Is this a ratio?

 

I've always held with the idea that physicists use division as ratio; well, as a way of trying to explain to classes that it doesn't have to have a colun in the middle to be a ratio. But I found myself writing that resistance is the ratio of potential difference to current. Is this a ratio? A bit of chasing references on the Internet suggests that mathematicians would want a ratio to be unitless ie both quantities to be divided would have the same units as in the turns ratio for a transformer. That is not the case here. However there is support for the idea that it is a ratio at http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmlaw.html which encourages me that it is an acceptable usage in physics.

Amending my Covid model

 

The R number is definitely falling in the UK. Using my model, I think it might have fallen to 0.7 this week. Last week I was wondering how to incorporate this fall into my model. I used data I had from earlier in the month and modelled the far in R as linear. I think this might be unrealistic. It puts R to zero after 150 days but has it down to 1 case in the entire UK in about 40 days. I will have to think about how to refine it.

Microstates 3

This was quite a complicated one for working out the microstates. I hope I've got it right.

I started by doing Level 2 as 123, 124, 125, 126, then 134, 135, 136, because anything with 2 in it would repeat, then 145, 146, finally 156 which is 10 cominations all containing particle 1 on Level 1.

Now I needed to do the combinations that didn't have particle 1 in them.

Start 234, 235, 236, then 245, 246, then 256. Next 345, 346, 356 Finally 456. That gives a grand total of 20. I've instinctively missed out many combinations as being repeats of earlier ones (number order doesn't matter here) but I hope I've not been careless.

Microstates 2

 This is my third possible overall pattern or macrostate to investigate.

Here are two further possible versions of it:

It can easily be seen that with particle 1 on Level 5, there will be 5 microstates possible, corresponding to 2, 3, 4, 5 and then 6 on Level 1. It retains a total of 6 quanta throughout. By putting 2, 3, 4, 5 and then 6 on Level 5 in turn, it gives a total of 30 possible microstates for this macrostate.

The same applies to this other macrostate:

Microstates and macrostates

 I have been working on my energy level analysis following the wording I got from a set of lecture notes I was given. We started with 6 particles on Level 1

I understand that this would be a macrostate. All six particles are on this one level and there is no other way to achieve this state. There are six quanta of energy.

Here's a second macrostate. It is possibe to have one particle on Level 6 and the rest on Level 0. There are still six quanta of energy.

But this time is is possible to have different numbered particles as the one on Level 6, for example:

These are wqhat I am taking to be microstates, different ways of ordering the same particles into the same larger overall pattern. There will be 6 microstates for this macrostate.

Why are metals shiny?

 The gilded cross on the top of the horse fountain was catching the light. I realised I'd never really thought about why metal reflect. Obviously they must absorb and reemit the photons that come towards them, but why shiny rather than dull. Even dull white surfaces are reflecting something - though that is diffuse reflection. I was interested in these answers https://www.quora.com/Why-are-metals-shinier-and-more-lustrous-than-non-metal-elements especially the one that links it to the layer of metal oxide. But I am also wondering if it is because the layers in the metal allow for a smoother surface and thus more specular reflection - the firing of the photons back in a more unified direction.

A ghost shadow

 

I spotted a strange white shadow in a field. It is longer than the current dark shadow. My best guess is that it was sunny earlier in the day for long enough to melt the frost in the field except where the shadow was at that time. Then the sun went in so that the unmelted strip remained white long enough for me to arrive.

Evaluating a value for the density of water

 

I put my empty jug on the scales. The resolution of the digital scale is +- 0.5 grams because another half a gram would tip it over to 76 grams. 

I added 100ml of water. This is the same as 100 cubic centimetres. The resolution of the scale is one scale division and the bottom of the meniscus should be sat on the line. So I have 100+-25cm^3 which has a 25% uncertainty. Very high.

I put the jug on the scales again. To find the mass of the water, I have to subtract the mass of the jug. 164 - 75 = 89 grams. Now when I am ADDING OR SUBTRACTING amounts, I always ADD the +- uncertainty, which is called the ABSOLUTE UNCERTAINTY (not percentage uncertainty). It was 164+-0.5grams and 75+-0.5grams, so the result is a mass of water which is 89+-1gram. 

The percentage uncertainty of the mass is 1/89 x 100 = 1.1%

To calculate the density I do mass/volume = 89/100 = 0.89 grams per cubic centrimetre.

When I MULTIPY or DIVIDE, I always ADD %U.

%U for mass + %U for volume = 1.1 + 25 = 26% (2sf)

Now 26% of 0.89 = 0.23 so I can write that my value for the density of water is 0.89+-0.23g/cm^3.

The true value for the density of water is 1g/cm^3, which lies within the uncertainty of my measurement.

I repeated the experiment with a larger volume:

This time I got 0.98+-0.05 grams per cubic centimetre. This shows that by measuring larger amounts with the same equipment, we reduce the percentage uncertainties and thus the final absolute uncertainty.

YOU NEED TO SHOW HOW I WORKED OUT THIS LAST RESULT FROM THE READINGS IN THE PHOTOGRAPHS!

Makling Covid predictions

 

Having calculated the R number as 0,85, I put my numbers into my model. The last week in January, the ONS said the prevalence of Covid in England was 1 in 65. Last June was the start of our coming out of lockdown and in June 2020 the rate was roughly 1 in 1000. My calculation above shows that unless the R number falls, we'll be waiting a long time until 1 in 1000 this year.

Calculating the current R number

 

Using my T=6.4 days from last week's post in my equation along with Office for National Statistics data from the last two weeks when the incidence in the population fell from 1 in 55 to 1 in 65, I get R=0.85. The official range this week is between 0.7 and 1. My number is half way so I'm guessing that the range must be the uncertainty added in.

Avoiding zero error

 Here is a picture of the gap between the ruoler and the scale on the wall. This gap can cause parallax error. I need to make sure that the top of the ruler is lined up with the bottom of the scale on the wall. The gap causes a problem - how do I know I am looking at it from the correct angle?

I got my special bendy ruler and set the angle to 90 degrees.

                                                  

I set it at 90 degrees to the top of the ruler and across to the wall. Then I could make sure they were in line. I'd have used a set square if I had on.

If the top of the ruler was accidentally 1cm below the bottom of the scale on the wall, every single reading would be 1cm too low. The zero on the wall scale would be in the wrong place - called a ZERO ERROR. Every reading would now be wrong for the same reason by the same amount - this is called a SYSTEMATIC ERROR.

Scale division and resolution

 

The picture shows a whole series of lines that are diving up a scale. The lines on a ruler that divide up the readings are called SCALE DIVISIONS. One gap tells you the smallest possible non-zero reading you can take. This is called the RESOLUTION. On the ruler, the scale divisions are 1mm apart on the left hand side, so the resolution is 1mm on the left hand side. On the right hand side, the scale divisions are 1cm apart so the resolution is 1cm. The scale on the wall also has a resolution of 1cm.

Parallax error

 These 3 pictures were all taken of the ruler and the wall scale I used when I was firing eleastic bands into the air. I didn't move the ruler at all - I just changed the angle I was looking at it. If I look at it from a bad angle, I will get bad readings. This problem is called parallax error. The problem is caused by the gap between the ruler and the wall. To solve the problem, we have to find ways to make sure we are looking at things from the correct angle, which is 90 degrees to the scale.