(a) (i) What is meant by a machine?
(ii) List two examples of a simple machine.
(iii) Explain the statement — the velocity ratio of a machine is 5.
(b) (i) Define the efficiency of a machine.
(ii) Explain why a machine can never be 100% efficient.
(c) A screw jack, 25% efficient and having a screw of pitch 0.4 cm is used to raise a load through a certain height. If in the process, the handle turns through a circle of radius 40.0 cm, calculate the;
(i) velocity ratio of the machine; (ii) mechanical advantage of the machine; (iii) effort required to raise a load of 1000 N with the machine. [Take \(\pi\) =3.14]
Explanation
(a)(i) A machine is a device by means of which a force or effort applied at one point is used to overcome load at the other point.
(ii) Examples of simple machines are: lever, pulley system, incline plane, Jack, wheel and axle and hydraulic press
(iii) This means that the distance moved by the effort is 5 times the distance moved by the load at the same time interval.
(b)(i) Efficiency of a machine is the ratio of work output to work input expressed in percentage.
(iii) The efficiency of a machine can never be 100% because part of the energy supplied to the machine is used to overcome friction and in moving other parts of the machine. (i) Velocity ratio, V.R = \(\frac{2 \pi r}{P} = \frac{2 \pi \times 40}{0.4}\) = 628
(ii) Efficiency = \(\frac{M.A}{V.R}\) x 100%
M.A. = \(\frac{\text{Efficiency x V.R}}{100}\) = \(\frac{25 \times 628}{100}\) = 157
(ii) M.A = \(\frac{load}{Effort}\); Effort = \(\frac{load}{M.A}\)
= \(\frac{1000}{157}\) = 6.4N