Unit of Work in Physics

SI unit of work = Joule (J)

Definition: 1 Joule = work done when a force of 1 Newton moves an object through 1 metre in the direction of the force.

1 J = 1 N·m = 1 kg·m²·s⁻²

Formula: W = F × d × cos θ

Where: • W = work done (in Joules) • F = applied force (in Newtons) • d = displacement (in metres) • θ = angle between force and displacement

Special cases: • θ = 0° (force and displacement in same direction): W = Fd (maximum work) • θ = 90° (force perpendicular to displacement): W = 0 (no work done) • θ = 180° (force opposite to displacement): W = −Fd (negative work)

System → Unit → Symbol SI → Joule → J CGS → erg → erg

Conversion: 1 Joule = 10⁷ erg 1 erg = 10⁻⁷ J

1 erg = work done by 1 dyne force through 1 cm displacement.

Other practical units: • Calorie (cal): 1 cal = 4.184 J (heat energy) • Kilowatt-hour (kWh): 1 kWh = 3.6 × 10⁶ J (electrical energy) • Electron-volt (eV): 1 eV = 1.6 × 10⁻¹⁹ J (atomic scale)

Dimensional formula of work: [W] = [Force] × [displacement] = [MLT⁻²] × [L] = [ML²T⁻²]

Work and energy have the same unit — Joule.

Work-energy theorem: Work done on an object = change in its kinetic energy. W = ΔKE = ½mv₂² − ½mv₁²

Power = Work / Time SI unit of power = Watt (W) = J/s 1 Watt = 1 Joule per second

Conditions for work to be done:

1. A force must be applied.
2. The object must be displaced.
3. The displacement must have a component along the direction of the force.

Examples: • Lifting a 1 kg object by 1 m: W = mgh = 1×9.8×1 = 9.8 J • Pushing a box 5 m with 10 N force (θ=0°): W = 10×5 = 50 J • Carrying a bag horizontally (force = vertical, displacement = horizontal): W = 0