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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?


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

Items in parenthesis () not present in original table