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.
You might like to refer to some of the ideas in the Plus issue
10 article, In
space, do all roads lead to home?. It's all done with
Jon Farradane supplied the following
For an n-bounce route, find the nearest 'n-times reflected'
image of one point as viewed from the other, using a mirror
boundary. The ray path gives the solution. Jon says this works only
for a boundary made of straight edges.
Jon also supplied a slightly more complex method which solves
the 1-bounce problem and works better if you wish to take advantage
of the curved areas of the table edge around the pockets. He
suggests investigating the family of ellipses which have their foci
at the two balls. The ellipse with the highest eccentricity that
makes a tangent to the cushion will touch it at the bounce point
for the shortest route.
Jon also raised the question of how to solve the problem for
circular tables. The ellipse technique still works, but it's not an
easy problem to solve analytically!