Half-value thickness for aluminium

First of all I measured the background count over a long integration time. I clamped a beta source to fire through aluminium into a GM tube and counter. I measured the thickness of the aluminium in several places with a micrometer screw gauge and calculated the mean. I took a reading of counts over the long integration time and subtracted the background count. I added more thicknesses of aluminium and took more data until I had enough data to plot an accurate curve. It was then possible to work out the thickness that halves the counts. It is best to do this in 3 places and find a mean. This is a thickness that halves the counts so is called the "half-value thickness" - sort of distance equivalent to half-life.

Efficiency of a wind turbine

 

Applying yesterday's wind power formula to one of the turbines at Watchtree where the swept area is 1735 square metres, I would get a power of 3514kW at a wind speed of 15m/s. Since the rated power output at that speed is 660kW, the efficiency is 660/3514 x 100 = 19%. That is a lot of energy that cannot be captured. As the wind speed goes up, the efficiency will come down because there will be more wind energy going in but the same 660kW output. The data website gives a figure called energy density. It turns out that it is the 660kW divided by the swept area. 

Wind pump at Wicken Fen

 We found this wind pump at Wicken Fen the day after Storm Eunice.

It is to pump water up to keep the fen wet.

The wind was strong so I estimated an average of 15 metres per second and worked out what mass hits the blades every second. The big assumption is that it just disappears as it hits the blades and passes out the other side rather than interfering with incoming wind.

I then stuck it into the equation for kinetic energy to give a figure for the mass delivered per second. I equated this with the potential energy equation and assumed the water was raised a metre. It assumes all wind energy goes to the mechanism which is unrealistic. At that wind speed, the maximum delivery of water per second would be 1.5 cubic metres or 1500 litres.

Do wind turbines blades all rotate at the same speed?

 

It's been incredibly windy at Watchtree but the turbines never seem to spin faster. In other words, their angular velocity seems to be the same. Is this true? There is a wonderfully detailed discussion of the topic here. It seems that once the blades are turning at the most efficient speed, they adjust the angle of the blades as the wind blows harder to keep at that speed. 

I'm on a roll: inclined plane

 

If you place a cylinder such as this chocolate roll on an inclined plane, it could get to the bottom in one of two ways: 1. It could slide down   2. It could roll down.  If you ran these two modes side by side, the one that slid would reach the bottom first. To explain why needs an energy analysis. At the top of the slope, the cylinder has gravitational potential energy and as it falls this turns into kinetic energy. The problem is that if it rolls, there are two types of kinetic energy to consider. There is the familiar linear kinetic energy based on its straight line speed and calculated by 1/2 m.v^2. But there is also the rotational kinetic energy. That is calculated by 1/2 I.omega-squared. I is the moment of inertia which has been on display at the Winter Olympics. When a skater holds her arms out wide, she spins slowly. When she pulls them in, she spins fast. Ease of motion depends on how far away the mass is so it is "moment of inertia". Omega is the angular speed in radians per second. So anyway, if the same gravitational potential energy is shared out between two types of kinetic energy, a smaller share goes to the normal linear kinetic energy so the cylinder goes down the slope slower. If the cylinder rolls it takes longer to reach the bottom than if it slides.

Bog oak at Wicken Fen: carbon dating

Trees are carbon-based lifeforms. During their life they constantly take in carbon dioxide from the air. Now some of that carbon dioxide contains a radioactive isotope carbon-14 which is made when high energy solar particles come into the atmosphere. The tree maintains a regular level of carbon-14 during its lifetime. When it dies it can no longer replace lost carbon-14. The carbon-14 starts to decay. By guessing that the level in a tree in the past would be the same as it is now, we compare to the amount in the wood dug up from the bog and work out how many half-lives have passed. For carbon-14, one half-life is 5600 years. The carbon-14 level in this one has not yet halved as it is only 4200 years old.
 

Inside a Geiger-Muller tube

 

Here is a view into one of our Geiger-Muller tubes. Note the cylindrical central anode. The window is made of a mineral called mica which has a low mass per unit area and thus allows alpha to pass relatively uninterrupted. There is low pressure gas inside - perhaps 1/10th of atmospheric pressure. When one radioactive detection occurs, it starts with the ionisation of one gas atom to make an ion-electron pair. The electrons are pulled towards the central anode, being accelerated as they go. They gain so much energy that they are able to ionise more atoms to create more electrons and so on. This electron avalanche effect produces enough to be detected.

Newton's First Law and the linear air track

 

I wanted to tell my youngest class that forces do 3 things: they change shapes of objects and change direction and speed of movement. I decided to use the linear air track for the latter two. The air track removes the friction so the glider travels at constant speed between the ends. The action of forces on the elastic bands changes the direction. I could have added that that the shape of the elastic changes. They don't know yet about hysteresis loops in the elastic but this dissipative process means that after each impact the speed visibly decreases. In between impacts, Newton's First Law applies.

What are wind turbine blades made of?

 

I had always assumed that the blades were made of low density metal like aeroplane wings. Turns out they are made of carbon fibre and are thus not recyclable. The Guardian ran an article about 5 years ago about the problems of recycling carbon fibre. See also https://www.latimes.com/business/story/2020-02-06/wind-turbine-blades

A weird dream about the thermometer

 I had a dream about the mis-calibrated thermometer. In it, I took the battery out and it worked again so I had a go.

I'm glad I did because I found some interesting stuff inside. The display is powered from the metal contacts at the top of the green board through the bendy piece that looks like a licorice all-sort - the pink thing with the black middle. It is flexible and slightly compressible so it makes good contact and I'm assuming that the black middle must be a conductor. When I put it all back together, itm was working correctly again - but a day later it went back to its old ways! Oh well...

Platinum Jubilee Hassock reminds me of Hofmann Voltameter

 

Mrs B made a Platinum Jubilee Hassock which was blessed today - an awful lot of work went into it! I knew platinum was ringing some bells - it is the platinum  electrodes. And I have used these in the Hofmann Voltameter. Platinum is used because it is so unreactive that it doesn't interfere with the reactions.

A badly calibrated thermometer

 

One of my students pointed out that this thermometer is reading below zero at normal room temperature. It is about 20 degrees Celsius too low. It has occurred to me that I would need to check it over a range of temperatures to see if the error remains the same each time so that there is a true systematic error. 

Something strange about the Watchtree turbine

 

Having said that the Watchree Vestas were 660kW, I noticed that the sticker on the new display turbine mechanism claims 1300kW and that it dates from November 2017. Questions to look into are 1. How long do the working parts of a wind turbine generator last? 2. Were the turbines upgraded or do you always fit a turbine with a higher spec on its name plate?