Work, Energy and Power
~10 min read
- Work: W = F·d·cosθ. Joule. Work-energy theorem: net work = change in KE.
- KE and PE: KE = ½mv². PE (gravitational) = mgh. PE (spring) = ½kx².
- Power: Rate of doing work. P = W/t = F·v. SI: Watt. 1 HP = 746 W.
Energy is a conserved quantity. Work transfers energy. Power is the rate. NDA tests formulas, work-energy theorem, and conservation of energy.
Work
- Definition: Work is done when a force causes displacement in its direction.
- W = F·d·cosθ, where θ is angle between force and displacement.
- If θ = 0° (force in direction of motion): W = Fd. Maximum positive work.
- If θ = 90° (force perpendicular to motion): W = 0. No work done. (e.g., centripetal force does no work in circular motion.)
- If θ = 180° (force opposite to motion): W = -Fd. Negative work (e.g., friction).
- SI unit: Joule (J) = N·m.
Kinetic and Potential Energy
| Type | Formula | Description |
|---|---|---|
| Kinetic Energy (KE) | ½mv² | Energy due to motion |
| Gravitational PE | mgh | Energy due to height above reference |
| Elastic PE (spring) | ½kx² | Energy stored in stretched/compressed spring |
| Mechanical Energy | KE + PE | Conserved in absence of friction |
Conservation of Energy
Energy cannot be created or destroyed; only transformed from one form to another. Total energy of an isolated system is constant.
Examples:
- Falling object: PE → KE.
- Pendulum at extremes (high) → KE = 0, PE = max. At bottom (low) → KE = max, PE = min.
- Spring oscillating: PE (compressed/extended) ↔ KE (at natural length).
- Hydroelectric: gravitational PE of water → KE of falling water → electrical energy.
Power
- Power = rate of doing work. P = W/t.
- For constant force and velocity: P = F·v.
- SI unit: Watt (W) = J/s.
- 1 horsepower (HP) = 746 W.
- Domestic electricity is billed in kilowatt-hour (kWh) — energy unit, not power. 1 kWh = 3.6 × 10⁶ J.
Collisions
| Type | Momentum | KE |
|---|---|---|
| Elastic | Conserved | Conserved |
| Inelastic | Conserved | Not conserved (lost as heat, sound) |
| Perfectly inelastic | Conserved; bodies stick together | Maximum loss |
NDA PYQ Examples
Q: The SI unit of power is:
(a) Joule (b) Newton (c) Watt (d) HP
Answer: (c) Watt = J/s.
Q: 1 HP equals:
(a) 100 W (b) 500 W (c) 746 W (d) 1000 W
Answer: (c) 746 W.
Q: When force is perpendicular to displacement, work done is:
(a) Maximum (b) Negative (c) Zero (d) Half
Answer: (c) Zero (cos 90° = 0).
Q: In a perfectly elastic collision:
(a) Momentum is conserved but KE is not (b) Both momentum and KE are conserved (c) Neither conserved (d) Only mass conserved
Answer: (b) Both conserved.
Drill Work, Energy and Power for NDA
NDA-pattern items on Work, Energy and Power with answer keys and explanations.
Start Free Mock TestFrequently Asked Questions
Why is centripetal force perpendicular to motion?
In uniform circular motion, the velocity is along the tangent. Centripetal force is directed toward the centre — always perpendicular to velocity. Since force ⊥ displacement, no work is done. Speed (magnitude) stays constant; only direction changes.
What is the work-energy theorem?
Net work done on an object = change in its kinetic energy. W_net = ΔKE = ½m(v² - u²). It connects work and energy directly.
Are KE and momentum the same?
No. Momentum p = mv (vector, conserved in collisions). Kinetic energy KE = ½mv² (scalar, conserved only in elastic collisions). Two objects can have same momentum but different KE (depends on mass).
What is potential energy?
Stored energy due to position or configuration. Gravitational PE = mgh (height above reference). Elastic PE = ½kx² (spring deformation). PE converts to KE when released.
How does a roller coaster work?
Initial mechanical work lifts cars to top of first hill (storing PE). Then PE converts to KE as cars descend. Friction dissipates some energy as heat, so each subsequent hill must be lower than the previous.