(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.