George Orwell's grave: coefficient of friction

When we were last at Crinan, we were able to look out over the water to the remote farmhouse on Jura where George Orwell wrote 1984. Within a year he was dead. It turned out we were staying in Oxfordshire near his grave. He wanted to be buried in an English country churchyard. I wonder what he'd make of the coins left by other visitors. Notice that as the edge of the grave stone gets steeper, the coins won't stay. Friction isn't strong enough to resist the component of weight pulling down the slope. Friction F is directly proportional to normal contact force N. The constant of proportionality is called the coefficient of friction mu.

 Above is the force diagram. Three forces act on a coin. I take components of the weight mg.

At the point at which the coin is just about to move, the perpendicular components must be equal and opposite. The same is true of the parallel components. So I can make the substitution shown at the bottom. Lastly, coefficient of friction = tan(theta). The angle at which the coins come off is about 30 degrees so the coefficient of friction for stone and metal is thus about 0.6.

Coriolis Effect and the Birmingham floods

The storms in the West Midlands last night made the news. One of the best lightning displays that I've seen in years. A lot of water fell in a short space of time. After the storm, the water was swirling down this drain at the service station. It was going anti-clockwise. They say water should always do this in the northern hemisphere but in reality it also depends on the geometry of the drain hole and on the initial conditions. The best thing that happened was when a passing car sent plane waves across the system. They were then bent round as they hit the sink hole producing an effect like spiral arms on a galaxy. For the definitive Coriolis Effect film, see https://www.youtube.com/watch?v=aDorTBEhEtk

Chasing shadows at Watchtree

 I was watching the shadow of a wind turbine at Watchtree as it raked across the meadow.

 Later we stood as the shadow came rushing across us.

When timing the shadow and the blades, you must have the same time for the same movement. But if the Sun is low and the shadow is being projected over a bigger distance, the shadow will move further than the blade in the same time. Thus the shadow will move faster in those circumstances. In theory it is possible for the shadow to move faster than the speed of light!

Vectors and the ferry to Threave Castle

We took the ferry to visit the wonderfully situated stronghold of Archibald the Grim. The boat shouldn't be aimed in a straight line between the two points because as well as the velocity vector of the boat's motor, there is also the velocity of the river water to contend with. It will tend to push the boat downstream so you need to aim slightly upstream.

Leslie's cube

Leslie's cube is a copper cube filled with boiling water. The sides are painted matt black, gloss black, white and unpainted. It is a closed system but energy crosses the system boundary as infra-read heat radiation. I used a thermopile and an old-fashioned spot beam galvanometer to detect the infra-red. The matt black side gave the highest reading today showing that it is the best surface colour for emitting infra-red.

Work done crossing the system boundary

We still own an old-fashioned bicycle pump! If you put your thumb over the end and pump, the pump case becomes quite hot. Air is trapped inside. It is a closed system. But work can cross the system boundary. The work done gives extra kinetic energy to the air molecules. This extra internal energy manifests itself as a rise in temperature.

Thinking about Olber's Paradox on Glasson Moss

We were sat having a picnic in the thin band of trees on the edge of Glasson Moss. I realised that although the band of trees is quite thin, I couldn't see through. In every direction , there was a tree trunk. This is really the opposite of Olber's Paradox, which asks why the sky is black at night. It was based on the idea that the Universe is static and infinite in size. If that were so, says the reasoning, then you'd be able to see a star in any direction you looked. That's like me seeing a tree in any given direction. But of course there isn't a star in any given direction. One explanation now is that the Universe is not infinite in time, so light from more distant galaxies has not had time to reach us yet.