Q1. A 2 kg ball falls from a height of 10 m. Find its speed just before hitting the ground (g = 10).
PE at top = mgh = 2×10×10 = 200 J → all becomes KE
½mv² = 200 ⇒ v² = 400/2 × ... ⇒ ½×2×v² = 200
v² = 200 ⇒ v ≈ 14.1 m/s
Work, Energy and Power — Class 11
Work transfers energy; power is how fast. Compute work, energy and power for any situation and practise the standard numericals.
WorkWork done by a force W = F·s·cosθ (force × displacement × cosine of the angle between them). Unit: joule (J).
Kinetic & potential energyKE = ½mv² (of motion); gravitational PE = mgh (of position). Both measured in joules.
Work–energy theoremThe net work done on a body equals the change in its kinetic energy: W = ΔKE.
PowerThe rate of doing work, P = W/t = F·v. Unit: watt (W).
Work · Energy · Power calculator Interactive
Change force, mass, speed and time to see work, kinetic energy and power update (g = 10 m/s²).
Work, W = F·s—J
Kinetic energy, ½mv²—J
Kinetic energy grows with the SQUARE of speed — doubling speed quadruples the energy (and stopping distance).
Numericals practice Interactive
Work, energy and power problems with steps (g = 10 m/s²).
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Solved numericals
Q2. A pump raises 100 kg of water to a height of 10 m in 20 s. Find its power (g = 10).
Work = mgh = 100 × 10 × 10 = 10000 J
P = W/t = 10000 / 20
P = 500 W
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Work | W = F s cosθ | joule (J) |
| Kinetic energy | KE = ½ m v² | J |
| Potential energy | PE = m g h | J |
| Power | P = W / t = F v | watt (W) |
| Work–energy theorem | W_net = ΔKE | J |
Common mistakes & exam wins
- No work is done when the force is perpendicular to the displacement (cos90° = 0).
- Use the work–energy theorem (W = ΔKE) to avoid finding acceleration.
- Energy is conserved: KE + PE stays constant when only gravity acts.
- Power P = Fv is handy when a force acts at a steady speed.
Frequently asked questions
What is the work–energy theorem?
The net work done on a body equals the change in its kinetic energy: W = ΔKE.
When is work done zero?
When there is no displacement, or when the force is perpendicular to the displacement (θ = 90°).
What is the difference between energy and power?
Energy (joule) is the capacity to do work; power (watt) is the rate at which work is done, P = W/t.