Applied Science question #3

 

I spotted this large solar panel on a farm from the train to Carlisle. It is not long after you leave Wigton. You can only see the back of it. It is the tilted rectangle on the pole. Assuming that the intensity of the sunlight is 1000W per square metre, calculate the number of Units of electricity generated THIS WEEK. At 12p a Unit, estimate how much money it might save them a year.

L6 estimation question #5: Fountains at Rydal Hall

 

The water follows a parabolic curve. It is an example of projectile motion. I want you to calculate the initial velocity of the water. To do that, you need to calculate the constant horizontal speed and the initial vertical speed. Combine them by Pythagoras to get the overall initial velocity.

Hint: The initial vertical speed is the same as the final vertical speed with which it hits the surface of the water, assuming no air resistance. So do the second half of the projectile motion, from the top of the curve downwards to make it like the problems we normally do. 

Polarised in Ambleside

 

These two pictures of the House on the Bridge in Ambleside were taken through my polarising sunglasses. I twisted the glasses through 90 degrees between the photographs. It shows that at the angle between me and the water, the reflected light from the water is polarised. There is little reflected sunlight from the surface of the water in the first picture but a lot in the second picture. Light is a transverse wave which means that the direction of propagation of the energy is at 90 degrees to the direction of oscillation. In other words, the waves vibrate side to side. A polarising filter is modelled as a slits through which waves have to pass. If they vibrate side to side in line with the slits, the light gets through. That's the second picture. Twisting the slits through 90 degrees means that the waves now vibrate across the slits and can't get through. Sound is a longitudinal wave: the direction of propagation of energy is in line with the direction of oscillation. It can never vibrate across the line of the slits so can never be polarised. (Please note: slits is a way of explaining. In truth, in a plastic polarising filter it is about long chain molecules absorbing waves in one direction but not at 90 degrees)

Hartlepool nuclear power station

 

This is a picture of Hartlepool nuclear power station. It works by having the nuclei of uranium atoms split when neutrons are fired at them. This process is called fission. When a nucleus splits, it releases thermal energy which heats up a material called the coolant. The coolant transfers thermal energy into water by conduction between pipes. The water boils to make steam which drives a turbine. A much advertised advantage of nuclear power is that nothing burns so no carbon dioxide or sulphur dioxide are released as chemical pollution into the air. A disadvantage is that radioactive waste is produced that will be dangerous for thousands of years. At the moment, this is sent to Sellafield to be treated and stored. This nuclear power station generates 1, 190 Megawatts of electrical power. If you were asked to compare nuclear power to wind power, they both have in common that they do not release chemical pollution into the air. I found some data that claims that there are 4366 wind turbines on land in the UK and that they generate 7,172 Megawatts of electrical power. http://www.renewableuk.com/en/renewable-energy/wind-energy/uk-wind-energy-database/index.cfm Clearly this depends on the weather and how much the wind is blowing. Just so you know, peak demand for electrical power in the UK is 60,000 Megawatts (60 Gigawatts).

Soft landing in Berlin

 

This is undercarriage from an American DC3 used in the Berlin airlift. Notice that the pole attached to the wheel is designed to go up into the grey tube above it. There will be suspension and shock absorbers. I'm not sure how the suspension is done in this case, but perusal of the Internet suggests that some modern aircraft use an airbag that compresses as the force of landing pushes the wheel up. This is like bending your knees when you jump down. It increases the time to stop which reduces the rate of change of momentum, thus decreasing the force of impact. Unless you include shock absorbers, it is likely that the suspension will spring backwards and forwards making the aeroplane wobble up and down. On a car, a shock absorber is a metal plate that gets dragged slowly through a viscous liquid. There are a lot of assumptions here. I didn't realise how little I knew about the specifics of aeroplane landing gear. The Physics is correct, though.

The closest I'll get to the Magdeburg hemispheres

 

When I realised that the coach was going past Magdeburg on the way to Berlin I got very excited. I tried to photograph the sign on the Autobahn but we were moving too quickly! So you get a picture of the outskirts of the town. It was at Magdeburg that they did a famous experiment about vacuums. They got two huge hollow steel hemispheres and put them together. The join was sealed with something airproof like Vaseline. There was water inside which was boiled. The steam was allowed out of a small hole and pushed the air out with it. The hole was sealed and the apparatus allowed to cool. The steam inside condensed to water leaving a pretty good vacuum inside. Two teams of horses couldn't pull the hemispheres apart because the high air pressure on the outside pushing in met no counter force from the vacuum. At least this is how it was told to me by my Physics teacher. Perhaps I should check that I've got all of the details correct...

Pumped storage at Loch Ness

 

The UK's coal-fired power stations take too long to get started to have them turned on and off on a regular basis. They run all the time, day and night. This is fine during the day but much less electricity is used a night. They generate power that is not used. There are several places in the country where the surplus electricity is used to pump water up hill. The water gains gravitational potential energy (mgh). The energy is stored until there is a shortage. The barriers are opened and the water flows back down hill through turbines that generate electricity again. The example photographed is on Loch Ness. The middle photograph shows the turbine shed in the distance. The water is pumped to Loch Mhor which is several miles away. The information says that there are two 150MW generators run by the turbines. It says that are peak flow, 200 tonnes of water flows every second. Use mgh to work out the gravitational potential energy lost in one second - this is the power input to the turbines. (You can get the heights by enlarging the bottom picture). Then work out the efficiency of the two turbine generators combined. (1 tonne = 1000kg. MW means Mega Watts which is 1 million Watts)

L6 estimation question #4: Cranes in Berlin

 

A large number of tower cranes is a sign of a prosperous city. Tower cranes have concrete blocks on the short end as a counter weight. Assuming they all have the same concrete load, you can estimate the weight of the concrete from the close up picture taken from my hotel window. (Look up the density of concrete and estimate the volume). Then calculate the maximum load that could be held on the far end of one of the cranes in the bottom picture without it tipping over, using the principle of moments.

Coal-fired power stations

 

This is Ferrybridge power station on the A1 in Yorkshire, as seen from the coach on the way back from Berlin. The top picture shows 8 cooling towers, which are used to make the steam from the turbines condense back into liquid water. The two tall narrow chimneys put smoke up into the air. Coal is difficult to light: have you tried lighting a coal fire? However, once it is going, it provides a massive amount of energy. We say that coal is a fuel with a high energy density. Coal-fired power stations are on all the time at full blast because of the difficulty of starting them. This means that at night the country produces more electricity than it needs. More on this later. Coal is a fossil fuel, the remains of ancient forests. The carbon in the plants was originally taken from carbon dioxide in the air and has been trapped underground for millions of years. If coal stays underground, there is less carbon dioxide in the air. If we take it out and burn it, more carbon dioxide is released into the air. The vast majority of scientists believe this will lead to global warming. Coal also contains small amounts of sulphur, which reacts with oxygen in the air when the coal is burned to make sulphur dioxide. Sulphur dioxide gas dissolves in raindrops to form acid rain. This erodes buildings and damages living things.

Why do birds stand on one leg?

 

Here is a picture of Curlews stood on one leg to sleep, with their long beaks tucked under their wings. I took the photograph on the Threave Estate. Birds have blood supplies down their legs and into their beaks. Where blood flows close to the skin, conduction will take thermal energy out to the surface where is dissipated by heat radiation and convection. The main body of the bird is covered with feathers. Air is trapped in small pockets between the feathers. Air is a poor conductor of heat because the particles in air are far apart and not joined. However air is good at convection. The small pockets of air mean that convection cannot get going. So Curlews tuck one leg and their beak into their feathers so that these parts of the body benefit from the insulation of the feathers when they sleep. The behaviour must have become widespread because of Natural Selection. Those that didn't got cold and died younger. Those that did tuck their leg and beak in lived longer, bred more often and passed their genes onto their offspring.

Third rail on the Berlin U-Bahn

 

Underground trains can't burn fuel because the fumes would poison people in a confined space. Instead they must use electric motors, but the problem is how to get a continuous electric current to a train. Above ground, overhead cables are used because they are hard to reach and so less of a danger. Underground, they use a live "third rail". You can see it as the yellow strip below the train in these pictures. I watched as the train came in and every carriage had a contact at each end that rubbed along the third rail. I looked it up - apparently it is 750V DC. Notice that it is on the side furthest from the platform for safety.

Mushroom cloud from the power station

 

We passed power station after power station around Leeds when we were on the A1 to Berlin. They are coal-fired and date from the era of intensive coal mining in the area. Now the coal is imported. They are also sited on major rivers to provide cooling water. The one pictured is on the River Trent. The picture shows evaporated water that has been used for cooling rising from a cooling tower. As it rises, it condenses in a cloud. Why the mushroom shape? It may well be that a horizontal wind was blowing at that altitude. It is unlikely, but not impossible, that there is a layer of warmer air above.

Layers of ash by Pillar Rock

 

We visited Pillar Rock using the High Level Route from Black Sail. The most exciting part is called the Shamrock Traverse, as shown in the bottom picture (best kept for a dry day). I found these rocks that are layers of volcanic ash, a reminder of the violent geological past in these parts. First notice how many layers there are. I wonder how many years these represent. Would it be in the millions? Then the banding. Different types of ash? It's a bit like tree rings except that they are not put down regularly so you can't guess the length of time. There is a great picture of the 2010 Icelandic eruption on APOD today with an explanation about why it produced so much ash. http://apod.nasa.gov/apod/astropix.html (if you are reading this tomorrow or beyond, you'll need to click on "Archive" and get the picture for 20 April 2014)

Systematic error at the secret cave in Langstrath

 

We returned to the secret cave in Langstrath. My friend has a watch with an altimeter in it. It detects air pressure, which decreases with height. The problem is that air pressure varies from day to day, sometimes changing during the day itself. The top photo shows the altimeter reading at the secret cave. We then took a reading lower down at a place that we knew from the map was about 190m. So the readings were all too high. A systematic error. It is possible to calibrate the altimeter to a known height and we should have done this on the way up. So if you want to know how high the secret cave is, you can do the maths. You're getting no other clues - it's a secret after all!

Berlin-Brandenburgische Akademie der Wissenschaften

 

I found this building in the Gendarmenmarkt on our first night in Berlin. It is the Academy of Science for the east end of Germany. There are many learned societies around the world that encourage research and conduct peer-reviews. The Royal Society of London would be an example. This group traces its line back to Gottfried Leibnitz, Isaac Newton's rival. Famous members have included Albert Einstein, Lise Meitner and Max Planck. The Akademie was affected by the political upheavals of the Twentieth Century but their website indicates that they are fully functional again.

Telling the time in Berlin - longitude

I found this wonderful device in the Technical Museum in Berlin. You move it across the globe and it tells you the time in a particular place as compared to Greenwich. As you move the arrow, the Greenwich time doesn't change. The other label says "Ortszeit". Ort means place and Zeit means time. Ortszeit is ahead of Greenwich which means the place must be east of Greenwich. The Earth rotates so that the Sun rises in the east, making noon arrive sooner there. If you can keep a Greenwich clock, you can work out your longitude. This was the famous problem in the 1700s and it was solved by the clock builder John Harrison. Do look up his story.

The Berlin Wall - crumbling concrete

 

I can hardly believe it but I have stood beside the Berlin Wall. It seemed such an impregnable structure when I was growing up. But now much of what is left is crumbling concrete. Concrete is a wonderful material but better used for speed and cost rather than lasting significance. The mixture of sand and small pebbles is held together by cement. It is really, really hard to crush. It was one of my jobs to test the ultimate compressive strength of our concrete samples during my degree. A huge force was needed. But the cement doesn't hold it together well if the forces pull or tear the concrete. That's where the concrete reinforcing rods come in. They are supposed to be buried inside the concrete to stop them rusting. In this case they would make the concrete stronger against sideways blows.

Tree rings in Ennerdale

 

This is an odd way of timing things. I love the term "dendrochronology". Apparently there is more growth in the spring so the wood is less dense and lighter. Later in the year, the opposite is true and a darker section is formed. I believe that you can tell what kind of a year it has been by the relative amounts of growth. I forgot to see if these photographs were of the same species. I suspect not because I think that the rings are wider in the bottom picture which might represent a  faster growing tree. These sorts of ideas are useful in analysing things like climate change.

Our crumple zones

 

We made crumple zones in class. The aim was to keep a marble on the trolley even after a crash. The brick wall caused the front to deform. You can argue by energy that the deformation uses up energy that would otherwise have been transferred as kinetic. But we used a momentum argument. Same mass and speed meant same change in momentum as the trolley came to a stop. But the crumpling means that it takes a longer time to stop. There is a smaller rate of change of momentum and thus a smaller force.

 

I did like the following design!

Napes Needle: Components of gravity

 

We picked our way round the Climbers' Traverse to the famous landmark of Napes Needle on Great Gable. No one was climbing it because of the horrible weather. We were out in the rain for 8 hours - not pleasant. I had been worried about the steepness of the slopes. They look as though they might be 75 degrees or something similar. However, looking at sideways photographs taken by other people suggests much less. I used my walking pole to try to gauge the slope and I'd say actually about 45 degrees. Why does it look so much bigger? It's probably to do with "distance foreshortening" but I need to think about it more. If you fall vertically, gravity makes you accelerate at a rate of 9.91 metres per second per second. But a 45 degree angle means that the acceleration would only be 9.81 x cos45 = 6.93 metres per second per second. I've heard this called "dilute gravity". And friction would reduce this further. However, that won't help if you hit a rock.

Condensation

 

Using the kettle in the hide at Threave caused problems. The hot water vapour hit the cold windows. Somehow the water vapour loses thermal energy and cools so much that it condenses back into liquid water. Is it conduction into the glass? Probably, because it works by contact. The window will then dissipate the thermal energy by conducting through and trying to heat the air outside.

Answer to the U6 estimation question #3

 

The trick is that the area of my hand doesn't matter. The flux has to pass through a metal loop so we are only interested in the flux passing through the ring itself. I used http://www.ngdc.noaa.gov/geomag-web/#igrfwmm to calculate the strength of the Earth's magnetic field for 55 degrees north and 3 degrees west. It gave me 49,623 nanoTeslas. The area through the middle of the ring through which flux can pass: well, radius is 1cm so area = 3.1 x 10^-4 square metres. Flux = field strength x area = 1.6 x 10^-8Wb. Flux linkage = flux x number of turns. There is only one turn here, so flux linkage = 1.6 x 10^-8 Wb(turns). By Faraday's Law, emf = rate of change of flux linkage. If I move my hand through 90 degrees, I go from full flux to no flux through the ring. It takes 0.1s. Hence emf = 1.6 x 10^-7V.

 

This emf makes a current flow round my ring. The resistance of my ring = (resistivity x circumference) / cross sectional area of the metal itself. Gold has a resistivity of 2.44 x 10^-8 Ohmmetres. The ring is 5mm deep by 1mm wide so cross-sectional area = 5 x 10^-6 square metres. I calculate a resistance of 3 x 10^-4 Ohms.

Current = emf/resistance so a current of 5 x 10^-4A flows. Not much to worry about there.

 

The only thing to add is that I have assumed you knew I was standing facing north, in line with the field.

Escapement in Penrith

 

I was in Penrith to ring bells and found this clock mechanism inside the front door of the church. I blogged about escapement mechanisms earlier in the year and got a good chance to inspect one here. In the top picture, there is a curved piece of metal above the top brass cog. It is attached the pendulum. What happens is that you wind up the clock. The place where you attach the winding handle is apparent in the bottom photograph (it wasn't clear whether you are winding a spring or winding up a weight but you give the mechanism some form of potential energy). This then drives the top brass cog round. The cog locks with the escapement mechanism, the curved piece of metal. This momentarily stops the cog, but then the cog pushes the curved piece out of the way and in so doing pushes on the pendulum. The pendulum then swings back and catches the cog on the other side. The process repeats. A pendulum would naturally stop swinging after a while but the mechanism is a way of taking the potential energy and giving it to the pendulum as extra kinetic energy. So the clock drives the pendulum. I'd always thought that it was the other way round. So what's the point in the pendulum? Well, by catching on the cog wheel all the time and momentarily stopping it, it forces the cog wheel to keep to the speed of the pendulum. So the pendulum regulates the speed at which the cog wheel turns and hence keeps it in time if the hands are attached to the cog. The tick and the tock are when the escapement mechanism hits the cog wheel to stop it.

Life in the flatlands - Goole

 

We went to the flatlands near Goole in East Yorkshire. It is very different to north Cumbria. Not just flat, but intensive arable farming. The visibility wasn't very good. It was a murky day. I wondered how far you could see. The furthest pylons in the distance were about 1 little finger width high - so about 1 degree. The usual calculation, based on the fact that a pylon is about 45 metres high, suggests they might just be 3km away. That' not very far considering that I could see a mountain 50 miles away in Scotland last week. Next time I visit I shall hope for better visibility and repeat the exercise.