WAEC Physics 2012 Theory — Question 12

Model answer

(a)(i) A machine is any device that makes work easier to perform, typically by allowing a small effort to overcome a larger load, or by changing the direction of an applied force. (ii) Uses of gears: (1) To transmit rotational motion/power from one shaft to another. (2) To change the speed or torque of a rotating system (e.g. in a bicycle, to make pedalling easier or to increase speed). (iii) The velocity ratio for a pair of gear wheels is defined as the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear (or equivalently, the ratio of the radii of the two gears, or the distance moved by the effort to the distance moved by the load). (iv) The mechanical advantage of a gear system can be increased by increasing the velocity ratio (i.e. using gears with a larger difference in the number of teeth between the driving and driven gears), or by reducing friction in the system to improve efficiency. (b)(i) Velocity ratio is read/calculated from the diagram based on the relative sizes (number of teeth or radii) of the pedal gear and the wheel gear shown — this is determined from the specific gear diagram given. (ii) Mechanical advantage (M.A) = Efficiency × Velocity ratio. Effort = Load/M.A. Using the given efficiency (90%) and the velocity ratio from (b)(i), the effort required is calculated as Effort = 70/(0.9×V.R). (iii) The calculated effort is less than the actual effort required in practice because of friction in the moving parts of the gear system (chain, gears, bearings), which was not accounted for in the ideal calculation, and this friction means additional effort is needed to overcome it.