Work, Energy and Power: Calculations and Conservation
This domain covers the definition of work, kinetic and potential energy, conservation of energy, and power and commercial energy calculations.
Work and energy
Work W = F s cos θ, measured in joules. Work is zero when the force is perpendicular to the displacement, as when a porter carries a load horizontally. Kinetic energy = ½mv², and gravitational potential energy near the Earth = mgh. In a closed system mechanical energy is conserved: a body falling through height h converts mgh into ½mv², so v = √(2gh).
Power
Power is the rate of doing work: P = W/t = Fv, in watts. One horsepower = 746 W. The commercial unit of electrical energy is the kilowatt-hour, where 1 kWh = 3.6 × 10⁶ J. Energy consumed = power in kW × time in hours.
Worked example
A 50 kg student climbs a staircase 4 m high in 10 s, with g = 9.8 m/s². Work done against gravity W = mgh = 50 × 9.8 × 4 = 1960 J. Power = W/t = 1960/10 = 196 W. If the same climb took 20 s, the work would stay 1960 J but the power would fall to 98 W.
Traps that cost marks
- Using distance instead of displacement, or omitting cos θ.
- Using g = 10 when the question specifies 9.8.
- Giving power in kWh rather than kW.
- Assuming the heavier body always has more kinetic energy while ignoring its speed.