Monday, 9 February 2015

The Great Circle - Flights to America

 We climbed up to High Cup Nick in the Pennines, Here's the view looking south onto a cloud inversion around the Howgills. can you spot the vapour trail in the middle of the picture? It's a truism in these parts that these planes are going to America because the shortest route is up and over. It's called the Great Circle. I got out my atlas and traced out the route from London to San Francisco - see below. On the flat map it would go west over Bristol.
 But then I got my globe out. On a curved suface, the shortest route will be different. It's easy to do by pulling a string tight between two points as shown below for the same route.  A Great Circle is drawn between two points on the surface of the sphere and is part of a continuous circle round the globe centred on the middle of the Earth. It's like an orbit in that regard.

                                       
 In close up, it does indeed go up and over Cumbria.
I used this popular website to test my theory http://www.flightradar24.com/ but I found that rather a lot of the flights over Cumbria are actually to Glasgow! There must be more of those than flights to LA. The globe showed me that the quickest way to New York is actually out over Bristol.

Sunday, 8 February 2015

Skiddaw by moonlight

We climbed up to the Watches above Bassenthwaite by moonlight and I took this lovely picture of Skiddaw. Well, I could see Skiddaw clearly but it hasn't appeared in the photograph. You can see the tip of my ice axe reflecting the moonlight. The CCD pixels in my camera are not as sensitive to light as the rod cells in my eyes. Rod cells are found round the edges of your eyes and cannot detect colour. The pigment in them is depleted in bright light but regenerates when it goes dark - hence the dark adapted eye. A rod cell can detect a single photon of light which makes it up to 100 times more sensitive than the cone cells in the middle of your retina. Also, more than one rod cell is connected to the same nerve fibre so it can amplify the signal. This does reduce the resolution of the image. They also record photons for a longer time - it takes about 0.2 seconds to build up an image. This makes the picture seem brighter but makes it harder to see very sudden movements. Being around the edge of your retina, it explains why the path seems bright until you look down at it directly.

Saturday, 7 February 2015

Measuring tyre pressure

I was sorting out the pressure on my van tyres. Pressure is out of fashion as a topic in school Physics at the moment. Pressure is force per unit area, and thus it would be measured in Newtons per square metre.
 The reading above is in the old Imperial units of pounds per square inch. They are not really dimensionally correct as units because pounds is a measure of mass not force. But it does give a good mental picture of what's happening. That's about 30 bags of sugar balanced on a square inch - say on the area of a couple of 2p pieces.
 Bar as a unit of pressure was introduced just over 100 years ago. 1 bar is roughly atmospheric pressure. 1 bar = 1000 millibars so air pressure in weather forecast is often given in millibars. A low pressure system might have a pressure of 980 mb, so not much below normal atmospheric pressure. My tyres were 4 1/4 times atmospheric pressure.
 And finally to proper Physics units. KiloPascals. 1 Pa is 1 Newton per square metre. As you can work out, 1 bar = 100,000 Pa.
 

Friday, 6 February 2015

An experiment involving Fleming's Left Hand Rule


As it happens, today we did an experiment which can be explained in part by Fleming's Left Hand Rule. We clamped a wire to the table and tensioned it with masses hanging over the edge of the table. We wired it up so that alternating current was flowing through the wire. The wire passed between the poles of a strong magnet. Hence we had UVW from yesterday's post - cause, connection and effect. The current is the cause, the magnetic field the connection and the force (movement) is the effect. The current keeps changing direction but the magnetic field is fixed. Hence the force also alternates and the wire oscillates. If the frequency of oscillation is such that half a wavelength fits between the two wooden wedges, you get a "one loop" stationary wave - the fundamental mode. Changing the mass affects the tension in the wire and thus how easily it can vibrate. Hence the length of the stationary wave loop changes.

Thursday, 5 February 2015

3-Finger-Regel (UVW-Regel)

I was given this wonderful mug with Physics equations on it. I was interested in Fleming's Left Hand Rule. The problem is that it is actually the RIGHT hand. In England, we use the right hand for the generator rule. The left hand is called the motor rule because it is about putting a current in and getting movement out. This is definitely the same rule because of the UVW mnemonic. Ursache is the cause and Wirkung is the effect. Technische Strom is conventional current which goes into the motor, so it is the cause. Kraft is the force - the effect. Richtung means the direction and, if you were wondering, Vermittlung can be translated as "connection". Here's the way I use Fleming's Left Hand Rule:
All that has happened is that the German rule swaps force with current and if you use right hand instead of left, magnetic field will point in the same direction.

Wednesday, 4 February 2015

Sugar thermometer - making marmalade for Dalemain

Mrs B was making marmalade for a competition at the Dalemain Marmalade Festival http://www.dalemainmarmaladeawards.co.uk/ She was using a specialist "sugar thermometer" because the sugary liquid boils at well above 100 degrees Celsius. We don't tend to use mercury thermometers anymore. Digital is the order of the day. These old-fashioned ones work by having a liquid like mercury inside a narrow capillary tube. As the liquid is heated it expands and the only place it can go is up the tube. If you look at the scale you will see that the expansion is linear. The scale on the right is Celsius and that on the right is in Fahrenheit. We tend to teach that the precision is the smallest scale division - in this case + or - 2 degrees Celsius. But most physicists argue that it should be half that because you can tell where you are in the gap. We could increase the precision by making the tube narrower because there would be the same volumetric expansion with a smaller cross-sectional area. This would make the scale divisions wider and often the chance to fill in finer scale division lines. A scale like this has to be calibrated first. It is normal to fix 0 degrees Celsius with melting ice/water mixture and 100 degrees Celsius with boiling water. But only the latter appears on this scale so I wonder what they use for the second point.

Tuesday, 3 February 2015

A question of balance

 Below is a picture of an old-fashioned amplifier that I received as an 18th birthday present! This article is about the balance control on the right hand side.
An exam question we did recently related to the balance control on a stereo. In the days before ipods, there used to be chunky bits of equipment that sat in the corner of the room connected to two different loudspeakers. It was called stereo because they record different tracks, one for each speaker. This continues, of course, but you'll notice it as different tracks to left and right headphones. The problem was that if you sat in one part of the room, you'd be closer to the right speaker than the left and so its track would be louder. The balance control allows you to turn up the volume of one whilst turning down the volume of the other. The exam question concerned the wiring. Look at my top diagram. Both speakers are controlled by individual variable resistors. Hence you can turn each speaker up or down individually. But you'd need two control knobs. The second circuit with a single potentiometer shows how it is actually wired. I've written on the potential differences assuming it is a linear potentiometer. You only need one control knob.