## Sunday, 6 July 2008

### Constants.. Falling Through... Douglas Adams keeps surprising us!

Thinking about constants today. Wondering about how many we could identify as understandable in the quest for a Universal Theory Of Everything. Until this arrives, I would settle for a small kit bag of simple constants.

Like:

The Speed Of Light. How remarkable is it that this is Constant under usual circumstances but a movable feast when played with in Quantum Physics.

The realisation that two different elements will fall at the same rate.

That there is a Terminal Velocity at all. As a sky diver plummets, he may reach a speed arrived at by the congruence of Gravitational Force and Drag Factor.. approximately 200 miles per hour.

Go on, have a go. It's ok. It won't bite..
$F = m g - q A C_d \,$

where

m is mass of the object
g is the acceleration due to gravity
q is $\frac{1}{2} \rho V^2$, which is commonly known as the dynamic pressure, where
ρ is the fluid density (e.g. density of air)
V is the fluid (or air) velocity
A is the cross-sectional area of the object
Cd is the drag coefficient of the falling object

The terminal velocity is reached when F = 0, so

$m g - q A C_d = 0 = m g - \frac{1}{2} \rho V^2 A C_d$.

Solving for V to obtain the expression for terminal velocity,

$V_t = \sqrt{ \frac{2mg}{\rho A C_d} }$
Lovely!

Fibonacci:

Broccoli by numbers!

Absolute Zero. Where weird things happen to elements at around −273.15 °C. If it were possible to achieve, then the Bose–Einstein condensate state appears. Something bonkers called the de Broglie hypothesis also happens and the world becomes unpredictable... *gulp* Fluids that spontaneously leave thier confines.. Plasma is no longer the final state..

But best of all is the apparent constant that governs the speed at which we fall through the earth.

Drill a tunnel from Morpeth to Aukland. (This is remarkably close!) Then drop through it head first. In a vacuum. With a pressure suit and thermal underwear. You will arrive on the other side, briefly topping the hole before disappearing back the way you came. The one way trip will take you.... 42 minutes. It's tempting to abandon scepticism and ask, did Douglas Adams know that this would eventually become common knowledge?

It gets better. Drill a hole from Morpeth to Cern. This trip will take.. 42 minutes. Wherever you go from and wherever you arrive, it will take 42 minutes to get there.
It's all about the variables of gravity, distance and the most universally applicable constant of all, Pi.