💡 Work and power
Work is energy transferred by a force acting over a displacement. Power is the rate at which work is done (or energy is transferred). SI units: joule (J) for work and energy, watt (W) for power.
Work & Power calculators
W = F d cos θ · P = W/t or P = F v
Force (F)
Displacement (d)
Angle θ (deg, from displacement)
deg
Work done
50 J
Work (W)
Time (t)
Average power
10 W
🏋️ Work & Power visualization
🧮Step-by-Step Solution▼ Show
| Concept | Formula | Meaning |
|---|---|---|
| Work done by constant force | W = F d cos θ | Work = force × displacement × cos(angle) |
| Work done by variable force | W = ∫ F dx | Area under force-displacement graph |
| Work-Energy Theorem | Wnet = ΔKE = ½ m vf² − ½ m vi² | Net work = change in kinetic energy |
| Power (rate of energy transfer) | P = W / t = dW/dt | Power = work per unit time |
| Instantaneous power | P = F v | When force and velocity are parallel |
About work and power
Work is done when a force causes a displacement. For a constant force at angle θ to the displacement, W = F d cos θ. For a variable force, work is the integral W = ∫ F dx (area under the F–x graph).
Work-Energy Theorem
The net work done on an object equals its change in kinetic energy: W_net = ΔKE. This links forces and motion via energy.
Power
Power P = W/t (average) or P = dW/dt (instantaneous). When force and velocity are in the same direction, P = F v. SI unit of power is the watt (W): 1 W = 1 J/s.