Power is the rate at which energy is expended or used up. Power is the rate at which work is done or the rate at which energy is transferred or transformed. In the context of physics, it is often expressed as the amount of energy per unit time and is measured in watts (W). It can also be measured in Megawatts(MW), Kilowatt (kW), Horsepower (hp), and Joules per second (J/s)
Mathematically, power (\(P\)) is calculated as the ratio of work (\(W\)) to time (\(t\)):
$$ P = \frac{W}{t} $$
$$ P = \frac{mgh}{t} $$
$$ P = \frac{F × s}{t} $$
$$ P = F × v $$
$$ \text{where v} = speed $$
$$ Note: $$
$$ \text{1 hp} = 746\text{ W} $$
$$ \text{1 kw} = 10³\text{ W} $$
$$ \text{1 MW} = {10^6}\text{ W }$$
Calculations
Example 1: A man of mass 50kg ascends a flight of stairs 5m high in 5seconds. If the acceleration of due to gravity is 10m/s², the power is? (JAMB)
Solution
$$ power = \frac{mgh}{t} $$
$$ m = 50kg $$
$$ h = 5m $$
$$ t = 5s $$
$$ g = 10m/s² $$
$$ P = \frac{50 × 10 × 5}{5} $$
$$ P = 500W $$
Example 2: An electric power heater rated 1.5KW lifts 200kg of water through a vertical height of 6m in 10s. What is the efficiency of the pump (JAMB)
Example 3: A car travelling with a uniform velocity of 30m/s along a horizontal road overcomes a constant frictional force of 600N. Calculate the power of the engine. (WAEC)
Solution
$$ power = Force × velocity $$
$$ F = 600N $$
$$ v = 30m/s $$
$$ power = 600 × 30 $$
$$ power = 18000W = 18kW $$
Example 4: A girl whose mass is 20kg climbs up 25 steps each of height 15cm in 10 seconds. Calculate the energy expended. [g = 10m/s²] (NECO)
Solution
$$ m = 20kg $$
$$ t = 10s $$
$$ h = 25 × 15 = 375cm = 3.75m $$
$$ power = \frac{mgh}{t} $$
$$ power = \frac{20 × 10 × 3.75}{10} $$
$$ power = 75W $$
Power Calculator
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