The volume of steel in my pan

                                          

It occurred to me to reverse Archimedes' famous process. Since I know the mass of my pan and can look up the density of stainless steel which varies slightly but is about 7850 kg per cubic metre. That's the same as 7.85 grams per cubic centimetre. Volume = mass/density so the volume of metal in my pan is 1293/7.85 = 164 cubic centimetres. That would be a cube of steel about 5cm on each side - quite a lot.

Pressure and breathing

 We have this model of the thorax in a human body. The balloons represent the lungs. The glass jar would be where the ribs are.

Underneath there is a rubber sheet which represents the thorax.

When you pull the sheet down, you make the space bigger which lowers the pressure inside the glass jar. The air pressure outside is now bigger than the pressure inside the jar, so air forces its way in filling up the lungs. Pushing up on the diaphragm reduces the volume of the thorax, increasing the pressure. The outside air pressure hasn't changed but now finds it is at at lower pressure than the pressure in the thorax. This means that air is pushed out of the lungs.

Coefficient of Friction on Bowscale Fell

 

We dropped off the end of the east ridge of Bowscale Fell. The ridge itself is a splendid high level walk and easy underfoot. The drop into Mungrisdale would be easier up than down.

I experimented with foot placement. Digging in a heel didn't work. Although the pressure would be higher, the torque as I moved forward meant that it was impossible to stay on the heel. The whole foot rotated.

I then started placing my foot down parallel to the slope. I was carefully to come down normal to the surface. Friction force = coefficient of friction x normal force so I hoped to maximise the friction to avoid sliding. Done slowly, it seemed to work.

Making a compass

I placed a magnet on a large floating cork. No matter which way it was twisted, it always oscillated until the same end started pointing north. That means that it is the north-seeking pole of the magnet. Our magnets have a dent in the side to indicate that end. Another time I'd need to see if the oscillations are a damped simple harmonic motion.

Plotting a magnetic field

 Take one plotting compass and put it near a magnet. Draw an arrow on the paper to show the direction that it points.

Repeat this at many points around the magnet.

Join up the arrows to form flux lines.

The lines come out of the North pole and go in to the South pole.

A new motor effect experiment

 

When I say "new experiment" I mean it's the first time I've used it with my classes but it came from the Nuffield O Level course and I've known about it for years. I had foil strips folded double and then bent up to the loose between the poles of a pair of magnadur magnets. When connected to 2V the foil was either pushed up or pushed down depending on the direction of the current.

Later I noticed that if the force was pushing the foil up and I pushed down with my finger, I could feel the force. I could let it spring up and down.

Investigating force components

In this experiment, mass hangers were tied to both ends of a piece of string and then hung over clamp rods. In the middle, a third mass hanger was added. Graph paper was held behind the string and the set up was drawn so that the angles could be measured. It is clear that although 5.9N and 4.9N are pulling upwards on the string, you can't just simply add them because the sum needs to add up to 6.9N or else there would be a resultant force upwards. So we need to take components. Vertically the total is 5.9sin(40) + 4.9sin(31) = 6.3N. It does not equal 6.9N because there is some friction on the rods that provides the other 0.6N. The percentage difference between the measured total and the actual total = 8.7%.

Litt's Memorial on High Seat: parallel plates

 

We found a reference in Wainwright's Guide to this memorial to a man who was following the Blencathra Foxhounds in 1880. https://en.wikipedia.org/wiki/High_Seat_(Lake_District)#Litt's_Memorial I'd seen pictures on the Internet and was expecting something like two gateposts because no idea of scale was given. They were much smaller than expected being only knee high. They were much further down the hill than expected, being just over the top of the steep valley of the stream that separates from Raven Crag. 

The unusual set up reminded me of the parallel plates of a capacitor. The equation for capacitance is 

With air between, Er = 1. The plates were exactly 2 metres apart. The stones were 60cm by 25cm. That means that were they metal and isolated, they would have a capacitance of 0.67 picoFarads.

More optical coronae at church

 

Steamed up glasses with a face mask is becoming an everyday occurence. This week's photograph shows better the full corona colours on the more distant lights but not on the closest. Next time I need to consider whether that is due to different parts of my lenses having different sizes of droplet.

Reflection in Lambfoot Dub: angle subtended

 

Lambfoot Dub is a beautiful pool on the side of Great End. It was like a mirror.

It gave me the chance to test an idea I'd been thinking about recently. Presumably the angle subtended at the eye by the object should be the same as the angle subtended by the reflection. I used my favourite finger measuring trick to find out.

It's true.

A vector on the Corpse Road

 

A vector is an important concept in Physics. Quantities that have both magnitude and direction are usually depicted by arrows. This vector made of stones shows where the old Corpse Road between Wasdale and Eskdale branches off from the route up Illgill Head. It's an important vector. I've taken the wrong turning on at least two occasions. We then found the vector below showing the way up Piers Ghyll

A piano that plays itself

 

My friend has a pianola piano, otherwise known as a player piano. It's a piano that plays music without your fingers touching the keys. It dates from early last century when recorded music wasn't good and allowed people to hear recorded music played live on an instrument in their own home. The music is recorded onto paper rolls with holes in them. The pianola has pedals that you push up and down to work a motor to wind the roll through and to operate a pump that blows air at the paper. Where there is a hole the air can get through to operate a mechanism that presses the key. The history of development is fascinating https://en.wikipedia.org/wiki/Player_piano To see a photograph of the internal workings of the Steck pianola see https://en.wikipedia.org/wiki/Steck_(piano) These days they can work from computer MIDI files. One of my favourites is Olafur Arnalds https://www.youtube.com/watch?v=TpO_8tk6yNQ About four minutes in you'll see what it looks like.

Looking at the Covid data again

 

I stopped looking at the Covid data a few weeks ago when it became clear that there were problems in the data. Anyone who had once had Covid but recovered and later died of something else was included. Now it only includes those who died within 28 days of a diagnosis. I have added one more point for this weeks 7-day rolling average and I have added a new line in red. It looks like It does rather follow the original trend for the natural logarithm. The anomalies now look like being caused by the lack of a cut off date.

Decommisioning Brent Alpha

 On the left of the photograph is the oil platform Brent Alpha being decommisioned at Hartlepool. I have always wondered about how oil rigs are supported. It turns out that this one was built up on a tower from the seabed because the sea is only 140 metres deep at that point. This website has a film about what they decided to do https://www.shell.co.uk/sustainability/decommissioning/brent-field-decommissioning/jacket.html So in Hartlepool they are only recycing the top section. Here is some more information about that oilfield  https://en.wikipedia.org/wiki/Brent_oilfield 

This page lists the different ways of supporting a rig  https://en.wikipedia.org/wiki/Oil_platform#Fixed_platforms

Force Crag Mine: another fluid dynamics problem

 

I watched the flow carefully through this section at Force Crag Mine.

The water in the middle seems to ride over the top of what is underneath. Then you can see its waves fanning out to the sides, looking a little like diffraction from a point source. I then watched a weak flo backwards along the edges. Inspection of the ramp shows that it is deeper at A so a greater mass of liquid can flow at that point than at the edge B. This explains the V-shaped flow pattern.

A strange ball that wouldn't move

 

At the foot of the right hand outflow pipe, there is an inflatable beach ball. The water was flowing fast from behind it and you'd think it should push the ball forwards but in the minutes that I watched it, the ball stayed where it was. This must mean that at the surface of the water, there must be a force backwards on the ball. It's a long time since I studied fluid dynamics. I wonder if there is something to do with Newton's Third Law going on, that when the incoming water pushes forwards on the main stream, the main stream pushes backwards on the incoming flow. 

A pipeline of nitrogen

I was wondering why there was a nitrogen pipeline at Seal Sands. Then I found this https://www.rigzone.com/training/insight.asp?insight_id=329&c_id=  Seal Sands is the heart of petrochemical works and nitrogen is in an inert gas in that it doesn't react at the temperatures and pressures involved. The nitrogen is safe to use because it won't explode so can be used to flush out pipes and pressure check. The article explains how it is made.

Diffraction corona due to Covid

 Face coverings are causing steamed-up glasses and the tiny particles of water are enough to cause diffraction of light. This is causing a diffraction corona around white lights when I look at them. You can tell that it is diffraction because red is outermost and violet on the inside (my photo has only got red and yellow - I couldn't manage to get a photo of exactly what I saw. With a diffraction grating, n.lambda = d.sin(theta) so larger wavelength red light is spread to a bigger angle. The implication is that it happens with tiny droplets but bigger droplets would produce Mie scattering and then give a white image. This article is brilliant http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/corfog.html#c1 but I suspect I will have plenty of time through the Winter to try to recreate the situations it describes.

Class 2 Lever at the mouth of the Nene

 

This gate is by the lighthouse that Peter Scott lived in during the 1930s and which was the inspiration for The Snow Goose by Paul Gallico. There is a twin lighthouse on the far bank. The gate is worked by a long arm. The effort is applied to the top and the load is the force of the compression spring holding the bolt in place. It is a Class 2 lever because the load is between the pivot and the effort. By the Principle of Moments, Effort x d2 = Load x d1. Since d2 is roughly twice d1, the effort is roughly half the force you'd need to apply to pull the bolt directly.

Cathodic protection anode

                

We found this at Seal Sands on Teeside. A lot of pipe lines run through the area. It turns out that it is a sacrificial metal anode that is more reactive than the metal in the pipeline. It is set up to make the pipeline the cathode (negative terminal) of an electrochemical cell. Metals make positive ions so they would tend to join the negative cathode. That means ions would tend to leave the anode. The anode would therefore corrode and the cathode would remain intact. It turns out that for pipelines, a power supply has to be used to maintain the system. The sign says 13A. https://en.wikipedia.org/wiki/Cathodic_protection

Clock time

A great article in New Scientist last week coincided with a trip to Saltholme and an encounter with the rabbit from Alice in Wonderland. The article says that we invented clock time based on the rotation of the Earth. This is not constant and unchanging. Sixty five years ago a clock was invented that used the frequency of a particular types of light as a "pendulum" and this led to the redefinition of the second. New and better clocks allow the second to be measured with greater precision. This should allow for testing of physics theories with even greater precision. For example it would allow further tests to see whether gravitational and inertial masses are really the same.

 

How far is two metres?

 

The rule has been two metres for social distancing in the UK. There have been many attempts to explain to people just how far this is. Here is a lovely example from Hartlepool. One issue in the UK is that the generation above me were taught in feet and inches so have no natural feel for metres. Even younger people seem to measure height in feet.