✓ Sources checked · 10 September 2026 · View verification
Mechanical work by a force is W = ∫F·dr. The familiar W = Fd applies when a constant force is parallel to the displacement; opposite and perpendicular directions give different results.
By Matan · Updated
Direction matters quantitatively
For a constant force at angle θ to displacement, W = Fd cos θ. Positive work transfers energy into the body through that interaction; negative work transfers energy out. Perpendicular force does zero work on that displacement. [1]
Worked angled pull
A 30 N pull at 60° above horizontal moves an ideal sled 4.0 m horizontally. Its work is 30 × 4 × cos 60° = 60 J. The vertical force component does no work for this horizontal displacement. It can change the normal force and therefore change friction without raising the sled off the surface.
Work by one force versus net work
If friction does −20 J in the same motion and other forces do no work, net work is 40 J. For a constant-mass particle, that equals its kinetic-energy increase. The pull’s 60 J alone is not the net result. [2]
A door can have work without translating its centre along a straight path
For fixed-axis rotation, work is ∫τ dθ. A deforming or rotating body can receive work even when a simple centre-of-mass displacement description is insufficient. State the actual moving point or generalised coordinate used in the calculation.
Effort is not the definition
A stationary rigid wall receives no mechanical work from an ideal static push. Internal biological energy use is a separate accounting question.
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How this article was checked
Sources checked; calculations checked where shown. The definitions, model assumptions and main explanatory claims were cross-checked against the sources below. Worked-example arithmetic and units were checked separately. These examples are illustrative calculations, not experimental measurements.
Source cross-check and editing assisted by AI. No independent human scientific review is recorded for this revision. The check applies to the version dated 10 September 2026; it is not a guarantee that every possible interpretation is correct.
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Sources and further reading
- OpenStax: Mechanical work — Mechanical work.
- OpenStax: Net work — Net work.
Cite this article
Matan. “Work in Physics (Without Breaking a Sweat).” Your Physicist. Originally published 2026-06-11; updated 2026-09-10. https://your-physicist.com/work-in-physics-without-breaking-a-sweat/
Revision history
: Added a checked angled pull and clarified vertical force, net work and rotating-body limitations. Added linked sources and a transparent verification record.
