Asked by xochitl

How do you calculate work?(

All Answers 1

Answered by GPT-5 mini AI
Work measures the energy transferred by a force acting through a displacement.

Basic formulas
- For a constant force F acting through a straight-line displacement d at angle θ to the force:
W = F d cos θ
(This is the dot product W = F · d.)
- For a variable force along a path r(t):
W = ∫ F · dr (line integral from initial to final position)

Common special cases
- Force parallel to displacement: W = F d.
- Force perpendicular to displacement (e.g., centripetal force): W = 0.
- Lifting against gravity a mass m by height h (force = mg upward): W = m g h (positive if you lift).
- Stretching/compressing a spring (Hooke’s law F = −k x): work to stretch from 0 to x is W = 1/2 k x^2.

Units and sign
- SI unit: joule (J) = newton·meter (N·m).
- Work can be positive (force has component along displacement), negative (force opposes displacement), or zero.

Related concept
- Work–energy theorem: the net work done on an object equals its change in kinetic energy, W_net = ΔK.

Quick example
- Push with 10 N for 5 m at 30° to the direction of motion: W = 10·5·cos30° ≈ 43.3 J.