### 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:

There are seven different Standardised International (SI) units of measurements from which all others are derived. These are:

 Name Phenomenon Units meter Length m second time s kilogram mass kg ampere electric current A kelvin thermodynamic temperature K mole Amount of substance mol Luminous intensity candela cd

There are 22 derived physical phenomena, shown below. The names, phenomena, units and base units have been mixed up.

1. Sort them into the correct order and work out how their units may be represented with base SI units.
2. For each pheonomena, how many examples of biological application can you find? Can you find an example from biology for each one of these processes?
 Name Phenomenon Units Base units becquerel, Bq capacitance A / V $\quad\quad$m$^2$m$^{-2}$cd degrees Celsius, $^\circ$ C electric conductance C / V $\quad\quad$K coulomb, C electric potential cd sr $\quad\quad$kg s$^{-2}$ A$^{-1}$ farad, F electric resistance J / kg $\quad\quad$m kg s$^{-2}$ gray, Gy electrical charge J / kg $\quad\quad$m$^{1}$m$^{-1}$ henry, H energy J / S $\quad\quad$m$^{2}$ m$^{-4}$ cd Hertz, Hz flux of light $\quad\quad\quad$lm / m$^2$ $\quad\quad$m$^{2}$ kg s$^{-2}$ joule, J force $\quad\quad\quad$N / m$^{2}$ $\quad\quad$m$^{2}$ kg s$^{-2}$ A$^{-1}$ katal, kat frequency N m $\quad\quad$m$^{2}$ kg s$^{-2}$ A$^{-2}$ lumen, lm illuminance V / A $\quad\quad$m$^{2}$ kg s$^{-3}$ lux, lx inductance V s $\quad\quad$m$^{2}$ kg s$^{-3}$ A$^{-1}$ newton, N magnetic flux W / A $\quad\quad$m$^{2}$ kg s$^{-3}$ A$^{-2}$ ohm, $\Omega$ magnetic flux density Wb / A $\quad\quad$m$^{-2}$ kg$^{-1}$ s$^{3}$ A$^{2}$ pascal, Pa plane angle $\quad\quad\quad$Wb / m$^2$ $\quad\quad$m$^{-2}$ kg$^{-1}$ s$^{4}$ A$^{2}$ radian, rad power $\quad\quad$m$^{2}$ s$^{-2}$ siemens, S pressure $\quad\quad$m$^{2}$m$^{-2}$ sievert, Sv radiation dose $\quad\quad$sA steradian, sr solid angle $\quad\quad$s$^{-1}$ tesla, T temperature $\quad\quad$s$^{-1}$ mol volt, V unit of catalytic activity watt, W weber, Wb

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

### Other problems

Try Universal Time, Mass, Length to investigate the units implicit in the fundamental constants of nature.