Back to looking at the Covid numbers part 1

Last week's New Scientist magazine had an update on the Covid mutations and on page 11 gave some data that can help me to complete the mathematical model I developed last June. My equationn below calculates the number of new cases from the number of old cases No based on 2 factors

• The R number
• The time that has elasped
• A mysterious factor T I had to put in which is the time it takes from a person getting the virus to them having spread it to the next group.

I had always thought it was around 7 days but New Scientist said that if there were 10000 caes with an R number of 1.1, then a month later there would be 16000 cases. I work in days, so I have used 30 days for a month and I now get T=6.4 days.

 

Universal Indicator

 

There are two things that make Universal Indicator paper better than litmus paper

1. You only need one bit of paper instead of two.

2. It not only tells you whether the substance is acid or alkali; it also tells you whether it is a weak acid or a strong acid.

Here are what 3 of the substances I tested looked like when I used Universal Indicator liquid instead of paper. But what are A, B and C?

Lunar corona and aureole

 

Alto-cumulus cloud tonight is producing a clear corona around the Moon. The central bright section is called the aureole and I often see that nut tonight I could pick out the "pastel colour" rings around the outside. https://en.wikipedia.org/wiki/Corona_(optical_phenomenon) says this is a diffraction effect rather than refraction for the halos. Not quite a Circle Round the Moon but I can recommend Cearcall mun Ghealaich which is number 11 here. Geat poem and great song.

Frozen equipotentials

 

We were interested in these ledges of ice overhanging the stream. It appears that there must have been some freezing when the water level was higher a few days ago and now the water level has gone down, leaving the ice suspended. It makes a nice illustration of a gravitational equipotential surface above the water.

How big is humongous?

I have posted a lot about the units for measuring. We received these wonderful marshmallows for Christmas and it makes clear on the front that they are large in a wonderfully tongue-in-cheek way. But in Physics, you also have to specify how big using accepted units of measurement so that sizes can be understood everywhere. Hence it says 400 grams on the back!
 

Using litmus indicator paper

 

I think litmus indicator paper is a nuisance because you need two bits of paper to tell whether a substance is acid, alkali or neutral. In my photo, the top paper of each paper started red each time and the bottom paper started blue. 

A substance is an acid if red litmus STAYS red and blue litmus TURNS red.

A substance is an alkali if red litmus TURNS blue and blue litmus STAYS blue.

A neutral substance, safe like water makes red litmus stay red and blue litmus stay blue.

Ahn odd thing was the toothpaste. I was taught that toothpaste was a very weak alkali. It looks neutral here. A brief bit of Internet research suggests that toothpaste can range from very weak acid, through neutral to very weak alkali. It depends on what you buy.

Is this why the snow was so powdery?

 

Look at the photograph of the graveyard outside St Mary's. You can see the perfect outline of every grave. That's unusual. To me, it was evidence that when the snow fell there was no snow. Usually it is blown around and piles up in different places. Here it seemed to be equal depth everywhere. The "snow on the ground" section of this webpage says that strong wind breaks up the snow crystals allowing them to pack more closely and so be more dense. The lack of wind will be the reason that the snow was so powdery.

What does snow melt do to the air temperature?

 

All of this snow in Wigton melted a week ago. I wondered what it does to the air temperature. When H2O changes from solid to liquid, energy is need to break the bonds. Thermal energy can be used to either raise the temperature of a chemical or to change the state, but it can't do both at the same time. So whilst the snow is turning from solid to liquid, it will be taking in thermal energy without the temperature of the snow changing. I have been assuming that the thermal energy comes from the surrounding air, so the mere process of melting should take thermal energy from the air so its temperature should fall, in the same way your hand feels cold when you grasp metal because of the conduction of thermal energy away from the hand. But I did find this which makes an interesting point about sublimation of snow using energy from the Sun. Under the new stores and pathways model, thermal energy from the air would pass to the snow by the "heating by particles" pathway and solar heating would be the "heating by radiation" pathway. The sublimation wouldn't result in a depressed air temperature.

I failed with a snowball slingshot

 

I was sent this link when it had snowed in Wigton. As it happened, I did have an empty bottle and a balloon here so I hurried out to try it. Sadly, it didn't work. Two main problems - the balloons were too small and the snow was very difficult. This snow was a very fine powder. It was like trying to roll a ball out of icing sugar. I tried to improvise by filling the balloon with air.

Sadly that didn't work either and the cold seemed to perish the rubber.

Since the snow has melted and balloons are definitely a non-essential item, I'll have to wait a while to see if I can get it working properly, but the set of experiments on the website looks very helpful.

Can PE with Joe make the world move?

 

The return of PE with Joe has been the best thing this week. He's had the best part of 100000 live streams and when we were all jumping in the air together, I was reminded of the question I have often been asked about whether everyone on planet Earth jumped in the air at the same time and in the same place, would they make the Earth move? I think I can just about manage to jump 50cm into the air doing a tuck jump (he was calling them moon jumps this morning!) From this I can use suvat to calculate my speed when I hit the ground using the equations of uniformly accelerated motion. I'm going to use v^2 = u^2 + 2as. I start falling from the top of my jump when my vertical speed u=0. Acceleration a = 10m/s/s giving the velocity v with which I hit the ground as 3m/s. Now imagine all 7.6 billion of us doing that. Say the average mass is 60kg. Total momentum = 7600000000 x 60 x 3 = 1.4 x 10^12 kgm/s. Suppose we all stop dead and all of that momentum transfers to the Earth. Mass of Earth = 6 x 10^24kg. That gives the Earth a speed of 0.00000000000002m/s In other words, the Earth won't move.

Year 12 Components questions

 

                                        

Year 9 gravitational potential and kinetic energy experiment

 In this experiment, we are going to lift up a pen so that it has gravitational potential energy and let it roll down a ramp, gaining kinetic energy. When the pen rolls onto the carpet, the force of friction will do mechanical work on the pen and dissipate its kinetic energy. Mechanical work = force x distance moved. We will assume that the friction force is the same each time for the same pen on the same carpet, so if the pen rolls a longer distance, the pen must have had more kinetic energy to dissipate in the first place.

If we double the height of the ramp, the pen will start off with twice as much gravitational potential energy. My hypothesis is that it will therefore have twice as much kinetic energy at the bottom of the ramp and therefore roll twice as far.

So I'm prediciting: double the height of the ramp, double the distance the pen rolls on the carpet. This would mean a straight line through the origin graph - that pattern on a graph is called directly proportional.

1. Prop your science book or something similar up to the height given in the results table. We are going to be deliberately changing the height so that is the independent variable.

The independent variable is the one that you can write into the results table before you start. The independent variable is usually on the left hand side of the results table.

 2. Hold a pen about 0.5 cm above the top of your book ramp and gently drop it onto the ramp.

 3. It will roll down the ramp. Try to get it to roll straight. If it rolls off to one side, do it again.

 4. Let it roll onto the floor - carpet is best. Measure how far it goes from the bottom of your book until it stops.

5. Repeat 3 times for each height of the ramp.

6. Calculate the mean by doing (1st go + 2nd go + 3rd go) = then divide 3 =

Always write the mean to the same number of decimal places as the readings.

7. You also need to be aware that the RANGE of the repeat readings for each height is (biggest repeat - smallest repeat)
and that there is a thing called the uncertainty = 1/2 x range of repeats

Warming stripes

 

We got this buff to support our efforts to walk 1000 miles this year. This was the first I'd heard of the warming stripes graphic. Each stripe represents a year, with the top stripe being 2019. A baseline average temperature was set, I think from 1971 to 2000, and the colours represent fluctuations above or below that mean. Red means above and blue below. The graphic shows that things generally were colder and are now getting warmer. It is explained here and you can get a more geographically specific version from https://showyourstripes.info/

Measuring a corona round the Sun

 

There was a corona around the Sun on Saturday made clearer by polarising lenses. To the eye it was clearly yellow and red around the outside. The Sun subtends 0.5 degrees and thus would be covered by my little finger. This picture shows that the central section would subtend about 2 degrees. That doesn't seem too bad on my bright centre. My image will be overexposed. Perhaps I was seeing more of the outer rings.

Quantum shuffling day 5

 

After 100 moves, I think that is enought for this week. It's shown me the mechanics of it - I think next week I need to record the frequency of the different microstates and see if I can get it to tie in with theory.

Day 4 of quantum shuffling

 

Today I almost ended up with them all on Level 1 again at one point. Then it occurred to me that the reason this hasn't happened - and I am now 80 moves in - is because it is actually an improbable situation. 

Day 3 of quantum shuffling

 

Another two rolls of the dice got me to this situation - so 42 legitimate rolls in total. Then I got stuck with a lot of disallowed rolls because it would only work if the green die came up 4. It was strangely stable in a way that I can't see being true in nature. At the end today, after 60 allowed rolls in total, I got to this

Second day of quantum shuffling

 

This is where I got to after 40 allowed moves. Today was mostly shuffling of pairs between level 1 and the ground state.

The quantum energy level shuffling experiment again

 Last May I had a short look at an old experiment from the Nuffield A Level Physics course that investigated quantum shuffling of particles on energy levels. More exciting things were happening and I didn't get far with it. We won't be going very far for a while so ....

The green squares are the particles and they all sit on energy level 1 at the start. Thus there are only 6 quanta of energy to share out. If one loses a quantum, another can gain. To choose randomly which, there are two dice. The blue decides which goes up and the green decides which goes down. Last time I had problems if the one to go down started in the ground state, level 0. This time I decided to rethrow both dice if such a forbidden move came up. It's proving tedious with a lot of rethrows. After 20 legal throws, here's what emerged.

Hayeswater Aqueduct and Boredale Hause - a possible explanation

 Our exploration of Boredale revealed that a pipeline extends all the way down to Penrith.

These covers are near the top.

The pipeline is obvious in the scree filled gully.

The pipeline must go under the path.

A bit of Internet research shows that Hayeswater was dammed in 1908 to provide water for Penrith. A filter house was built later below Hayeswater https://thefilterhouse.co.uk/history I had got it into my head that an aqueduct needed to be always heading downhill so I was expecting some sort of tunel through the hillside but an inspection of the original Wainwright Far Eastern guide showed that the aqueduct went down through the filter house into the valley at Hartsop and then back up the slanting path from Dubhow to Boredale Hause (this is not shown in the later editions that I now prefer) - see Angletarn Pikes page 4. I checked on the maps. Boredale Hause is 399m above sealevel but crucially Hayeswater is about 420m. If you put water into a u-tube it should flow down and then back up to its original height. Here it doesn't have to flow up as far so will be able to go over Boredale Hause and back down to Penrith. The aqeuduct is actually a pipeline. When I can get back into the lab, I intend to build a model.

Get a grip!

 

Running on icy surfaces is not much fun but it was possible with these pull-on studs. They dramatically reduce the surface area on which my weight acts. Pressure = force/area so same weight on smaller area means increased pressure. More pressure means more damage - the studs go into the ice and give me something to push against. I know that with ice skates, the pressure is enough to melt the ice. I wonder if that happens with these studs, and if so, how would I tell?

Eddy formation

 

I was interested in the number of eddies being formed on the stream at Patterdale. It is clear that they were forming where a fast layer of water down the middle of the stream made contact with a stationary layer at the side of the stream. There must be shear forces involved. So far the best that I can find is that the process is associated with turbulent flow and a high Reynold's number but I was hoping to find out how the forces operated to pull the water first backwards and then round into the right direction.