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Calculate work done (W = F × d × cos θ), power from work and time (P = W/t), or work from power and time. Covers the work-energy theorem and real-world applications in mechanics and engineering.
In physics, work is done when a force causes displacement in the direction of the force: W = F × d × cos θ. Work and energy share the same unit (Joules). Power is the rate of doing work (P = W/t), measured in Watts. Understanding work and power is essential for engineering, motor selection, and energy analysis.
In physics, work (W) is defined as the product of force and displacement in the direction of the force: W = F × d × cos θ, where θ is the angle between the force vector and displacement vector. Only the component of force parallel to motion does work. A force perpendicular to motion (like centripetal force in circular motion) does zero work. Work is measured in Joules (J) — the same unit as energy, because work is a transfer of energy.
Power (P) is the rate at which work is done or energy is transferred: P = W/t = ΔE/Δt. Power is measured in Watts (W) where 1 W = 1 J/s. High power means doing the same work in less time. A 100 kW engine and a 10 kW engine doing the same work take 10× different times to complete it.
| Situation | Work Done | Explanation |
|---|---|---|
| Lifting a weight | W = mgh (force × vertical dist.) | All force in direction of motion |
| Pushing on incline | W = F × d × cos θ | Only parallel component counts |
| Friction (kinetic) | W = -f × d (negative work) | Opposes motion, removes energy |
| Centripetal force | W = 0 | Perpendicular to motion always |
| Gravity (free fall) | W = mgh (positive, downward) | Force and motion in same direction |
| Compressed spring | W = ½kx² | Stored as elastic PE |
Efficiency (η) = useful power output / total power input × 100%. No real machine is 100% efficient — energy is always lost to friction, heat, sound, and other dissipation mechanisms. Internal combustion engine: 25-35% efficiency (65-75% heat loss). Electric motor: 85-97% efficiency. Steam turbine: 35-45%. Photovoltaic solar cell: 15-25%. LED light: 40-50% (vs incandescent 5%). Hydroelectric: 85-95% (most efficient large-scale generation). Human body: 25% mechanical efficiency for cycling, 20-25% for running. A cyclist generating 200W mechanical power requires ~800W food energy input.
Net work done = change in kinetic energy: W_net = ΔKE = ½mv_f² - ½mv_i². Braking force calculation: Car (1500 kg) braking from 100 km/h (27.78 m/s) to 0. ΔKE = ½ × 1500 × 27.78² = 578,700 J. If stopping distance = 40m: Braking force = W/d = 578,700/40 = 14,467 N = 14.5 kN. This equals μ × mg: μ = 14,467/(1500 × 9.81) = 0.984 ≈ dry asphalt coefficient. Power required to maintain constant speed: P = F_drag × v. At 100 km/h (27.78 m/s), aerodynamic drag ~800 N: P = 800 × 27.78 = 22,224 W = 22.2 kW ≈ 30 hp just to overcome air resistance.
1 Joule (J) = 1 N·m = 1 kg·m²/s². Common conversions: 1 kWh (kilowatt-hour) = 3,600,000 J = 3.6 MJ (used for electrical energy billing). 1 calorie (thermochemical) = 4.184 J. 1 food Calorie (Cal) = 1 kcal = 4,184 J. 1 BTU (British Thermal Unit) = 1,055 J. 1 horsepower (hp) = 745.7 W. 1 electron-volt (eV) = 1.602×10⁻¹⁹ J (used in atomic/nuclear physics). 1 ton of TNT = 4.184 GJ. Energy consumption: USA average home ~900 kWh/month = 3,240 MJ/month. Human daily food intake ~2000 Cal = 8,368 kJ.
Always ensure units are consistent before calculating. This calculator uses SI units (International System): meters (m) for distance, kilograms (kg) for mass, seconds (s) for time, Newtons (N) for force, Joules (J) for energy, Watts (W) for power, and Pascals (Pa) for pressure. When converting from other unit systems (imperial, CGS), convert all values before entering them into the calculator.
Gravitational acceleration on Earth: g = 9.81 m/s² (standard: 9.80665 m/s²). Speed of light in vacuum: c = 2.998×10⁸ m/s. Universal gravitational constant: G = 6.674×10⁻¹¹ N·m²/kg². Speed of sound in air at 20°C: 343 m/s. Atmospheric pressure at sea level: 101,325 Pa = 1 atm. These constants appear in virtually every branch of physics and engineering.
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