Q1. A 2 kg ball is dropped from a height of 5 m. Find its kinetic energy just before hitting the ground (g = 10).
At the top: PE = mgh = 2 × 10 × 5 = 100 J
By conservation of energy, all PE → KE
KE just before impact = 100 J
Work and Energy — Class 9
Work, energy and power are three of the most tested ideas in Class 9. Compute each one live, then drill the numericals until the formulas stick.
WorkWork is done when a force moves a body in its own direction: W = F·s. SI unit: joule (J). No displacement ⇒ no work.
Kinetic energy (KE)Energy of a moving body, KE = ½·m·v². It equals the work needed to bring the body to that speed.
Potential energy (PE)Energy stored due to position or height, PE = m·g·h (gravitational).
PowerThe rate of doing work, P = W/t. SI unit: watt (W). 1 horsepower ≈ 746 W.
Work · Energy · Power calculator Interactive
Try different forces, masses, speeds and heights and watch the energies change (g = 10 m/s²).
Work, W = F·s—J
Kinetic energy, ½mv²—J
Potential energy, mgs—J
Notice kinetic energy depends on the SQUARE of speed — double the speed means four times the energy (and braking distance).
Numericals practice Interactive
Work, KE, PE and power problems with full solutions (g = 10 m/s²).
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Solved numericals
Q2. An electric bulb of 60 W is used for 5 hours a day. Find the energy in kWh used in 30 days.
Energy/day = 60 W × 5 h = 300 Wh = 0.3 kWh
In 30 days = 0.3 × 30 = 9 kWh (units)
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Work done | W = F·s | joule (J) |
| Kinetic energy | KE = ½ m v² | J |
| Potential energy | PE = m g h | J |
| Work–energy theorem | W = ΔKE | J |
| Power | P = W / t | watt (W) |
| Commercial unit of energy | 1 kWh = 3.6 × 10⁶ J | kWh |
Common mistakes & exam wins
- No work is done if there is no displacement, or if the force is perpendicular to the motion (e.g. carrying a bag horizontally).
- Kinetic energy ∝ v² — that small extra speed carries a lot more energy.
- By the work–energy theorem, net work done = change in kinetic energy.
- 1 unit of electricity = 1 kWh = 3.6 × 10⁶ J — used in every cost-of-energy numerical.
Frequently asked questions
When is work said to be done?
Work is done only when a force acts on a body and the body moves in the direction of the force: W = F·s.
What is the work–energy theorem?
The net work done on a body equals the change in its kinetic energy: W = ΔKE.
What is the difference between energy and power?
Energy (joule) is the capacity to do work; power (watt) is how fast that work is done, P = W/t.
What is the commercial unit of energy?
The kilowatt-hour (kWh), also called a "unit". 1 kWh = 3.6 × 10⁶ J.