(a) (i) What is a machine? (ii) State two uses of gears. (iii) Define the velocity ratio for a pair of gear wheels. (iv) How can the mechanical advantage of a gear system be increased?
The diagram above illustrates the gears system of a bicycle. (i) Determine its velocity ratio. (ii) If the bicycle has an efficiency of 90%, calculate the effort required to overcome a load of 70N. (iii) Why is the calculated effort less than the actual effort required?
Explanation
(a)(i) A machine is a device in which an effort applied at one end is used to overcome a load at another point. Machine makes work easier. (ii) Uses of gears are: - to change speed to change direction of motion - to magnify force. (iii) Velocity ratio of a gear wheel is the ratio of number of teeth on driven wheel to number of teeth on driving wheel OR Velocity ratio = \(\frac{\text{Time rate of revolution/speed/radius of driven wheel}}{\text{Time rate of revolution/speed/radius of driving wheel}}\) (iv) To increase the mechanical advantage, the driving gear is made smaller with fewer teeth than the driven gear. (b) Number of teeth on driven gear = 12. Number of teeth on driving gear = 18. (i) V.R. = \(\frac{\text{no. of teeth on driven gear}}{\text{no. of teeth on driving gear}}\) = \(\frac{12}{8} = \frac{2}{3}\) (ii) Efficiency - \(\frac{M.A}{V.R}\) x 100% = x 100% = \(\frac{L/E}{V.R}\) x 100% 90 = \(\frac{70/E}{2/3}\) x 100% (iii) This is due to: - Friction between the tyres and load. - Friction between chain and gear.
