Work and Power

Study Notes

Power is the rate of doing work or the rate of energy consumption
Power is a scalar quantity
Formula for power: P = W/t (Power = Work done / Time)
Power can also be calculated as: P = F × v (Power = Force × Average speed)
Factors affecting power:
- Amount of work: Directly proportional to work done (P ∝ W)
- Time taken: Inversely proportional to time taken (P ∝ 1/t)

SI unit of power is the watt (W)
1 watt = 1 joule/second (1 W = 1 J/s)
Other units include kilowatt (kW), megawatt (MW), gigawatt (GW), milliwatt (mW), and microwatt (µW)
Conversion factors:
- 1 kW = 10³ W
- 1 MW = 10⁶ W
- 1 GW = 10⁹ W
- 1 mW = 10^-3 W
- 1 µW = 10^-6 W
Horsepower (HP) is another unit of power
Conversion factors for horsepower:
- 1 HP = 746 W
- 1 HP = 0.746 kW

Sum 2: A boy weighs 350 N, climbs 30 steps, each 20 cm high, in 1 minute.
- Work done = 350 N × 6 m = 2100 J
- Power spent = 2100 J / 60 s = 35 W
Sum 3: A man uses 6.4 kJ of energy to displace a body 64 m in the direction of the applied force in 2.5 s.
- Force = 6400 J / 64 m = 100 N
- Power spent = 6400 J / 2.5 s = 2560 W = 3.43 HP
Sum 4: A weightlifter lifts a 200 kgf load to a height of 2.5 m in 5 s (g = 10 N/kg).
- Work done = 200 kg × 10 N/kg × 2.5 m = 5000 J
- Power developed = 5000 J / 5 s = 1000 W
Sum 5: A machine lifts a 750 N load to a height of 16 m in 5 s.
- Energy spent = 750 N × 16 m = 12000 J
- Power = 12000 J / 5 s = 2400 W

Power: Rate of doing work (measured in Watts)
Work: Result of applying force over a distance in a particular direction (measured in Joules)
Power depends on time, while work does not.

Power: Rate at which energy is used or transferred (measured in Watts)
Energy: Capacity to do work (measured in Joules)
Power depends on the rate at which energy is used/transferred, while energy does not.