How far is it to the sky?

Mrs B found this lovely book for me. It contains this page

Which begs the question: how far away is the sky? This led me to find out about the Karman line https://en.wikipedia.org/wiki/K%C3%A1rm%C3%A1n_line Karman calculated the altitude at which an aircraft would not be able to travel fast enough to generate enough lift to support itself without travelling faster than the orbital speed for that altitude. So this is where the sky is said to end and space begins. It's arbitrary but I like that it is based on a calculation.
There was a new moon tonight just visible through the trees.

So

Midsummer Chronophage in Cambridge

This weird clock and another similar are star attractions in Cambridge. It took me a long time to work out how to read them. The outermost light races round in a second. I took repeat shots that show that the shutter is not always open for the same amount of time. One complete lap lasts a minute. The inner lights show that the time was roughly 20 to 5.

Another mathematical bridge

I have been past this bridge at Iffley Lock many times but hadn't realised that it is a replica of the Mathematical Bridge in Cambridge. The angled or horizontal long sections are tangents to the circular arc of the bridge. The almost vertical short posts are radii.

Knitted mathematics in Cambridge

Being someone who knits, I was amazed to find in the Whipple Museum of the History of Science these mathematical surface models knitted by a scientist over a century ago. There is more about them here: http://www.sites.hps.cam.ac.uk/whipple/explore/models/knittedinterpenetratingsurfaces/ It reminded me of when I was trying to make a model of a Riemann surface out of paper five years ago. http://wigtonphysics.blogspot.com/2015/01/trying-to-make-riemann-surface.html

Mathematical Bridge in Cambridge

I'd heard about this and also heard that there were myths about it, but now I understand it, I'm really impressed. The diagonal timbers are all tangents to the circular arc of the bridge and the upright posts are radii of the greater circle. https://en.wikipedia.org/wiki/Mathematical_Bridge I'm now on the hunt to find the replica near Oxford.

Josephson Junction

I also found this at the Cavendish Laboratories. I'd heard of Josephson Junctions but had never bothered to look it up. It turns out to be quantum tunnelling with superconductors, so that it is Cooper pairs of electrons that tunnel through the barrier. https://en.wikipedia.org/wiki/Josephson_effect

JJ Thomson and the electron

I was very pleased to visit the site of the old Cavendish Laboratories in Cambridge. It prompted me to look up JJ Thomson. https://en.wikipedia.org/wiki/J._J._Thomson He was experimenting with cathode rays. Following the chain back, it seems that the line of research started with the passing of big voltages through gases - an old-fashioned streetlight, in other words. Then they started to improve vacuums until they could remove all of the gas. They realised that they had a straight line ray. This is where Thomson came in. He was able to bend the rays with magnets and electric fields, to work out the charge-to-mass ratio. He realised that the particles were negative and smaller than an atom. The world of sub-atomic particles was born. I'm amazed by the number of Nobel laureates that he taught, including Wigton's own William Henry Bragg.

An interesting fact

This is a birthday card that I received. I think it is an ironic take on the spurious correlations that get noticed. My favourite is the one that says that the more ice creams that are sold, the more people drown. There is no causal link. The ice creams don't cause the drowning but are consumed on hot days when more people go wild swimming. On this card, there is clearly a causal link but it is trivial.

Light in the sea

I was interested in this display at Maryport Aquarium. If the top 200m makes up 25% of the oceans, then the oceans cannot be as uniformly deep as I'd imagined. The detail on the absorption of  different light colours is exceptional. I recently found out that ABSORBANCE = log10(intensity in/intensity out). If only 20% of light has reached 10 metres, the absorbance = (1/0.2) = 0.70.

Life cycle analysis

I have had to teach Life Cycle Analysis in recent years. This is a tool to calculate the impact of a particular product based on the energy and environmental damage involved in raw materials, manufacture, transport and disposal. I was surprised by one that I saw that put polystyrene cups ahead of waxed paper cups. The latter are lighter and so less fuel is used in transport. The balance on that one might have shifted now that waxed paper cups might be becoming more recyclable. In the case of the paper towels, they need raw materials and are heavy to transport. The wet paper won't be recycled. So this is another example of where a paper product might seem to be a better option than using electricity, but masking the fact that more electricity and fossil fuels were used in manufacture and transport. I think people prefer paper towels because they seem to give drier hands faster.

More electrolysis with the head torch

To clean the copper sulfate from the copper contacts in the head torch, I put that part of the case in dilute hydrochloric acid overnight. Somehow it seems to have acted as an electrolytic cell. The top contact seems to have been cleaned and has a layer of new copper. The other contacts have been cleaned to some extent but now have a layer of what is presumably copper chloride. There was no battery connection so there should have been no potential difference between the contacts. I'm surprised at what has happened because there was no difference in metal like there was on the human electrolyte cell I found at Green's Mill two weeks ago. Anyway, the acid has done the trick and the head torch is working again.

Problems with Charles' Law

We are fortunate to have a set of apparatus for performing the Charles' Law experiment. The problem is trying to get the concentrated sulfuric acid plugs into the capillary tube. Concentrated sulfuric acid is sued because it absorbs water vapour from the air column making sure that it is just dry air pressure being measured. We dry the empty tubes in the oven before up-ending them into the acid. The idea is that the air then cools and contracts, pulling the acid down the tube. It doesn't go down far enough so that the air column is covered by the water bath. It doesn't seem to affect the results but is still not very satisfying.

Copper sulfate corrosion in a head torch

I was amazed to find blue copper sulfate crystals in the battery compartment of this head torch. To be fair, the alkali cells were 5 years beyond their label date. The contacts are copper, but where did the sulfate ions come from? The were 2 AA alkaline cells in the compartment. The electrolyte is thus potassium hydroxide. Mrs B is suggesting that it might be from the plastic in the case. Rubber is vulcanised by using sulfur to provide cross-links. Sulfur trioxide will react with potassium hydroxide to make sulfate ions.

I should have timed the oscillation

The second non-barbed wire down on this fence at Dinorwig Quarry skips the next pole and thus spans 5 metres between nodes. That would give a 10 metre wavelength when oscillating as a stationary wave. It made a note that was inaudible. I should have timed the oscillation to get the frequency. Next time, with frequency and wavelength, I'll be able to calculate the wave speed. I can estimate the mass per unit length and thus get the tension. I need to find another fence!

Physik im Advent

Heute ist der erste Adventstag. Jedes Jahr gibt es einen Physikkalender mit vielen Experimenten. Es hat begonnen. Man kann es hier finden. https://www.physics-in-advent.org/ Man kann Deutsch oder Englisch waehlen.

Waterwheel at Llanberis Slate Museum

It took 45 seconds for the wheel to complete one full turn. The diameter is 15.4 metres. That means the rim has a linear velocity of 2*pi*r/T = 1.1 metres per second. It all seemed to be moving so slowly but that is the speed of the a fast sprinter.

Is this a voltmeter?

This meter has no units so what is it measuring? I'm assuming that it is a voltmeter measuring the emf generated by placing your hands on the different metals. https://www.exploratorium.edu/snacks/hand-battery This site explains that the electrolyte is actually the sweat on your skin which allows the metals to give and receive electrons. The aluminium is more reactive so it finds it easier to lose electrons to form positive ions. Copper finds it harder to lose electrons so there is a net flow of electrons from aluminium to copper. https://www.mpoweruk.com/chemistries.htm

Why they are called sails on a windmill

The board above explains that windmills were turned by a wooden framework over which a sail was spread. In very windy conditions, you could wrap up the sail so the wind was catching less of an area and so providing a smaller force. I like the solution with spring-loaded shutters. A stronger wind puts a bigger force on the spring, opening the shutter and letting some of the wind straight through.

Notice that the windmill has been done with two of each. And notice that they are diagonally opposite each other. The spring loaded sails will adjust to wind strength automatically whilst a human has to make a decision on the canvas sails. This could lead to uneven torques if different types are paired up. I suppose that the diagonal pairings act as a couple in the technical sense.

Lightning conductors in windmills

The end of the sail on Green's Mill appeared to have a lightning conductor on it. I'm wondering how that connects to the earth given that the contact must be rotating as the sails turn. It could be done with carbon brushes like in an electric motor. I read of one old wind powered corn mill that survived a lightning strike when the current was conducted down an external chain used to raise sacks of corn. Lightning strikes on modern wind turbines are a big topic https://www.windpowerengineering.com/preparing-turbines-for-lighting-strikes/ has some good information. I was interested to read that the average energy release is 55kWh, in other words, enough to run my convection heater non-stop for two days. It also says that static charge is generated in the metal blades as they sweep through the air. There must also be some kind of emf between the blade tips and the centre, but that needs a separate post.

Chaotic pendulum at Green's Mill

 This chaotic pendulum was at Green's Mill in Sneinton. It consists of a magnet on a rod above 3 other magnets, which it cannot quite reach. Notice that the socket for the rod is not above the centre of the magnet disc, which can be rotated.

 Further inspection showed that the swinging magnet attracted to one of the magnets below but was repelled by the other two.

The magnet describes an oscillatory motion but it should never fully repeat itself even if released from what seems to be an identical position. This is what it means for a system to be chaotic. A normal orbital motion goes round and round endlessly and predictably repeating itself. The weather goes in cycles, doing roughly the same thing at the same time every year but never fully repeats itself. This magnet will always settle over the attracting magnet at the end as it loses energy. The weather often settles into certain patterns that seem hard to shift. These patterns would be called the attractors of the the system. At the moment, we seem stuck in a pattern of very rainy weather over the southern UK. However, just as I could put some energy in to knock the magnet out of its attractor state, something will eventually inject the energy to knock the weather out of this attractor and it will settle into another state.

Green's Functions

Green's Mill was run by the mathematician George Green. I finally understood Green's Theorem after 30 years http://wigtonphysics.blogspot.com/2018/01/greens-theorem.html and so was keen to go back to the mill. I wanted to see the Local Heroes film by Adam Hart-Davies which uses clockwork toys to explain aspects of the theorem. I looked for it on the Internet when I was trying to understand the theorem but couldn't find it. They still have it playing. But they also have this film about Green's Functions https://www.youtube.com/watch?v=ji-i6XCkgC0. No wonder I cam across them when I was working on perturbation theory in quantum mechanics. If you disturb a linear system in one place, they allow you to calculate the effect time T later in another place.

GCSE required practical to prove the wave equation

I'm interested that it been suggested that the stationary wave demonstration should be used to illustrate the equation wave speed = frequency x wavelength as well as the ripple tank. It requires explaining that two "loops" make up one wavelength and requires trust that the wave speed remains constant if the same tension is on the string. It can then show that if you double the frequency, the wavelength halves (ie number of "loops" doubles). It's the first time I've tried it with weighted string. I've previously used a clamped piece of thin rubber tubing. On the string, I could only get 4 "loops" but I've have up to 8 on the rubber tubing.

Centrifugal governor at Green's Mill

We visited Green's Mill in Sneinton. The governor was invented by Christiaan Huygens for this purpose of ensuring the flour was evenly ground. The adjuster arm for the millstone separation has manual control on one end with the T-bar screw and the governor is the automatic control at the other end. As the mill spins faster, the heavy balls are dragged round faster. Their inertia causes increased tension in their angled supports. Since their weight mg=Tsin(theta), where theta is the angle to the horizintal, if T goes up, theta must go down. In other words, the balls tend to be nearer to the horizontal when they go faster. If you look, this would act to pull upwards on that adjuster bar.

Pigeons in space-time at Stonebridge City Farm

The way these pigeons were making the netting sag at the farm in Nottingham reminded me of the way that masses cause space-time to curve in Einstein's General Theory of Relativity. Fortunately none of them was heavy enough to cause a black hole.

After the chocolate

I really enjoyed the hot chocolate made by this machine and was keen to investigate. It turns out that the stirrer is held in magnetically. There must be a rotating magnet or some kind of induction motor effect in underneath. Previously there would have been a sealed spindle up from the motor below but that would still have left joints down which liquid could seep. I first saw magnetic stirrers in the lab nearly 30 years ago so it is interesting to see that they have now made it into the kitchen.

Henley's electrometer

I found this electrometer in the Whipple Museum in Cambridge. In terms of analysis I normally use two balls with identical charge on threads - a symmetrical problem.

So how do we model the Henley electroscope? Will the ball and the the central pole have the same charge? It looks like a rod not a string. Does that make a difference? Anyway, here's my first sketch:

I don't know whether the electroscope was to show relative charge or actual charge using Coulomb's Law but the latter looks possible once the angle is known.

Curved space-time and Hawking

I suppose that the fame that Einstein attracted a century ago has been mirrored in our own time by Hawking. The are linked by curved space-time. Einstein's equations described it. Hawking studied the black holes that came out of the equations. These days we describe space-time as like a sheet of Lycra with a bowling ball on to represent the mass of a star. Sadly I've never had a large enough sheet of Lycra to do it. 50 years ago Hawking had these models made. The top one shows the way a star (the yellow centre) dents space-time. The bottom one shows that a black hole does something very extreme to the space-time.