### 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.

# Pumping the Power

##### Stage: 5 Challenge Level:

An electric power source produces an AC voltage $v = V_0\sin(\omega t)$, where $V_0$ is the peak voltage. A filament light bulb resistor R is placed across the source. Can you find a formula for the power (which changes over time) produced in the bulb? What is the average power produced in terms of $V_0$ and $R$?

If you would like to keep using the power formulae you learned for DC electricity, what would be a good representative voltage for this AC source, in terms of $V_0$?

Can you draw a graph of the light produced by the bulb over time if the bulb has been on for a long time?