If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
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?
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
A standard English snooker table is 6' x 12'. We know that the
shortest path between any two points on the table is given by the
straight line between them. How do we figure out the shortest
distance between two points if the ball must bounce off one wall?
What if it must bounce off 2 walls? 3 walls?
If you want to try one yourself, let the bottom left hand corner
of the pool table be the origin. Consider the case when the cue
ball is at (5,5) and the target ball is at (10,2). Which wall gives
the shortest path to the target?