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.

Turbo Turbines

Stage: 5 Challenge Level:

As in many applied mathematics problems, the first part of the problem involves making the right equation from the given facts. Such aspects are important and often a major part of the the problem solving process.

Finding $V_{crit}$

The total rotational force (moment) on each of the arms is $M = \int^L_0{F}dx$. Moment and torque are equivalent.

Rotational version of Power = Force $\times$ Velocity

For the two terms on the right hand side, use their rotational equivalents.