Work (Physics) Calculator
Compute work W = F·d·cos(θ). Force in N, displacement in m, angle in degrees.
W = — J
Work in physics: W = F·d·cos(θ)
Work measures the energy transferred by a force acting on a body that undergoes a displacement: W = F·d·cos(θ), where θ is the angle between force and displacement. The unit is the joule (J = N·m). Work is zero when F ⊥ d (centripetal force does no work) and negative when θ > 90° (friction, brakes). The work-energy theorem states that W_total = ΔEc. Conservative forces (gravity, elastic) yield work independent of the path; non-conservative forces (friction) depend on the trajectory. Example: pushing a 50 N box for 10 m horizontally gives W = 500 J; if the force is at 30° to the motion, W ≈ 433 J.
Applications
Strength training quantifies work as the load lifted times the height. Mechanical efficiency η = W_useful / W_total describes engines: gasoline ~25%, diesel ~40%, electric ~90%. In thermodynamics, work appears in the first law (ΔU = Q − W) and drives heat engines and refrigerators.
FAQ
Why is work zero when carrying a box at constant height? Because the lifting force is vertical and the displacement is horizontal — θ = 90°, cos(θ) = 0.
What's the difference between work and energy? Energy is a state (stored capacity); work is the process of transferring energy. Work changes the energy of a system.
Can work be negative? Yes — friction, air drag, and brakes all do negative work, removing kinetic energy from the body.
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