Practice

W = Fd Formula – How to Calculate Work (Practice)

W = Fd — Work when force and displacement are parallel

Mechanical work measures energy transferred by a force acting through a displacement. When force and displacement are parallel, W = F d. At an angle, use W = F d cosθ.

Guide — how to use this formula

1. 1. Confirm force and displacement directions (or use cosθ).
2. 2. Convert distance to metres and force to newtons.
3. 3. Compute W = Fd (or Fd cosθ), then P = W/t if asked for power.
4. 4. For slow vertical lifts against gravity, W ≈ mgh.

Derivation

Work is defined as the line integral of force. For constant force:

1. Only the component of F along d contributes:
   W = \vec{F}\cdot\vec{d} = Fd\cos\theta
2. If θ = 0° (same direction), cosθ = 1:
   W = Fd
3. If θ = 90°, cosθ = 0 and W = 0:
   W = 0

Units: N · m = J. Work can be positive or negative depending on the angle.

Examples

Example: 30 N through 4 m

W = (30)(4) = 120 J.

Example: perpendicular force

Any F with θ = 90° → W = 0.

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