Elastic collisions at Wray Castle?

I hadn't played snooker since I was in the Sixth Form. I still can't get the angles right. But this is such a brilliant example of the laws of mechanics that there should really be one in every lab. The idea is that momentum is preserved in each collision. The balls have equal mass. An elastic collision is one in which momentum is conserved AND kinetic energy is conserved. In this case kinetic energy cannot be conserved because you hear the click of one ball into another - some kinetic energy is transformed into sound. I shot the white ball with initial velocity u into a red ball that was initially at rest. After the collision both balls moved on. Say the white ball has v1 and the red ball v2. Here are the equations for conservation of momentum and kinetic energy:

Combining the equations you get

This means that kinetic energy can only be conserved if v1=0 and the white ball stops dead. So the fact that the white ball goes on a bit is evidence of an inelastic collision. I hadn't realised that before.

Abingdon bun throwing

Sadly we were unable to be there but friends who were said it was great. Here's the video of this weird old ceremony http://www.oxfordmail.co.uk/news/14551727.VIDEO__Cloudy_with_a_chance_of___buns__Crowds_in_Abingdon_covered_with_bread_for_Queen_s_Birthday_ceremony/?ref=arc Buns are thrown from the top of the old building onto the crowds below. I tried timing the fall. The motion is parabolic. Vertical fall is independent of horizontal movement. I think a time of about 2 seconds is quite close. Timing from individual hand on the roof to hitting the ground is difficult. The equation needed is height = 1/2 x g x time-squared = 1/2 x 10 x 4 = 20 metres. Not too bad.

Rayleigh at Wray Castle

The National Trust's Wray Castle by Windermere using to be a Merchant Navy college and the rooms are named after physicists who worked on related areas. I teach Rayleigh's criterion (see http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/raylei.html) but reading about him, I notice that he won the Nobel Prize for discovering Argon. He used the idea of Rayleigh scattering to explain why the sky is blue. This is a brilliant explanation of what is going on if you carry on down through the articles  http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html#c3 The actual equation for Rayleigh scattering is hideous but seems to be crying out for some spreadsheet analysis when I have time. I like the diagrams showing the difference with Mie scattering. The issue seems to be that Rayleigh scattering is fairly uniform in all directions whilst Mie scattering massively favours the forward direction.

Making a model of a lunar standstill

The lunar standstill involves some difficult 3D reasoning so I tried to build a model. You can see the Equator drawn in black on the tennis ball. I've added the axis of the Earth sticking out of the North Pole. Here the Earth is shown upright but actually it is tilted at 23 degrees to the plane that contains the Sun and the other planets. So I've added that plane in clear plastic and tilted it at 23 degrees to the Equator. The Sun appears to do a circle around the Earth. I've drawn it on. It is called the Ecliptic. The Moon takes about 4 weeks to go round the Earth. It appears as a blob of putty on a wire. It is not on the ecliptic. It's orbit is tilted by another 5 degrees.

This is the situation at a lunar standstill. Notice how far above the Equator the putty Moon is - the Moon will appear very high in the sky.

It takes 2 weeks for the Moon to reach the other side of its orbit. Now notice that you are having to look down through the ecliptic so the Moon will appear very low in the sky. This is essentially a lunar standstill - that in 2 weeks the Moon goes from its highest possible to lowest possible position (when viewed looking due south from us).

But the orbit itself doesn't stay still. In the same way that a spinning top goes round in an arc whilst continuing to spin, so the orbit twists - it's called precession. It takes 18.6 years to get back to the position shown in the earlier photographs.

Zodiac signs on the Balmoral sundial

This sundial was in the garden of Balmoral Castle. I was interested that it had the odd cross-hatch pattern on it and zodiac signs round the outside. Turns out that the curves going laterally across the sundial are the loci of the shadow of the tip of the gnomon. The shadow length will be different in different seasons. Thus the shadow length can be linked to a zodiac sign, which in this case is used to denote where the Earth has reached on its orbit around the Sun. I guess that you have to know whether you are before or after midsummer to select which of the two signs offered at the opposite ends of the curve.

Mental arithmetic in the hills part 1: Grasmoor

We climbed Grasmoor by the improbably steep Red Gill.It was a lot further than it looked from the bottom. I resorted to the little finger method to try to work out how far we'd gone. No calculator with me so this is how I did it in my head: My little finger is worth a 1 degree angle. There are 360 degrees in a circle which is 2 pi radians. So 360 degrees is the same as 6.28 radians. I degree is worth 6.28/360 radians. I said 628/360 is approximately 2 so the 1 degree is approximately 0.02 radians. If you enlarge the lower picture you can see our car park to the right of my finger. The car takes up about 1/10th of my finger so a car is worth about 0.002 radians. A car is about 2 metres long. Arc length = radius x angle in radians. Thus distance to the car (the radius) = arc length/angle. The car acts as the arc length in this sector so distance from car = 2/0.002. Dividing by 0.2 is the same as x5. So dividing by 0.002 is the same as x500. Distance to car = 1000m. By comparing with neighbouring hills I knew that our altitude was about 600m so distance is about right!

Lunar standstill at Tomnaverie Stone Circle

We visited this stone circle when we were staying in Tarland in Aberdeenshire. I wondered what the bit in the middle picture meant about the limit of the movement of the Moon. It turns out that it is called a lunar standstill and was not an unusual thing for a stone circle to mark (see https://en.wikipedia.org/wiki/Lunar_standstill) I'm finding it quite hard to understand. Try this video of the event at the Calanais stone circle on Lewis https://www.youtube.com/watch?v=e98oObp4nwM I don't think that the analysis is scientific and you may want to take some of the comments with a pinch of salt but it seems like a reasonable visual recording of the event. The film shows the Moon crawling along the horizon so I guess this is what they mean for Tomnaverie. I had never heard of this and will need to get back to my 3D rotational mechanics to understand what is actually going on!