Max's Bells in a Factory
In his factory Max needs an alarm that rings every hour. He pulls apart an old bicycle and builds a machine using the bicycle chain and one of the sprocket wheels. He breaks the chain, hangs it over the wheel and attaches a bell to each end as shown. Max attaches a motor that turns the wheel clockwise for exactly one hour and then anticlockwise for exactly one hour, both at the same constant rate. This is shown in the diagram (url is below).
He positions the centre of the wheel on the wall so that at 12 noon the bell on the left hits the floor and rings. The wheel turns clockwise for one hour so that exactly 1pm the right bell hits the floor and rings. Then the wheel turns anticlockwise so that at exactly 2pm the left bell hits the floor and rings. This process continues alternately every hour.
A) At 2.10 p.m. the difference in height between the 2 bells is 80 cm. How far off the floor is the left bell at 3 p.m.?
B) The diameter of the sprocket wheel (to the center of the chain width) is ten centimetres. How many revolutions (rounded to 2 decimal place) does the wheel make each hour?
C) As the years go by, the sprockets on the wheel wear out so that the chain starts to slip. Max replaces the worn wheel with a 14 cm diameter sprocket wheel from the old bicycle. The motor still turns the wheel clockwise and anticlockwise at the same constant rate as before. To make sure the bells still ring every hour he changes the height of the centre of the wheel on the wall. By how much, to the nearest millimetre, does Max raise or lower the centre of the new wheel?