# Cálculo do Trabalho

Simulação interativa do trabalho por uma força: W = F·s·cosθ

> Página canônica: https://elysiatools.com/pt/visualizations/work-calculation

- **Categoria:** Physics

## Visão geral

Interactive simulation of work calculation demonstrating W = F·s·cosθ with force, displacement, and angle visualization. Features work formulas: constant force W = F·s·cosθ, variable force W = ∫F·ds, power P = W/t = F·v, force components F∥ = F·cosθ (parallel, does work) and F⊥ = F·sinθ (perpendicular, no work). Multi-scenario visualization system includes: (1) Horizontal Pull scenario showing box on horizontal surface, applied force F (red arrow), displacement s (blue arrow), friction force f (gray arrow opposing motion), work done W = F·s, simple case with θ = 0°; (2) Angled Pull scenario displaying force applied at angle θ (0-90°), force decomposition into parallel component F∥ (green arrow, does work) and perpendicular component F⊥ (purple arrow, no work), work calculation W = F·s·cosθ decreases as angle increases; (3) Inclined Plane scenario showing box on 30° incline, horizontal pulling force F, gravity components mg∥ (orange, opposes motion up incline) and mg⊥ (yellow, normal to surface), demonstrating work against gravity. Real-time visualization features: animated box motion across surface, dynamic force arrows scaling with magnitude, force component vectors with color-coded arrows (red=applied force, green=parallel component, purple=perpendicular, gray=friction, orange=gravity parallel, yellow=gravity perpendicular), work area visualization showing effective force component, displacement markers with distance labels, energy bar showing work by force (green) vs work against friction (red). Adjustable parameters: force F (10-200 N), angle θ (0-90°), friction f (0-50 N), displacement s (1-50 m), mass m (1-100 kg), velocity v (0.1-10 m/s). Display options: show/hide force components (parallel/perpendicular arrows), show work area (highlight effective force path), show energy bar (work distribution bar). Animation controls: Animate button to show box moving with force arrows, Reset to default parameters. Real-time calculations: work W = F·s·cosθ (J), parallel force F∥ = F·cosθ (N), perpendicular force F⊥ = F·sinθ (N), net work (positive work - friction work), power P = F·v (W). Educational content covers definition of work as energy transfer, sign convention (positive work adds energy/accelerates, negative work removes energy/decelerates, zero work when F⊥s), force component decomposition using trigonometry, practical examples (lifting, vehicles, escalators, springs), work-energy theorem W_net = ΔKE = ½mv²² - ½mv₁², power vs work distinction (rate vs total). Color scheme: amber/yellow theme with oranges (#f59e0b, #fbbf24) for headers, blue box (#3b82f6), red force arrows (#ef4444), green parallel component (#10b981), purple perpendicular component (#8b5cf6), gray friction (#9ca3af), orange gravity parallel (#f59e0b), yellow gravity perpendicular (#fbbf24), blue displacement (#0891b2), green positive work (#10b981), red negative work (#ef4444). Multi-language support (zh, en, de, fr, es, ru, pt) with complete translations for all UI elements, formulas, scenarios, and educational content. Interactive controls: force magnitude slider, angle adjustment, friction control, mass and velocity parameters, scenario switching (horizontal/angled/incline), animation playback and reset. Historical context: James Prescott Joule (1818-1889) and the mechanical equivalent of heat, Gaspard-Gustave Coriolis's 1829 definition of work as 'force-distance product'.

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