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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?

### 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?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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