Work Power Energy SI Units
Work Power Energy – SI Units
1. Mass.
It is quantity of matter contained in a body.
Unit of mass is kilogram (kg). Other multiples commonly used are :
1 quintal = 100 kg, 1 tonne = 10 quintals = 1000 kg
2. Force.
Unit of force is newton (N). Its definition may be obtained from Newton’s Second
Law of Motion i.e. F = ma.
If m = 1 kg ; a = 1m/s2, then F = 1 newton.
Hence, one newton is that force which can give an acceleration of 1 m/s2 to a mass of 1 kg.
Gravitational unit of force is kilogram-weight (kg-wt). It may be defined as follows :
or
It is the force which can impart an acceleration of 9.8 m/s2 to a mass of 1 kg.
It is the force which can impart an acceleration of 1 m/s2 to a mass of 9.8 kg.
Obviously, 1 kg-wt. = 9.8 N
3. Weight.
It is the force with which earth pulls a body downwards. Obviously, its units are the
same as for force.
(a) Unit of weight is newton (N)
(b) Gravitational unit of weight is kg-wt.
Note. If a body has a mass of m kg, then its weight, W = mg newtons = 9.8 newtons.
4. Work,
If a force F moves a body through a distance S in its direction of application, then
Work done W = F × S
(a) Unit of work is joule (J).
If, in the above equation, F = 1 N : S = 1 m ; then work done = 1 m.N or joule.
Hence, one joule is the work done when a force of 1 N moves a body through a distance of 1 m
in the direction of its application.
(b) Gravitational unit of work is m-kg. wt or m-kg
If F = 1 kg-wt; S = 1 m; then W.D. = 1 m-kg. Wt = 1 m-kg.
Hence, one m-kg is the work done by a force of one kg-wt when applied over a distance of one metre.
Obviously, 1 m-kg = 9.8 m-N or J.
5. Power.
It is the rate of doing work. Its units is watt (W) which represents 1 joule per second.
1 W = 1x(J/s)
If a force of F newton moves a body with a velocity of ν m./s then
power = F × ν watt
If the velocity ν is in km/s, then power = F × ν kilowatt
6. Kilowatt-hour (kWh) and kilocalorie (kcal)
1 kWh = 1000 ×1x(J/S) × 3600 s = 36 × 105 J
1 kcal = 4,186 J
∴ 1 kWh = 36 × 105/4, 186 = 860 kcal
7. Miscellaneous Units
(i) 1 watt hour (Wh) =
1x(J/S) × 3600 s = 3600 J
(ii) 1 horse power (metric) = 75 m-kg/s = 75 × 9.8 = 735.5 J/s or watt
(iii) 1 kilowatt (kW) = 1000 W and 1 megawatt (MW) = 106 W
Calculation of Kilo-watt Power of a Hydroelectric Station
Let Q = water discharge rate in cubic metres/second (m3/s), H = net water head in metre (m).g = 9.81, η ;
overall efficiency of the hydroelectric station expressed as a fraction. Since 1 m3 of water weighs 1000 kg., discharge rate is 1000 Q kg/s. When this amount of water falls through a height of H metre, then energy or work available per second or available power is
= 1000 QgH J/s or W = QgH kW
Since the overall station efficiency is η, power actually available is = 9.81 η QH kW.
Read article – Units of Resistivity
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