. So in 1 second, a volume of pi x 0.25squared x 8.9m is stopped. That's 1.7 cubic metres of air. Let's go with air having a density around 1kg per cubic metre. Going for 1 significant figure, then 2kg of air is stopped every second. Kinetic energy = 1/2 x mass x speed squared = 81J. Let's say the turbine is 30% efficient. That works out at no more than 30W.

Sunday, 19 July 2015

Preparing for L6 Physics #8: Stationary waves on my bass guitar

I'm learning bass guitar. Like all stringed instruments, the strings are fixed at each end. When you pluck the string, you create a wave on the string that travels along the string and reflects off the far fixed it. It crashes into the bits of the wave that have not yet arrived. If you get two waves travelling in opposite directions with the same frequency, speed and amplitude, then you get a STATIONARY WAVE. The peak doesn't move along. The peak in this case is in the middle of the string and it just goes up and down in that skipping rope pattern. Fixed points are called NODES and this oscillating maximum in the middle is called an ANTI-NODE.