George Orwell's grave: coefficient of friction

When we were last at Crinan, we were able to look out over the water to the remote farmhouse on Jura where George Orwell wrote 1984. Within a year he was dead. It turned out we were staying in Oxfordshire near his grave. He wanted to be buried in an English country churchyard. I wonder what he'd make of the coins left by other visitors. Notice that as the edge of the grave stone gets steeper, the coins won't stay. Friction isn't strong enough to resist the component of weight pulling down the slope. Friction F is directly proportional to normal contact force N. The constant of proportionality is called the coefficient of friction mu.

 Above is the force diagram. Three forces act on a coin. I take components of the weight mg.

At the point at which the coin is just about to move, the perpendicular components must be equal and opposite. The same is true of the parallel components. So I can make the substitution shown at the bottom. Lastly, coefficient of friction = tan(theta). The angle at which the coins come off is about 30 degrees so the coefficient of friction for stone and metal is thus about 0.6.

Coriolis Effect and the Birmingham floods

The storms in the West Midlands last night made the news. One of the best lightning displays that I've seen in years. A lot of water fell in a short space of time. After the storm, the water was swirling down this drain at the service station. It was going anti-clockwise. They say water should always do this in the northern hemisphere but in reality it also depends on the geometry of the drain hole and on the initial conditions. The best thing that happened was when a passing car sent plane waves across the system. They were then bent round as they hit the sink hole producing an effect like spiral arms on a galaxy. For the definitive Coriolis Effect film, see https://www.youtube.com/watch?v=aDorTBEhEtk

Chasing shadows at Watchtree

 I was watching the shadow of a wind turbine at Watchtree as it raked across the meadow.

 Later we stood as the shadow came rushing across us.

When timing the shadow and the blades, you must have the same time for the same movement. But if the Sun is low and the shadow is being projected over a bigger distance, the shadow will move further than the blade in the same time. Thus the shadow will move faster in those circumstances. In theory it is possible for the shadow to move faster than the speed of light!

Vectors and the ferry to Threave Castle

We took the ferry to visit the wonderfully situated stronghold of Archibald the Grim. The boat shouldn't be aimed in a straight line between the two points because as well as the velocity vector of the boat's motor, there is also the velocity of the river water to contend with. It will tend to push the boat downstream so you need to aim slightly upstream.

Leslie's cube

Leslie's cube is a copper cube filled with boiling water. The sides are painted matt black, gloss black, white and unpainted. It is a closed system but energy crosses the system boundary as infra-read heat radiation. I used a thermopile and an old-fashioned spot beam galvanometer to detect the infra-red. The matt black side gave the highest reading today showing that it is the best surface colour for emitting infra-red.

Work done crossing the system boundary

We still own an old-fashioned bicycle pump! If you put your thumb over the end and pump, the pump case becomes quite hot. Air is trapped inside. It is a closed system. But work can cross the system boundary. The work done gives extra kinetic energy to the air molecules. This extra internal energy manifests itself as a rise in temperature.

Thinking about Olber's Paradox on Glasson Moss

We were sat having a picnic in the thin band of trees on the edge of Glasson Moss. I realised that although the band of trees is quite thin, I couldn't see through. In every direction , there was a tree trunk. This is really the opposite of Olber's Paradox, which asks why the sky is black at night. It was based on the idea that the Universe is static and infinite in size. If that were so, says the reasoning, then you'd be able to see a star in any direction you looked. That's like me seeing a tree in any given direction. But of course there isn't a star in any given direction. One explanation now is that the Universe is not infinite in time, so light from more distant galaxies has not had time to reach us yet.

Under pressure: crushed bottle on Ben Nevis

This bottle was emptied at over 4000 feet up a mountain and sealed. This morning it looks like it has been crushed. If the seal is good enough, the theory goes that the air inside was at lower pressure and bringing it down has meant that higher pressure air at sea level has crushed it. Is this repeatable? At what heights can it work? Is it only certain bottles? Needs researching!

Freeze-thaw and Napes Needle

The top block of Napes Needle has a big crack underneath it. I was wondering if freeze-thaw might eventually make this too dangerous. Although the covalent bonds inside the water molecule are strong, there are weak hydrogen bonds holding the molecules together. At room temperature, the thermal agitation keeps breaking these bonds. Below 4 degrees and into the solid state, the thermal agitation is not enough and the molecules are able to stay together. These intermolecular bonds take up angles that push the molecules apart so ice has a bigger volume than liquid water. Water penetrates cracks with ease but the expansion on freezing pushes against the rock.

Ring main on the camping field

It's a long time since I've taught about ring mains. In essence, the live and neutral wires both form loops from the box going back to the box. Appliances are then connected between live and neutral. This means that the appliances are in parallel and thus independent of one another. The mark schemes used to point out that as current could flow either way out along the live wire to the appliance, only half as much current went through any one wire so the wires could be thinner.

Searching for a meaning for the partition function

The partition function is used in statistical physics to help define distributions but I've been struggling to work out what it actually is. Here's a speculative attempt. I remembered that if there are large numbers of gas particles with equally stepped energy levels then the distribution should be such that there is a common factor between levels. In the case below, n1/n0 = 0.5, n2/n1=0.5. In other words there is a common probability that a particle will in one level higher. Note that if you add them up, the total number of particles here is 124. N=124

 This probability is called the Boltzmann factor and it is given as shown below.

 I calculated the probabilities of being in any given level above the ground state.

 The theory for the Boltzmann distribution calculates the number nj in any given level using the equation shown. Remember that our total number of particles N=124. The summation on the bottom of the equation is the PARTITION FUNCTION. It looks like a summation if Boltzmann factors. (Note that beta is often used in the derivation before it turns out to be -1/kT)

 So I added up all of my probabilities. I got 1.9375.

 I then used this in the equation and it works in predicting the number on that level. So I am going to tentatively say that I think that the partition function can be thought of as a sum of the individual probabilities for a particle to be on any given level above the ground state.

Complicated circuit for line working telephone

 I found this old line working telephone in the museum of the South Tynedale Railway in Alston.

I've been looking at the rather complex circuit diagram and trying to make sense of it. At first I assumed that the blocks of 4 diodes would be bridge rectifiers. Underneath it calls this section a "regulator". It turns out that if you put a diode into a series circuit with a resistor such that they share the p.d., even if the p.d. changes the diode will always take just 0.7V because that is its forward bias to conduct. This fixes the p.d. across the diode and regulates the voltage. I think that RLP probably stands for "resistor in low pass circuit". If you follow the wiring across to IC you find inductances - loops of wire. When AC flows through such a wire, the changing flux that is set up links its own coil so causes a back emf to be induced. This acts against the current. The higher the frequency the worse it gets, so you can use it to allow low frequencies through.

Resolution in Alston

At GCSE we are now using the word RESOLUTION to mean the smallest scale division on a meter. The resolution of this scale in the railway museum in Alston is therefore 0.5 lb.

Water mill at Acorn Bank

 The working water mill at the National Trust's Acorn Bank property near Penrith was having time out for work on the mechanism. There was an interesting display explaining the history of milling. It started with a pestle and mortar before developing into hand-driven stones before animals were used  and then mills. I was interested in the idea that the first water wheels were horizontal because they drove the shaft directly. I've been thinking about how you would deploy such a wheel. If it were in the stream, surely the stream would be pushing equally on both sides of the wheel and there would be no resultant torque. If only half the wheel were in the water, how would you stop water escaping?

 Vertical mill wheels turn a horizontal axle. For this to turn a vertical axle through the millstones, beveled gear wheels are needed. The mill wheel drives the gear wheel at the back in the picture above and a beveled wheel sits against it. I wonder how much energy is lost by transferring the drive between these two wheels. However much, it must have been more efficient to do it this way.

Trebuchet rocks at Caerlaverock Castle

This sandstone trebuchet rock at Caerlaverock has a diameter of about 24cm and thus a radius of 12cm. Hence volume is about 7000 cubic centimetres. The density of sandstone is about 2.3 grams per cubic centimetre so the mass of the rock is about 16kg. I was wondering about dealing with the energy flow by using the First Law system boundaries and having either heat or work flow over the boundary. Could the boundary be drawn around the ball itself? If so, I can see work flowing in when the ball is fired, but is it possible to do this with a solid instead of a gas, and dealing with bulk energies like kinetic rather than internal energy? More thought required.

Caerlaverock Castle: quantum tunneling

Four years ago Jim Al-Khalili made a BBC4 documentary about Quantum Biology that involved filming a large red ball passing through the walls of Caerlaverock Castle. I've now been! The ball was to demonstrate the idea of quantum tunneling, when a particle can tunnel through an energy barrier that is too high for it to surmount normally. My dumbed down explanation goes like this: Heisenberg's Uncertainty Principle says that the more sure about the momentum of a particle you are, the less sure you are about the position. So as the ball approaches the wall, become very sure about the momentum and the position blurs so much that it can include the inside of the wall. The ball goes through the wall! This is all much better explained by the wave function and discussing probabilities but I got the explanation past profs the other year when speaking to Sixth Formers. The BBC programme was explaining how Quantum Mechanics speeds up photosynthesis. Here's an link http://www.bbc.co.uk/earth/story/20160715-organisms-might-be-quantum-machines

Atomzahl

I have been used to using this representation of atomic mass number A and atomic number Z for any element X. I thought that they had chosen A and Z because they are the start and the end of the Latin alphabet. But I found out today that Z is from the German word Zahl meaning "number". I am not certain but I think A is for Atomgewicht or atomic weight. A different language, a different perspective!

How far away is that Pied-billed Grebe?

We went to the remote Loch Feorlin in Argyll to find this Pied-billed Grebe from America. Last month I had worked out that the field of view in my telescope is worth 1 degree or 0.0175 rad. Last time I didn't photograph the bird. The water was calmer this time. Measuring the screen, the grebe therefore subtends 2/80 x 0.0175 = 4.36 x 10^4 rad. The grebe is about 30cm long. Angle subtended in radians = arc length/radial distance. So distance to the grebe = 0.3/4.36 x 10^4 = 690 metres. Map measurements suggest 400 metres. So at least 50% uncertainty in this method.