### Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

### Stonehenge

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

### Maximum Flow

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

# New Units for Old

##### Age 16 to 18 Challenge Level:

 Name Phenomenon Units Base units becquerel, Bq (radioactivity) $(\textrm{s}^{-1})$ $\textrm{s}^{-1}$ degrees Celsius, $^\circ$ C temperature (relative) $(\textrm{K}$) $\textrm{K}$ coulomb, C electrical charge ($\textrm{A s})$ $\textrm{A s}$ farad, F capacitance $\textrm{C V}^{-1}$ $\textrm{A}^2 \textrm{ kg}^{-1} \textrm{ m}^{-2} \textrm{ s}^4$ gray, Gy radiation dose (absorbed) $\textrm{J kg}^{-1}$ $\textrm{m}^2\textrm{ s}^{-2}$ henry, H inductance $\textrm{Wb A}^{-1}$ $\textrm{A}^{-2}\textrm{ kg m}^{2} \textrm{ s}^{-2}$ hertz, Hz frequency $(\textrm{s}^{-1})$ $\textrm{s}^{-1}$ joule, J energy $\textrm{N m}$ $\textrm{kg m}^2 \textrm{ s}^{-2}$ katal, kat catalytic activity $(\textrm{mol s}^{-1})$ $\textrm{mol s}^{-1}$ lumen, lm flux of light $\textrm{cd sr}$ $\textrm{cd m}^2 \textrm{ m}^{-2}$ lux, lx illuminance $(\textrm{cd sr m}^{-2})$ $\textrm{cd m}^2 \textrm{ m}^{-4}$ newton, N force $(\textrm{kg ms}^{-2})$ $\textrm{kg ms}^{-2}$ ohm, $\Omega$ resistance $\textrm{V A}^{-1}$ $\textrm{A}^{-2} \textrm{ kg m}^2 \textrm{ s}^{-3}$ pascal, Pa pressure $\textrm{N m}^{-2}$ $\textrm{kg m}^2 \textrm{ s}^{-2}$ radian, rad plane angle (dimensionless) $\textrm{m m}^{-1}$ siemens, S conductance $\textrm{A V}^{-1}$ $\textrm{A}^2 \textrm{ kg}^{-1} \textrm{ m}^{-2} \textrm{ s}^3$ sievert, Sv radiation dose (equivalent) $(\textrm{m}^2\textrm{ s}^{-2})$ $\textrm{m}^2\textrm{ s}^{-2}$ steradian, sr solid angle (dimensionless) $\textrm{m}^2 \textrm{ m}^{-2}$ tesla, T magnetic flux density $(\textrm{A}^{-1} \textrm{ m}^{-1} \textrm{ N})$ $\textrm{A}^{-1} \textrm{ kg s}^{-2}$ volt, V electrical potential $\textrm{W A}^{-1}$ $\textrm{A}^{-1} \textrm{ kg m}^2 \textrm{ s}^{-3}$ watt, W power $\textrm{J s}^{-1}$ $\textrm{kg m}^2 \textrm{ s}^{-3}$ weber, Wb magnetic flux $\textrm{V s}$ $\textrm{A}^{-1} \textrm{ kg m}^2 \textrm{ s}^{-2}$

(date sourced from the Bureau International des Poids et Mesures http://www.bipm.org/)

Items in parenthesis () not present in original table