Borrowdale Banksy on Dalehead: does friction oppose gravity?

 

We thought there were only two pieces by the Borrowdale Banksy but we found a third on the path up to Dalehead from Honister Slate Mine. You can't miss it if you follow the fence. It got me thinking again about what keeps the stones up around the top of an arch. I was thinking friction because the slate is made from volcanic tuff which is a bit rougher than slate metamorphosed from mudstone. But then I remembered that the stones are always leaning in slightly on the ones above so that with gravity pulling the ones above down, there is a normal contact force from the lower stones pushing back. This is at 90 degrees to the surface and provided the stones are angled, they will have some vertical component that opposes the weight. In other words, this should work without friction. Even so, hats off! I can discuss the abstract Physics but wouldn't manage the practicalities.

Amazing pinhole camera

 The technicians made me some fabulous pinhole cameras. You can see the view of the trees in the distance in the first picture. It was better is real life because putting my camera to the hole let in too much light from the back.

The design is based on a Pringles tube but the screen is most of the way down the tube and the rest of the distance from the eye hole to the screen is just to keep the screen dark enough to see the view. Wonderful!

Update on the length of the adit at Seathwaite Tarn mine

 

Wigton Library has reopened and I found a great book. Last month I was trying to estimate the length of the adit at Seathwaite Tarn mine. I came up with 300m. John Adams quotes 200 yards. Not too bad as an estimate - only 50% out!

Brian Greene on Desert Island Discs

 The string theorist Professor Brian Greene was on Desert Island Discs last week. He is very creative artistically as well as being a top theoretical physicist https://www.bbc.co.uk/programmes/m000w3lf

Thinking about hydroelectric

 

It struck me at Greenside Mine that the pipe feeding the Glenridding Hydro has exactly the same drop as the water in the river because the hydro is next to the river at the bottom. So why not just put the turbine in the river? My first thought was about energy. The amount of white water and sound suggests a lot of dissipation in the stream and there will probably be less of that in the pipe. The question is whether water in the pipe will reach the bottom faster than water in the stream that set off at the same time, as it should end up with more kinetic energy if less of the gravitational potential energy is dissipated. On a more practical level, the flow in the stream is very variable and the turbine could be left without water if placed in the stream. There is also the way it would be pelted with stones and other debris is spate.

Oak before ash

I spotted my first leaves on an ash tree this year. The oak leaves have been out for a couple of weeks now. There is a weather prediction that says that if oak comes before ash then the summer will be dry. Old lore often has some basis and I was hoping for an explanation. However https://www.bbc.co.uk/blogs/natureuk/2011/05/oak-before-ash-in-for-a-splash.shtml says that due to global warming, oak is out first almost every year now and that there is no link to rainfall.
 

A real yardstick

 

A yardstick is a well-used metaphor in English but I have spent my career using metre sticks. I've now found a real yardstick. The resoltion is 1/8th of an inch which is not as good as my +-1mm resolution metre sticks.

Three horsepower at Penrhyn

 

This sign perfectly illustrates the concept of horsepower. Horsepower is literally a measure of power, the rate of doing work. It turns out to be nearly 750 Watts in modern units which doesn't sound that much!

AC mains sonometer

 

In this experiment, constantan wire was clamped at one end and the other hung over a clamped pulley with slotted masses hanging from the end. The wire runs over two prisms that act as knife edge support. Two pole-faced Magnadur magnets from an electric motor kit sit between the prisms and AC is fed into the wire at either end. The wire was 36swg and I used 2 Volts. I started with 100 grams and then went up in increments of 50 grams. The wire oscillates because the magnetic force on it is perpendicular to the current in the wire and dependent on the direction of the current. Hence AC makes it change direction with a frequency of 50Hz. For 100 grams, the prisms were about 30cm apart and that increases as the mass increases. I came up with a measure for mass per unit length of the wire by knowing the density and measuring the radius with a micrometer screw gauge. Using this equation I plotted L-squared against T and was able to use the gradient to get a value for the frequency.

Furlongs on the milestone

 

I was interested by the distance to Capel Curig from Bangor: 14M 3F means 14 miles and 3 furlongs. I have never seen furlongs used like this before. I had to look up a furlong - apparently from "furrow length" and thus how far a team of oxen could plough without resting. There are 8 furlongs in a mile so Capel Curig is just under 14 and a half miles away.

Gwna Group Melange at Porth Wen

 

I couldn't help noticing these amazing rocks next to the brickworks at Porth Wen. I took it for a conglomerate although the embedded fragments are very angular which would suggest that they had not been transported very far. They also seem to span many layers in the rock, which is odd because it would suggest that they would span more than one age surely. But also, the layers seem metamorphosed like slate. It looks to me like these rocks belong to the Gwna Group and are called a melange, a term I've haven't come across before in geology. It seems that the cause was a vast underwater slide caused by an earthquake which resulted in rock fragments being mixed with mud. See also this excellent site about Anglesey geology.

NOT gate at Porth Wen Brickworks

 

This gate is on the hill above Porth Wen Brickworks on Anglesey. I'm calling it a NOT gate because although the hinge is there and still turns, there is no gate. In electronics, a NOT gate is what is used to turn a 1 into a 0 or a 0 into a 1 in a logic circuit. On other words, what comes out is NOT what goes in; it is the opposite.

How to measure the diameter of a wire properly

 Notice that in these pictures I have the micrometer screw gauge first vertical and the horizontal. To get an accurate value for the diameter it is necessary to meaure at half a dozen places and take a mean. But it is also important to change the orientation of the gauge as it goes along.

Radial to linear on Mungrisdale Common

 

On Mungrisdale Common all paths converge on the summit cairn. They can be seen heading out like a radial field, like spokes on a wheel. However the panoramic view has mapped them into parallel lines.

Equalising the pressure on the beetroot

 Maybe it's old age creeping up on me, but I couldn't get the lid off the beetroot jar. Knowing that the pressure inside is lower than the pressure outside, I knocked a nail through the safety button. I was then able to open the jar. It seems that it was not just friction but was also the difference in pressure making it hard to open.

I gather that the food is cooked and then placed in the jar. The lid is screwed on. As the food cools, the air around it cools. The particles are not moving as fast so they don't collide with the lid as much. The pressure decreases. They also take up a smaller volume so the button, which is more flexble than the rest of the lid, is pulled in. By putting a hole in the lid, I allowed more particles in so there were more collisions raising the pressure inside to that outside.

How does air resistance affect a bullet?

I've been doing the maths on how the air resistance would affect the distance travelled by the bullet on the rifle range. I've used as the resultant force F the drag equation used in the previous post. A bit of calculus shows that the rate of change of velocity with distance depends on velocity, not velocity squared. Integration below shows that the factor is divided by mass, so maybe I've got the start of how ballistic coefficient is derived. 

If range would be when v = 0, then no proper inegral can be done because that would give the range as infinite in this model. So I have just worked on the idea that velocity decreases exponentially with distance. Mass of a .303 bullet is about 175 grams. Putting in the data I used in the last post, I made a spreadsheet to see what happened.

Over the length of the rifle range, air resistance makes very little difference so my calculation of a 5 metre drop for the bullet over the range should still stand. However I have not factored in that the bullet is supersonic.

Air resistance on the rifle range

 

Having done yesterday's calculation, I realised that I had neglected air resistance. I discovered that there is a complicated discipline called external ballistics but I've opted to try a simpler drag coefficient that I might understand. If viscous drag = 1/2 x density x velocity-squared x drag coefficient x cross-sectional area then if I use a drag coefficient of 0.3 (suggestion is that a bullet would be between 0.1 and 0.3) then I'd get drag force = 1/2 x 1.2 x 745^2 x 0.3 x 5 x 10^-5 = 4.6 Newtons. I calculated a cross-sectional area based on the .303 diameter bullet. More thinking to be done because it depends on speed so will decrease in size as the air resistance slows the bullet. It seems in the full analysis, they use something called ballistic coefficient instead of drag coefficient which seems to incorporate mass as well.

Applying suvat to the Great Mell Fell rifle range

 I finally got to visit the old rifle range behind Great Mell Fell.

The red-roofed building in the foreground is behind a wall and a bank of earth that would have been where the targets were placed.

The map shows that the whole range is 1km long from fence to fence. The actual firing distance would be shorter. I looked up the muzzle velocity of World War 2 rifles and 745m/s seems to be the British choice. So let's say the bullet was fired 745m down the range. It would take 1 second to hit the target. In that time it would be being pulled downwards by gravity. To calculate the fall I use s = ut + 1/2at^2. Acceration a = 9.81m/s^2. Initially it was falling vertically at 0m/s. So if t=1s, then s = 4.9m. That is much, much bigger than I was expecting!