The dimensional formula of Power is [ML²T⁻³]. Power is defined as the rate of doing work (P = Work/Time) or equivalently P = Force × velocity. The SI unit of Power is Watt (W) = Joule per second (J/s) = kg·m²·s⁻³.
Dimensional formula of Power = [ML²T⁻³].
Derived from P = W/t: [ML²T⁻²]/[T] = [ML²T⁻³].
Also from P = Fv: [MLT⁻²][LT⁻¹] = [ML²T⁻³].
SI unit: Watt (W) = J/s = kg·m²·s⁻³.
1 horsepower = 746 W.
Power × Time = Energy: [ML²T⁻³] × [T] = [ML²T⁻²] ✓
Method 1: From P = W/t (Power = Work / Time)
Dimensions of Work: • W = Force × displacement = [MLT⁻²] × [L] = [ML²T⁻²]
Dimensions of Time: • t = [T]
Therefore: [P] = [W]/[t] = [ML²T⁻²]/[T] = [ML²T⁻³]
Method 2: From P = F × v (Force × velocity)
• Force (F) = [MLT⁻²] • Velocity (v) = [LT⁻¹]
[P] = [MLT⁻²] × [LT⁻¹] = [ML²T⁻³] ✓
Both methods give: [ML²T⁻³]
SI Unit: • Power unit = Watt (W) • 1 Watt = 1 Joule per second = 1 J/s • In dimensional terms: kg·m²·s⁻³
Definition: Power = Work done per unit time = Rate of doing work P = W/t = F·v = E/t
Units of power: • SI unit: Watt (W) — named after James Watt • 1 kW (kilowatt) = 1000 W • 1 MW (megawatt) = 10⁶ W • 1 horsepower (hp) = 746 W ≈ 750 W • 1 kWh (kilowatt-hour) = unit of energy (3.6 × 10⁶ J) — not power
Relation between energy and power: • Energy = Power × Time • [E] = [ML²T⁻²] = [ML²T⁻³] × [T] = [ML²T⁻²] ✓
Comparison of dimensional formulas: Quantity | Dimensional Formula Power | [ML²T⁻³] Work/Energy | [ML²T⁻²] Angular Momentum | [ML²T⁻¹] Pressure/Stress | [ML⁻¹T⁻²] Force | [MLT⁻²] Velocity | [LT⁻¹]
[ML²T⁻³]. Derived from P = Work/Time = [ML²T⁻²]/[T] = [ML²T⁻³]. Or from P = Force × velocity = [MLT⁻²][LT⁻¹] = [ML²T⁻³]. SI unit: Watt (W) = J/s.
Watt (W), named after James Watt. 1 Watt = 1 Joule per second = 1 J/s = kg·m²·s⁻³.
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