Radial field on Brae Fell

 On the summit of Brae Fell, obvious paths leave in a radial pattern. There were more behind me. This is true on the grassy summits like this and Mungrisdale Common.

Lower down these radial paths up and down the fell are crossed by sheep tracks that follow the contours.

It reminded me of a radial field patterns. The paths up and down the fell would be the field lines and the sheep tracks would be the equipotentials.

An experiment with components of force

 

I recently rediscovered this practical from the old Nuffield course. The angled force T can be said to be made up of a horizontal component H and a vertical component V. A little trigonometry will show that for horizontal equilibrium, Tsin(theta) = F and for vertical equilibrium Tcos(theta) = W. We worked on the latter and plotted cos(theta) on the y-axis against 1/T on the x-axis. It's not easy to get clean data to get a straight line but the gradient = W and can be checked against the true value.

Marie Curie film

                                            

We didn't get to see the film at the cinema because it came out just as Covid was closing in but it is now out on DVD. I liked the film. It's strength is that it gives Marie Curie a character. Who knows if there take is really accurate but it makes me think that I know her better. One key point for me was the amount of physical experimentation in the labs. The book I'm reading about particle physics at the moment posits that things are going wrong because this is no longer possible. It inspired me to go away and look up the other Nobel laureates. I'm amazed that I haven't heard of many of them.

Latest on corona coronas

 

I noticed several things about the coronas through steamed up glasses this morning but only one of them photographed. The side lights in church produced the same spiky corona as the lights in the Youth Hostel. Photographing exactly what I see is proving problematic. The colour rings look like zig-zag circles with spiky edges sticking out of the circles.

Thinking about slopes on Mungrisdale Common

 We climbed Mungrisdale Common by the Bob Graham route. The slope starts very steep by starts to level off much higher up as you can see.

We would normally call that a convex slope. I was modelling it in my head on the way up as the graph for the square root of positive numbers. f(x) = x^1/2 for x>0. I was differentiating it in the my head. First derivative gives the gradient f '(x) = 1/2x^-1/2 which gives a bigger number for smaller x. Second derivative tells us about the way the gradient changes f ''(x) = -1/4x^-3/2. This will always be negative showing that the gradient is levelling off. However it seems that mathematicians call it a concave function https://en.wikipedia.org/wiki/Concave_function 

The apothecaries' system

 

The display in the Ambleside chemist opened a big can of worms for me. I now understand why we needed an SI system of measurement. https://en.wikipedia.org/wiki/Apothecaries%27_system explains that different professions used to use different systems of weights for trading. Metal workers and apothecaries needed precise measurements so their systems were well developed. 

Pressure on cutting the cake

 We were very pleased to find that you can still buy Charlie the Caterpillar cake. It won't cut very well if the knife blade is upside down. You can push with a big force but it is the pressure that does the damage. The blunt side of the knife has too big an area so the pressure is too low.

Smaller area means higher pressure for the sharpened side of the knife.

The tip has an even smaller area so has the highest pressure and goes in most easily.

Correct voltage for a Geiger-Muller tube

 

I was showing my class how to detect background radiation. The tube works by setting up an electric field between an anode needle in the middle and a cylindrical cathode round the outside. There is a low pressure gas between. When the gas is ionised by incoming radiation, it triggers and avalanche of ionisations that result in a strong electrical pusle that can be counted. A particular voltage has to be maintained between the anode and the cathode to make this happen. I had it in my head that the correct voltage is 415V. Looking it up, I found this https://spark.iop.org/geiger-muller-tube#gref It suggests an experiment that I have never tried. The amount of ionisation depends on the voltage but there is a plateau section where a range of voltages will give a steady reading. So one particular voltage isn't necessarily the right answer and there is an experimental method to find the optimum voltage for my tube.

Another Corona corona

 

More steamed up glasses due to masks. This one was taken outside Ambleside Youth Hostel. I was really taken by the spiky effect and the full spectrum. You can tell that it is diffraction through the condensation on the glasses because it looks like the light has come through the window frame on the right. The spreading must therefore have happened after the light passed through the window and before it hit the camera.

Rush bearing (my weight) on Wansfell

 

Having just passed the plaque to the vicar who wrote the Ambleside Rushbearing Hymn, we climbed Wansfell. It was still very damp after the recent deluge. Walkers had made use of Soft Rush (Juncus effusus) to cross some of the very wettest patches. Why do the rushes work? It could be to do with pressure because, flimsy though they are, they do seem to be increasing the area of my feet. This reduces the pressure and thus reduces the "damage" done by my feet. Here's the hymn https://www.amblesideonline.co.uk/useful-information/local-events/rushbearing/rushbearing-hymn/

A dram in Ambleside

 

We were intrigued by scales that measured in drams. According to https://en.wikipedia.org/wiki/Dram_(unit) the unit appears to have started life as a coin/weighing mass in ancient Greece and will therefore be related to the drachma currency. It was taken up by apothecaries, hence its display in the window of a chemist's shop and made it into avoirdupois system, which is pounds and ounces. I thought that was the Imperial system but I think the Imperial system adopted the earlier avoirdupois and standardised it a bit more. Anyway, under that system, a dram became 1/16 ounce.

Air in the brakes

 I found this old model of hydraulics that someone had lovingly made. The idea is that when you push one syringe, it puts pressure on the liquid. Liquid is incompressible because the particles in at are basically touching each other. So the pressure transmits through the liquid to the other end. The same pressure acts at the other end and causes a force to act on the plunger at the other end, pushing it out. This is how car brake pedals push on the brake pads that are attached to the wheels.

But the model has seen better days. Air has got into it. When you push on air, the particles are far enough apart to be pushed closer together. The pressure at the far end is not the pressure that you push in. The brake pads would not push on the wheels as hard.

Measuring the gas pressure

 

When they came to check the gas taps they used a manometer to test the pressure. A manometer is a U-tube. This is a U-shaped tube full of liquid. Normally the liquid level is the same on both sides because if it is disconnected, air pressures pushes down equally on the liquid surface on each side. To measure pressure, you leave one side open to the air and connect the other side up to a gas pipe. The pressure in the gas pipe should be higher than atmospheric and will push the liquid down on that side. By using the formula for pressure in the depth of a liquid (pressure = height of liquid x density of liquid x g) you can calculate how much higher the pressure is in the pipe than in the air.