Sunset on the longest day

Sunset on the solstice was almost 10pm BST and here the sun set in the north west. It's wonderful having sunlight all evening. I was reading about summer solstice in Barry Lopez's book Arctic Dreams. He points out that on the summer solstice at the exact geographic North Pole, the Sun would go round in a circle at the same height above the horizon for 24 hours. It stands to reason but is still amazing.

U-value of a thatched roof

We came across thatching in progress and were amazed at how thick it is. I'd never seen a cross-section of thatch before. U-values are used to measure the effectiveness of an insulation material. The rate of heat loss = area x u-value of insulation x temperature difference between inside and outside. Thus u-value is measured in Watts per square metre  per degree Celsius and the lower the u-value, the better the insulation because the fewer the Watts are lost. According to one website, the maximum allowed u-value is 0.15 https://www.thegreenage.co.uk/getting-to-grips-with-u-values/ I found a site with values for thatch https://www.uttlesford.gov.uk/CHttpHandler.ashx?id=2139&p=0 which gives 0.29 and 0.23 depending on the reed used. So a thatched roof on its own does not meet current regulations and would need internal insulation. But it's not far off. The trapped air between the reeds acts a good insulator.

Pressure at the fountain in Lancaster

We found this fountain in Williamson Park in Lancaster. I'm estimating that the water fountain goes up 4 metres. By using the idea that kinetic energy turns into gravitational potential energy or 1/2mv^2=mgh, you get v = sqrt(2gh). So the velocity of the water coming out of the nozzle is about 9 metres per second. Volume flow rate in cubic metres per second = cross-sectional area of hole x velocity. I'm going to estimate a cross-sectional area of 1 square centimetre or 1 x 10^-4 square metres so volume flow rate = 9 x 10^-4 cubic metres per second. Mass flow rate = density of water x volume flow rate = 0.9 kg per second since the density of water is 1000 kg per cubic metre. Newton's second law says that force = rate of change of momentum = mass flow rate x velocity = 0.9 x 9 = 8N. Pressure = force per unit area = 8/1 x 10^-4 = 80000Pa.

Pine tree cantilever oscillations

I watched the pine tree in the centre right of photo oscillating freely after being driven by the wind. I timed 6 oscillations in 27 seconds, so time period was 4.5 seconds. I looked for an equation and found one here
https://physics.stackexchange.com/questions/171198/derive-equation-for-a-cantilever-in-shm
Time period = 6.19*L^2/d x sqrt(density/Young Modulus). I looked up density of pine (510 kg per cubic metre) and Young Modulus of pine (9GPa). I d is the width of a rectangular cross-section. I used diameter instead which I estimated at 0.15m, though it is not uniform. I get a length of 21m. I think that's probably a bit big but not by much!

Distance and displacement at Burnham Overy Staithe

These Shelduck were making interesting tracks in the mud, crossing backwards and forwards over the places they had already walked. They had walked quite a long way but hadn't ended up far from where they started. Distance is a scalar quantity and is the actual length they have walked. Displacement is a vector and is just the distance measured in a straight line from the start point, with direction from the start given.

Electromagnetic wave emmission at Dobies

I took the picture in the depths of winter. I've been teaching about black-body emission this year. This is another good example. I say that the heater gives off infra-red. If you are close by you can really feel it. However, infra-red is not visible but the heater is clearly giving off a lot of red. This shows that electromagnetic waves are given off over a range of wavelengths. It is merely that the peak for intensity is in the invisible range. Just imagine how bright that would look to our eyes.

Bridge over the Atlantic

This bridge is from the mainland over to Seil Island just south of Oban on the west coast of Scotland. Yes, that is the sea underneath the bridge. The island is that close to the land. And if you head west from the island next stop is America so technically the sea is actually the Atlantic Ocean. So this is known as the Bridge Over The Atlantic.

Now imagine the car PARKED on top of the bridge. The upward reaction force R would equal the weight mg. When you are driving the car at a steady speed over the bridge, it will be constantly changing direction due to the curvature. It will be accelerating because acceleration is rate of change of the velocity vector. Vector includes direction change. Such an acceleration requires a centripetal resultant force. The resultant is directed downwards towards the centre of curvature so resultant force = mg - R. The faster you go, the bigger the centripetal resultant needs to be. mg can't change so the only way to get (mg-R) bigger is by R getting smaller. In the extreme case, R = 0 which means no normal contact force on the ground. You have taken off!