(a) Explain (i) work: (ii) power
(b) Show that the efficiency E, the force ratio M.A. and the velocity ratio V.R. of a machine are related by the equation: E = M.A. x 100% V.R.
(c) An inclined plane of angle 15° is used raise a load of 4500N through a height of 2m. If the plane is 75% efficient calculate:
(i) velocity ratio of the plane;
(ii) work done on the load
(d) Explain Charles’ law using the Kinetic theory of matter.
Explanation
(a)(i) Work is the product of force and distance moved in the direction of the force
(ii) Power is the time rate of doing work. Unit of power is watts or J / sec.
(b) E = \(\frac{\text{Work output}}{\text{work input}}\) x 100% work input
E = \(\frac{\text{load x distance moved by load}}{\text{effort x distance moved by effort}}\)
But Ma = \(\frac{Load}{effort}\) and V.R = \(\frac{\text{distance moved by effort}}{\text{Effort distance moved by load}}\)
E = \(\frac{MA}{1} \times \frac{1}{VR}\) x 100%
E = \(\frac{MA}{V.R}\) x 100%
(c)(i) VR = \(\frac{1}{sin \theta}\) = \(\frac{1}{sin 45^o} = \frac{1}{0.2588}\) = 3.86
75% = \(\frac{9000}{Win}\) x 100%
Win = \(\frac{9000 \times 100}{75}\) = 12,000J
work input = 12000 J.
(d) At constant pressure, the number of collision per unit time is constant. An increase in temperature causes average Kinetic energy increases. The molecules then move faster. The volume therefore increases so as to maintain the number of collision per unit time.