### 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.

# Moving Stonehenge

##### Stage: 5 Challenge Level:

Stonehenge is formed from massive stones made from Dolerite, which is has a density of $2.9$ tons $m^{-3}$. Interestingly, the quarries where such stones are found are a great distance from Stonehenge itself. It is usually assumed that the massive blocks were transported by water.

If we assumed that rafts were used to transport the blocks, what is the minimum length of trees, of diameter 20cm, that would have been required to transport each stone? An indicative density of wood is $\frac{3}{5}$ that of water, and assume that a typical Stonehenge stone can be approximated as a cuboid 5m high with 60cm square side length.

How would things change if barges were used instead of rafts?

You might want to experiment with wooden rods and kilogram weights to see how much weight a small raft can actually support. In order to do this, you will need to work out an estimate for the actual density of your wooden rods. Do your results tie in with the theory? What other mathematical and modelling issues arise?