Hit it or heat it or how to keep the coldest fridge cold

We drove past Lancaster University on the M6. The Physics labs are behind the trees on the left and perhaps 100m from the motorway at the closest point. All this traffic causes problems.

Remember the wobble cube:

The temperature is a measure of the kinetic energy of the vibrating particles. There are two ways to make them vibrate more: add thermal energy or hit them. Technically the latter is called "doing work". This is a very rough statement of the First Law of Thermodynamics: you can raise the temperature of something if you hit it or heat it. All that traffic on the motorway is wobbling the environment and rattling the particles in the coldest fridge in the world. This would raise the temperature of the contents. The solution is to have the whole fridge floating on an air suspension. You really can push the huge concrete structure with one hand! Here's the view underneath

Also the windows and walls are lined with metal to repel unwanted electromagnetic waves like radio waves or mobile signals, because these also have energy that they can give to the particles to make them wobble more. In the coldest place in the Universe, there should be no wobble.

 

Phases of the Moon or eclipsed in Southport?

This is a piece of public art on the seafront in Southport. It certainly looks like the phases of the Moon, an idea supported by the sculpture on top of the pole above it.

But these discs on the other side cannot be phases of the Moo. They can only be the start of a solar eclipse when the shadow of the Moon starts to move across the Sun.

Art being art, you can do what you want. Perhaps the idea is that we show we are clever by understanding when the artist has chosen to twist reality....

Low pressure in Stonehaven

We arrived in Stonehaven on the day of one of the biggest storms of the year - the one that obliterated various walking routes in the Cairngorms. We found the plaque on the wall of the old town hall down by the harbour. I love the idea of a public barometer, though there was no evidence of it. The storms that lash Britain are the result of areas of low pressure in the atmosphere. So it wouldn't be good to go out to sea in low pressure, unless you had to. Hence the need for a fishing port to have a public barometer in the days before satellite weather forecasts, I looked up how low pressure areas form in the atmosphere. In some places like deserts it is because extra thermal energy from the Sun causes the air to expand, become less dense and rise, In other places, it is said to be due to the divergence of winds. In other words, streams of air from the same place end up going in different directions. This pulls the air in that place apart. Fewer molecules left behind means fewer collisions and so less pressure. My research on the Internet suggests that it happens because of shear forces caused by the rotation of the Earth. Shear forces are tearing forces. The spin of the Earth causes tear on the air. It all has to spin at the same rotational speed but that means the air nearer the poles will have a lower linear speed. I need to relearn Coriolis forces and find out more about Rossby waves to get a full understanding of all this.

But it was ironic that there was a yacht called Pascal in the harbour given the unites for pressure ... 

7 hours a day on XBox??

We found the Eco Centre in Southport. It contains displays with information about energy uses and consequences. I love having data to ponder. As such, the display above is wonderful. The pale green colour is for games console usage. I have to say that I know nothing about that at all. It's just not me. Too old! So I poked around on the Internet. XBox 360 seems to claim a 203Watt power supply. The pale green section of the graph might be 250 kWh per year. 250 divided by 0.2kW gives 1250 hours per year. That's 7 hours per day. I suppose it depends on how many people are using games consoles in one house, The display suggested that standby was to blame, I can't find a precise figure for that but found games consoles rated between 3W and 15W on standby. 15W would give about half of the annual usage suggested if the console was left on 24-7. In financial terms, if 1kWh is about 10p, then the total cost would be £25 per year.

Cast iron - my brittle knowledge

This is the view from the end of Southport Pier looking towards Blackpool. You might spot Blackpool Tower if you magnify the picture but you might also notice that the pillar tells you that it is made of cast iron. I thought I knew about cast iron but my knowledge has turned out to be somewhat brittle, It turns out that cast iron has more carbon in it than steel. For years I've been thinking that it was purer because it was called iron. In a perfectly pure metal, the layers of atoms can slide over each other easily. The introduction of carbon molecules makes this harder because they are a different size to the iron atoms and disrupt the lattice, making the movement harder. The higher the carbon content, the more the layers are locked together. Steel is ductile. This means that there is some give in the metal before it breaks, in the same way that a Mars Bar loses its perfect shape and narrows as you pull on it. That distortion gives us a warning that it is going to break. The extra carbon in cast iron means that there is no give before it breaks. It snaps like a Rich Tea biscuit would. We say that it is brittle. I know this, having smashed an old cast iron gutter by clouting it with a hammer. It broke like glass. I'm sure that I was taught correctly about the carbon content of cast iron. I wonder at what point I lost that bit of information?

Getting stressed on Southport Pier

I was looking at Southport Pier and trying to estimate the stress in one of the support pillars. I'd say that the sets of pillars were about 15 metres apart. Let's say the iron work had a width of 1cm and if the lattice spaces were taken into account, had a depth of 30cm. The volume of iron would be 0.045 cubic metres. Let's estimate the density of iron as 8000 kg per cubic metre. That gives a mass of iron held up by one pillar as 400kg to 1sf. On each set, the pillars are about 2 metres apart. Let's estimate the depth of the wooden deck as 5cm. The volume of wood would be 1.5 cubic metres. If the wood were able to float I could estimate it's density as 800 kg per cubic metre, giving a mass of 1200 kg. So let's say 1600kg is held up by one pillar. Pillars have a diameter of about 15cm. I'm going to assume that they are hollow and the iron is 2cm thick. This gives an area of cross-section as 0.008 square metres. Stress = force x cross-sectional area = 1600x10/0.008 = 2 million Newtons per square metre. The iron is in compression - it will take a much larger stress to break it than in tension, And then there's the tram that goes over periodically. Say that is 10 tonnes. The load will be spread over at least 4 pillars, giving at most an extra 2500kg per pillar but will more than double the stress.

The coldest place in the universe

This is the inside of a fridge at Lancaster University that is sometimes the coldest place in the universe when it is working. The very cold bit is actually a small pot at the bottom of the structure hanging from the ceiling. The temperature is a small fraction of a degree above absolute zero, zero Kelvin. This is -273 degrees Celsius. I explained absolute zero to my class using this model

It has been branded the "Wobble Cube"! I use it as a more accurate than normal representation of a solid: atoms are joined and in a regular pattern but are free to move. Temperature is a measure of the amount of "atom wobble": the more they are wobbling, the higher the temperature. Absolute zero is when they stop wobbling altogether. You can't get "negative wobble" so that's the coldest possible temperature. Celsius is a wonderfully human temperature scale: I experience ice and boiling water every day. But it's limitation is the need for negative temperatures. -273 degrees Celsius exists but -274 degrees Celsius is as real as a unicorn! You can say it but that doesn't make it real.

Half life of a tub of chocolates

With my birthday coming up, I left a box of chocolates in the staff room. Following a suggestion that the removal of the chocolates would be exponential, I had the tub weighed at regular intervals during the day.

I then plotted Ln(mass) against time in hours working on the assumption that the equation would be something like M=M0exp(-lambda.t). It's a much better straight line than I expected. I had thought that because break and lunchtime would be heavy on consumption, the graph would be distorted.

The gradient is -0.2332 /hr. The -gradient is the decay constant lambda. Now half life = Ln2/lambda = Ln2/0.2332 = 3 hours to 1 sf. Look at the graph below. It's not a bad fit.

 

 

Link to Sixth Form Institute of Physics membership

If you are in the Sixth Form and are interested in free membership of the Institute of Physics, here's the link http://www.iop.org/education/student/youth_membership/page_41684.html It explains the benefits. If you are considering Physics in the future or are just interested, it's a good thing. You get a free electronic copy of Physics World - and if you want a paper copy you can borrow mine.

Newton's Cradle on my desk

Here's how it works: The left hand ball (let's call it A) has momentum. When it hits the ball second from the left (let's call it B), then B exerts a force on A to stop it. That force must be acting to the left. By Newton's Third Law, an equal and opposite force from A must then act on B. I was brought up to call this a reaction force. The reaction force pushes B to the right but C applies a force on it to stop it moving. A reaction force from B onto C pushes C forwards. And so on until E stops D moving. The reaction force from D onto E has nothing to stop it. E has a resultant force on it and off it goes.

Malham Cove as a concave mirror

The amazing concave shape of Malham and the overhang meant that when we stood below the climbers at the bottom of Malham Cove, we could hear a lot of what's being said. It's not perfect. There will be no clear focal point. So we would say that as a mirror for sound it suffers from spherical aberration. It would have needed to be parabolic to work perfectly and I don't think melt water from glaciers does that to order.

What was wrong with the last post

I have realised that I was using the equation for water flow in an enclosed pipe to calculate the Reynolds' number. Problem is that in the photograph, the water was clearly falling through the air. The viscous drag on the outsides of the column will therefore be reduced. I can't easily find an equation for this situation but I did find a short film covering this topic https://www.youtube.com/watch?v=VoBc60iUq2I

Onset of turbulence in my kitchen

I followed up yesterday's turbulence post with an experiment in my kitchen. Look at the top picture. The dribble out of the tap is clear and see-through in the top part of the picture. That means laminar flow. Half way down, the stream turns white. That's because it has become turbulent and is reflecting light. The Reynold's number must have passed 2000 half way down. I'm guessing because the water has accelerated by falling and the extra speed has tipped it over 2000. So how fast is it going? I put a measuring jug underneath and collected water for a minute. The double line in the jug is because of the meniscus so we need the lower line. It looks like 105 ml. The scale divisions are 25ml apart but they are wide so it is easy to work out steps between them. I'd say the precision is more like +/- 5ml. So I can say that there was 1.8 ml per second, given to only 2 sig figs because the % uncertainty in the reading is 4%. Volume flow rate = cross-sectional area x speed. Diameter = 2mm so cross-sectional area is about 3 x 10^-6 square metres. This gives speed = 0.6 metres per second. Speed where? I'm not sure since all of the mass has definitely made it regardless of acceleration. It might be speed in the pipe but the pipe is wider than the dribble of water. Anyway, Reynold's number turns out to be about 1 using these numbers, so definitely not turbulent. Working backwards from 2000 would give a speed of over 1000 metres per second for onset of turbulence if my calculations are right. So I've either miscalculated or some of the assumptions about diameter are wrong.

Turbulence and Glenridding Hydro

I've been interested in doing some calculations of the flow rates through the system to try to estimate the input energy into the generators. I was able to estimate the efficiency of the Loch Ness scheme but I've been thinking about this in a different way. I estimate a 120m fall. Loss of gravitational potential energy means gain in kinetic energy means 1/2 mv^2=mgh so vsquared = 2gh and v=49 metres per second. That's over 100mph. Clearly not true. There are serious frictional losses in the system. There is some excellent information about flow rates in pipes on this website http://www.johnhearfield.com/Water/Water_in_pipes.htm but he points out that the lovely equation only works for laminar flow. If the water is turbulent, it doesn't work. We assess whether or not it is turbulent by using Reynold's number. Re=speed x diameter /hydraulic viscosity. I'd estimate the diameter at 0.3m. Hydraulic density is about 0.0013 at that water temperature. So Re = 11000 (2sf). Turbulence starts above 2000. Now I'm stuck.

A wonderful piece of old equipment

The ball bearings represent gas particles and are fired around by a motor-driven plate bouncing a piece of rubber glove up and down. The ball bearings move at varying speeds. It would be interesting to see a Maxwell-Boltzmann type curve for them. In a gas, the average velocity is zero because there are as many negative velocities as positive. So we have to use root mean square (rms) as a sensible average. Each molecule hits the polystyrene at the top. There is an impulse force. This keeps the polystyrene up. Unlike ideal gases, the collisions involving the ball bearings cannot be elastic.

Return to Glenridding Hydro

Having photographed the upper catchment for the hydro-electric plant in February, imagine my surprise when I found that the generator down in the valley was next to the toilet block on the campsite I was staying on at Gillside Farm. Here are the notices on the door:

We walked up to the catchment pool at the top. From the map, I think that there is a 120m drop between the upper pool and the generator. It is said by sources I have found to be a 1.7km pipeline. It starts with the blue section on the left of the photograph but I couldn't find any other evidence of it near the generator hall. But I did find the outflow back into the river just below the generator.

It's nearly 3 decades since I studied fluid mechanics. I have been trying to figure out how to calculate the likely fluid flow rate in the pipe but the equations are hard. I hope to post more about this later. However, I did find some very interesting data on Capacity Factor. http://www.variablepitch.co.uk/stations/288/output/ It's interesting that the best it can manage over a month is to produce 50% of its theoretical maximum output. In other words, saying that it is 500kW is one thing but it can seldom operate at that power. It also clearly varies with the rainfall. It is so unobtrusive that it seems an excellent use of resources. It says it is not attached to the National Grid but I can only imagine that the houses are attached to make up for any shortfall when water levels are low.

Upper Sixth Estimation Question #4

What is the maximum tension in one of the ropes holding up this swing as I go backwards and forwards? Make sensible estimates and show your workings.

Ear defenders and decibels

We got some ear defenders for use when operating the chain saw, here modelled by Mrs B's koala bear.

 

They came with a leaflet outlining their performance. I was interested that it is broken down by frequency. The table uses the word "attenuation". This means the reduction in the amplitude of a wave. Decibels is a logarithmic scale. The way it works is that if you ADD 10dB, you MULTIPLY the power output by 10. Logarithmic scales are non-linear so if you remove 3dB, you halve the power output. Now this doesn't necessarily mean that you have the perceived volume because of the way in which ears work. I have read that to halve perceived volume, you need to lose 10dB. I know from experiments that I have conducted that 4000 Hz is the most sensitive frequency for my ear. Notice that the attenuation is greatest at this end of the spectrum. Bearing in mind what I've read, I think that at that end of the spectrum, the volume might be 10% of normal. I need to think of a way to test it (and then actually try it!)

Fractal edge on Broom Fell

Here's a view from Lord's Seat back across to Broom Fell. Look at the ragged lower edge of the cloud. It's an example of a fractal pattern. Think of 3 dimensions - up/down, backwards/forwards side-to-side. So 2 dimensions is essentially a very flat piece of paper. And 1 dimension is a perfectly thin line. But fractals are "fractional dimensions". So the line of the bottom of the cloud fills space more than a line does but less than a piece of paper does. It will have a dimension between 1 and 2. Fractals are a bit more complicated than this basic outline but that's the gist. The idea is that details repeat at smaller and smaller scales making a very complicated shape made of simple building blocks.

Angular momentum on the beach at Glen Brittle

Not me this time, although I enjoyed the sunshine on the beach at Glen Brittle on Skye in the summer. If you haven't seen the Danny Macaskill film where he cycles along the Cuillin Ridge, you really need to treat yourself. It's only 7 minutes long.  http://www.youtube.com/watch?v=xQ_IQS3VKjA After 6 minutes, he perfects a somersault onto the beach. The front wheel of the bike pivots against the fence. A force from the fence acts on the wheel to stop it. But that force is not inline with the upper half of his body, so that can't be stopped. It's momentum keeps his upper half moving forward. He's pivoted so it becomes angular momentum. I'll need to think about how he goes from having no angular momentum to some angular momentum. It must be due to an external torque acting (ie the fence). The angular momentum keeps him spinning until another external force acts - this time the beach. I ought to suggest that you don't try this at home!

The Physics of a twisted ankle

I went over on my ankle on the Corridor Route. Fortunately no damage was done but it made me think. The rock made me put my foot down at an angle. The line of action of the force as shown by the red arrow on the photograph was outside the base area of my foot. This created a resultant moment with the edge of my boot as the pivot. The twisting motion wasn't good for my ligaments and tendons. I was hurrying to catch up at the time so the rate of change of momentum for each footfall was bigger with a bigger resultant force. Hence a bigger resultant moment and more damage. Moral of the story is for me to avoid hurrying and watch where I put my feet!

A Yorkshire moment in Malham

The flags of Yorkshire and England flying outside the pub in Malham. The flagpole is an example of a cantilever - a beam sticking out horizontally with one end fixed. The beam itself will have weight - if it is uniform this is modelled as all existing at its centre of mass half way along. Then the weight of the flag will add to that. These weights will pull downwards on the flagpole and try to turn it anti-clockwise around the fixed point. So we would say that there was an anti-clockwise moment - an anti-clockwise turning force. But nothing is turning so the support on the wall must provide an equal and opposite clockwise moment. The size of this equal and opposite clockwise moment will depend on whether there is a flag on the pole so it must be self-adjusting, which is quite clever. There will also be sideways forces when the wind is blowing, producing moments in a horizontal plane. Again there will be equal and opposite moments at the wall.

Mobile phone cell overload on Scafell Pike

There were rather a lot of people on top of Scafell Pike when we went. Lots of them were calling people on their mobile phones to tell of friends about their triumph. I tried to text someone. My phone repeatedly lost signal. I am convinced that the network cell was overloaded. This has happened after disasters in cities. I need to re-learn the uses of the word "bandwidth". When I was at university it meant the difference between the highest and lowest frequency used when a signal is transmitted. But these days it is also used to mean data transfer rate. I have not yet worked out which is the best usage of the word with mobile phones. More research needed!

Supernumerary rainbow over Scholars Green

Look at the underside of this rainbow. There are some other colours in two smaller bows. These are called supernumerary rainbows. They are formed by interference not by refraction. As a light wave bends to go into a small water droplet, some wavefronts go a longer distance through the drop that others because of the rounded edges of the drop. In other words, if the drop curves away from that part of the wave, the wavefront travels further. This puts wavefronts out of phase with each other resulting in constructive and destructive interference. This is a good A Level topic but it is the only way to explain these extra bits of the rainbow. See http://www.atoptics.co.uk/rainbows/supform.htm and http://www.atoptics.co.uk/rainbows/supdrsz.htm for more information. Apparently smaller drops are better and the supernumerary bows are often better nearer the top of the rainbow because smaller raindrops are found there.

Return to Haweswater and Mardale: what's it like on the bottom of a reservoir?

We were tempted back because the TV had said that the village had reappeared. Compare these photographs to those I posted in August and you'll see that the water has only fallen another couple of metres. It will take a fall of up to 10m more to see the village. So we walked down the lane.

Notice that this stream is still in its old stream bed. It has had a channel built under the wall and it still goes under the bridge on the lane. This shows that conditions must be quite sedate at the bottom of the reservoir. There can be no strong currents because surely they would obliterate features like this. There was a reasonable layer of mud but deposition was not too bad considering that it has had 80 years to build up. So I've learned something about hydrodynamics.

The church and the main bridge in the centre of Mardale are still underwater to the left of the islands. More walls have appeared on the near shore since August. I now think that the island is probably a roche moutonee. A "sheep rock" is formed when a glacier flows over harder rock. Here the glacier would have gone left to right. That smoothed the left hand side but pulled chunks out of the right hand side leaving it craggy.