Convection at Christmas

This decoration clearly works by convection. The candles heat the air, which expands, becomes less dense than the surrounding cold air and floats upwards. It was pointed out to me that more the condles burn down the faster the rotor turns. One hypothesis was that the wick is bigger on a burned down candle so there is a bigger flame and more thermal energy fuelling the convection. This could be tested by taking part burned candles and propping them up to the height of the unburned candles at the start. If the hypothesis is true then the blade should turn faster. Another hypothesis is that the same thermal energy is released but that the extra distance means the resultant force onn the hot air due to the density differences is able to accelerate the air to a higher speed, The air will thus have more momentum and thus a greater rate of change of momentum on hitting the blades. In other words, a bigger force on the blades so a greater torque and faster turning.

Less effort at Coniston Hall

I was looking at the ramp up to the big doorway on this wonderful old building. Work has to be done to move an object. Work done = force x distance moved, with the force acting along the line of the distance measurement. Lifting things up to the doorway is work done against gravity. The height is about 2.5 metres. If you push things up the ramp, they end up at the doors just the same, so the same work must have been done against gravity. But you will have moved a bigger distance so the force needed will be smaller. Ramps reduce the effort required - although accounting for friction, slightly more work will end up being done.

Auto-exposure in Coniston

I took these two photographs in exactly the same place at the same time. The camera was on an automatically adjusyed exposure time, The sky was much brighter than the foreground, In the top picture, the camera muat have sensed the darkness and gone for a longer exposure time, That meant that too much light arrived from the sunlit snow covered mountains in the distance. They merged with the sky. Pointing at the brighter sky gave a shorter exposure time and the mountains became visible. I need to look up how the light is read and then used to adjust exposure time.

Pomanders and elliptical geometry

I have decided to try to get through Roger Penrose's 1000 page epic The Road To Reality at a few pages a day over the next year. I have been reading about non-Euclidean geometry. Euclid was a Greek genius who wrote down the rules for shapes drawn on a flat page. You'll be familiar with the idea that the angles in a triangle add up to 180 degrees. This Christmas I made a pomander decoration. It involves shoving cloves into an orange. They were used centuries ago when it was believed that bad smells caused disease. They thought the nice smell of the cloves would keep them from catching contagious diseases. Doh! But look at the triangle below. The two yellow ribbons cross at 90 degrees at the top. Each yellow ribbon crosses the central red ribbon at 90 degrees. So the triangle has three angles adding up to 270 degrees. The normal rules don't apply on a curved surface like a sphere. This is important when studying the Universe because Einstein showed that space-time is a surface that is curved by the gravity.

Optic fibre Christmas Tree

I was interested in how a tree I saw produced the different colours at the tips of the branches. I know it uses optic fibres to bring the light up from below but assumed that it used LEDs. I was wrong.

It's actually a patterned colour filter disc that has a halogen lamp shining through it from below. The core of the tree is then an optic fibre bundle shown below that fans out to make the branches. 

Looking at the International Space Station

We were tipped off that it would be possible to see the International Space Station last night so were able to spot it. It was a white dot moving steadily across the southern sky. You can get an app to show you where to look. We used two websites: http://iss.astroviewer.net/ and http://space.channel4.com/tracker/ The latter site was most interesting and we were amazed to find out that when we last caught sight of the ISS it was actually above Italy. Just shows how far you can see if something is high enough up. Off to look for a comet underneath Orion tonight!

NORAD Santa Tracker

A favourite end of term activity with Physics teachers at this time of year is to get classes to calculate how fast Santa would have to go to deliver all the presents in one night. The idea is to show how many laws of Physics would have to be broken. Those of you who don't believe might want to follow Santa's progress tonight on the North American air defence radar system http://www.noradsanta.org/  They've been following him since 1958. It is s system normally used to track enemy missiles!

More about sundials

I went away and did some geometry about sundials. The top picture shows why the angle of the gnomon to the horizontal must be the angle of latitude L. The idea is that we are on a slant because of the curvature of the Earth's surface and the angle makes sure that the sloping surface of the gnomon is upright as regards the Sun. It is perpendicular to the Equator. This means that on the Radley church sundial, which is vertical in orientation, the latitude angle of 51 degrees is from the top down, not from the wall up. The cardboard sundial came from Jodrell Bank. The hour lines are equally spaced. They are 15 degrees apart because the Sun moves 360 degrees in 24 hours. 360/24 = 15 degrees. It got me thinking about a sundial on the Equator where the angle of latitude is zero. I was thinking about a stick sundial. I think that in the situation shown in the top diagram, the shadow would not go in a circle - I think that it would go as a line along the Equator. All this neglects that the axis of the Earth is tilted by 23 degrees away from the vertical. I will need to think more about how this affects things.

Almost the shortest day in Radley

Radley is a village just south of Oxford. Its church is very old. Part of it was destroyed in a battle in the Civil War. I'm not sure how old the sundial is but I suspect it's been through the Winter Solstice a few times. 

If you enlarge the photograph you will see that the shadow on the left hand (west facing) dial is 3.45pm. Notice that the lines are not evenly spaced. 

I've blogged about sundials before. Every time I read about them I discover that they are more complicated than I expected. This type of sundial has a slanted shadow stick (gnomon). I think the angle is fixed by the latitude of the place. In this case, Radley is 51 degrees North of the Equator. I was interested in the west facing sundial which has a gnomon clear of the wall. Is the gnomon to the same angle? I need to take some measurements next time I go. I also need to remember to see if sundials in the south really do have a different angle to those up here in the north. Also notice that the hour lines are not evenly spaced.

Interesting ice crystals

These interesting ice crystals were on the car roof the other morning. They look like fractal patterns. I don't really know where to start on an analysis but will note the conditions on similar occasions.

Insulated in Grange

I spotted these appartments being built in Grange over Sands. They had fitted what appeared to be in the innermost walls. Note that the outside surface is silver. This will be to reduce the emission of infra-red heat radiation. There will be another wall built outside it. It is thus not unlike a vacuum flask, except that there will be no vacuum between the layers!

Symmetry breaking in Wigton bell tower

In the bell tower, we hang the ropes from a device that lowers from the ceiling. It is then pulled up again to get the ropes safely out of the way. Ours is a lovely carved wooden bell but it is often called a spider because it hangs from the ceiling and has 8 legs. When we have finished ringing and before we hang the ropes, it is empty, as shown below:

I have been blogging about symmetry recently and at this point there is perfect symmetry. It will look the same from every side. Any of us could hang our rope anywhere. But someone is always first...

Now I have no choice about where to hang my rope because they are always hung in order from the lightest to the heaviest. There is now only one hook on which I can hang my rope. When no ropes are hung, I could choose any of the 8 hooks and it would make no difference. That's the symmetry. Once one rope is hung, I have to choose one particular hook to make sure the order is correct. This would be what physicists call "symmetry breaking". A particular mystery in Physics is the fact that the Universe is made almost entirely of matter with very little antimatter. It is not symmetric in this regard. It is believed that the Universe began with symmetry, so what caused the symmetry breaking?

Symmetry in space means conservation of momentum

Following the lecture on the Higg's Boson a couple of weeks ago, I've been working on trying to understand Noether's Theorem that shows that any symmetry in physics results in a conservation law. I was given a clue that I might need to look into some harder maths so I've been working on Lagrange and Hamilton's formulations of mechanics. I have an outline understanding. But here's a mere illustration of what we might mean by symmetry in space or translational symmetry. My class did an experiment this week mixing hydrochloric acid with sodium hydroxide to make sodium chloride and water.

I took photographs in different parts of the room but they all looked the same because it doesn't matter where in the space the experiment is done - you get the same results. Translation mathematically means moving something around in a given space. With the experiment, a translation to a different part of the room affected nothing. That's a symmetry - you get the same everywhere. Noether's Theorem shows that this is equivalent to saying that there is conservation of momentum. I almost understand some of the mathematics involved but will spare you at the moment in case I get it wrong.

Measuring using Pepper's Ghost

I was using Helmholtz coils to bend an electron beam into a circle. You can see the curve of the beam within the top of the Helmholtz coils. I wanted to measure the diameter of the beam but it was inside the glass bulb and there was no ruler scale inside the tube. So I put a sheet of glass outside the tube. 

 Then I set up a ruler and illuminated it with a lamp. There was a partial reflection in the glass so the ruler appeared to be inside the glass bulb. The great thing about the glass is that you can see through it as well as seeing reflections in it. This is the source of the Victorian music hall special effect called Pepper's Ghost. It is important that the ruler be the same distance in front of the glass as the glass is distant from the centre of the bulb. That's because a reflection is always the same distance behind the mirror as the object is in front of the mirror.

Here's a clearer picture of the electron beam, bent into a circular path by the uniform magnetic field.

Jim Al-Khalili Quantum Physics programme on the iplayer

Jim Al-Khalili had a nice programme on BBC4 last night explaining some of the peculiar aspects of Quantum Physics. It will be on the iplayer until next Tuesday. http://www.bbc.co.uk/programmes/b04tr9x9

Refraction or diffraction at Saltholme?

I was watching the waves bend round the end of the island at Saltholme RSPB reserve. The strong wind was pushing the waves from top left to bottom right in the picture. When they reached the right hand tip of the island (roughly in the middle of the photograph) they bent right round the tip. That sounds like diffraction. But actually I think it was refraction. Waves slow down and change direction if they are incident obliquely on a different medium. And they were hitting shallower water. That makes them slow down. I think they were hitting it an angle so they changed direction as well. In the end, I noticed that the waves got closer together, thus having a smaller wavelength. The frequency must remain the same so it is clear evidence of slowing down from the wave equation: wave speed = frequency x wavelength. So it was refraction not diffraction this time.

Vulcan bombers and the speed of sound

I went looking for a Black Redstart. It turned out to be under this Vulcan bomber on display at Carlisle Airport! I'd always thought that Vulcans were supersonic but the data I've found suggests not. I've seen a top speed quoted as 645mph. This is 287 metres per second. I teach the speed of sound as being 330 metres per second. But then I remembered that the speed of sound varies with temperature. And surely it must also vary with pressure since it must be harder to transmit the vibration when the particles are more thinly spread. So I found this: http://en.wikipedia.org/wiki/File:Comparison_US_standard_atmosphere_1962.svg The Vulcan bomber got up to about 15km max so the speed of sound would be down to 295 metres per second at that altitude. Still sadly not low enough for supersonic flight.

Wigton lights: an ISO experiment

Above are the Wigton lights on ISO 100.

Now it is ISO 200.

Finally ISO 400.

If you double the ISO, you double the sensitivity to light. Hence you need half the light to take the same picture. They say that means the exposure time is less. I am certain that the exposure time was longer on ISO 400. It may be that some of my other choices meant that it wasn't a fair test (I had it on a night setting which must surely give a longer exposure). One article I read said that increased light sensitivity on a digital camera just means amplifying the signal more. Hence the noise is amplified as well and the picture isn't as sharp. That's certainly true. They also say that noise affects smaller pixels more. My cheap camera is small so the pixels on my CCD won't be very big. I'm beginning to get the hang of it but still more work needed.

ISO 400: In the moonlight on Ling Fell

We climbed Ling Fell by moonlight - no torches needed this time. I was trying to get better shots than last week on my very cheap camera. This week I went for the lightest image I could select on the exposure setting and then tried ISO 400. I don't actually know anything about ISO so some work to be done here but we thought that it might make it better. The result is the view of Cockermouth above. ISO alters the sensitivity of the image to light. I was hoping that more sensitivity might mean I'd pick up more light. I'm not sure it works like that because they say it makes the image more blurry. So I've got an excuse for more experiments.

Physik im Advent

You should look at this wonderful series in the run up to Christmas. http://www.physik-im-advent.de/ The German Physical Society are posting a short video clip of a fun experiment every day. They ask a question and post the solution the next day. You don't need great German to follow what's going on. I shall be trying some of the experiments myself.

Upside down Moon in Australia

Here's Grasmoor with the Moon on Sunday afternoon. During the walk I was asked how this could be the same Moon that is seen in Australia or New Zealand. I know that it has to be but that it will not be visible to them at the same time that it is visible to us. The rotation of the Earth brings us past the Moon and away again, then bringing them past the Moon. So I emailed friends in Sydney and in New Zealand asking for photographs. I got a surprise this afternoon looking at the photographs. If you enlarge my photograph, you'll notice that the right hand side is lit. It's a half Moon. By the time I received the photographs, the phase had moved on to 3/4 Moon, but look carefully at the picture below from Sydney and you'll notice that it is the left hand side that is lit up, not the right. So from Australia the Moon does appear to be upside down. Wow! There'll be more on this when I've done some thinking.

Bird-on-a-wire potentials

Last night I heard a wonderful lecture by Dr Harald Fox from Lancaster University. He was explaining the need for the Higgs Boson. He started with Noether's Theorem. Emmy Noether was a brilliant mathematician who proved that if you have a symmetry in nature, then you will have a conservation law. I'm beginning to get my head round this so there will be a some posts about it to help me to understand it. One example of a symmetry is that of electromagnetic potential. He described it as a "bird-on-a-wire" potential so I was very pleased to spot this bird this morning. Normally they perch on the very top wire, which is the earth wire and has no current or potential. This bird was perched on one of the lower wires. Judging by the number of insulators, I'd say the lines would be at least 10,000V. So why isn't the bird hurt? The answer is because both legs are at 10,000V. You need a potential DIFFERENCE to get a current to flow. As long as the bird only touches wires at that potential, there is no difference and the bird is safe. If we transferred the bird to a higher voltage line, say 425,000V, then the same thing would apply and the bird would still be safe. Provided there is no difference in the voltage (potential) for each leg, then the bird will be safe wherever. That's what we call a SYMMETRY. You can change the condition but get the same result. The overall situation looks the same although we have changed one condition. So we have a symmetry with electromagnetic potential (voltage). There must be a conservation law connected with it. In this case, it is conservation of CHARGE. And that's what we check when we are looking at particle interaction equations to see if they will work.

Drying the homework

I had an accident and my water bottle leaked onto the homework. I have dried it out and it has now been marked. But consider this method of drying on a radiator. I was taught that radiators are badly named and that they work principally by convection. This is true. If you hold your hand above a radiator you can feel the warm air rising. So why would you hang things next to a radiator? Try holding your hand a couple of centimetres from the side surface. You can feel warmth. That will be infra-red thermal radiation. White is said to be a bad emitter of radiation (remember that white reflects all the colours) but the point is that it is a bad emitter of visible wavelengths. It does emit quite well at infra-red wavelengths, so the homework dried. See the previous post about Leslie's Cube for more information http://wigtonphysics.blogspot.co.uk/2014/09/leslies-cube-and-why-my-physics-teacher.html

Hypothesising on Blake Fell

When we were driving down to Loweswater, Blake Fell was clear. When we arrived, the mist had settled high on the sunny side of the fell. It was a still day and got me thinking. My hypothesis is that the rising sun started to increase the evaporation on the sunny side which increased the humidity. That then took the amount of water vapour in the air above the amount needed for saturation at that temperature. Then it cleared at lunchtime, probably because the air temperature had risen and was no longer at the saturation level.

We looked across to Grasmoor in the afternoon. There was a cloud stubbornly lingering in the high corrie to the right of the summit. It stayed there all afternoon. So I came up with a hypothesis that the lack of wind inside the corrie would allow the humidity to remain high enough by not shifting the water vapour. The horizontal wisp of cloud half way up the cliffs was another interesting feature. It also persisted at exactly that level. Could that be to do with the temperature decreasing as you go up to be low enough for saturation at that altitude? I'm not sure how true all of this is but I have had a great time coming up with theories and thinking about them.