Work and Energy — Class 9 Physical Science
1. Work — The Scientific Definition
In everyday language, 'work' means any physical or mental effort. In PHYSICS, work is done only when a FORCE causes DISPLACEMENT. W = F × s × cos θ, where θ = angle between force and displacement.
Conditions for Work to Be Done
- A FORCE must act on the object.
- The object must undergo DISPLACEMENT.
- The force (or a component of it) must be in the DIRECTION of displacement.
Unit of Work: Joule (J). 1 J = 1 N × 1 m. 'One joule is the work done when a force of 1 newton displaces an object by 1 metre in the direction of the force.'
When Is Work ZERO?
- No displacement: You push a wall. You get tired. Your muscles do INTERNAL work. But PHYSICS says: zero displacement → zero work done ON the wall.
- Force perpendicular to displacement: A porter carries luggage on his head and walks horizontally. θ = 90°, cos90° = 0 → W = 0. The vertical force does NO work in horizontal displacement.
- Orbiting satellite: Gravity is always perpendicular to instantaneous velocity. No work is done (circular orbit).
Worked Examples
Example 1 — Positive Work: A force of 10 N pushes a box 5 m forward. θ = 0°, cos0° = 1. W = 10 × 5 × 1 = 50 J.
Example 2 — Negative Work: Friction of 8 N opposes motion. Box moves 3 m. θ = 180°, cos180° = −1. W = 8 × 3 × (−1) = −24 J. 'Negative work means the force OPPOSES the motion — energy is being REMOVED from the object.'
Example 3 — Work at an Angle: A force of 50 N pulls a sled at 30° to the horizontal. The sled moves 10 m. W = 50 × 10 × cos30° = 500 × 0.866 = 433 J. Only the HORIZONTAL component does work.
2. Energy
ENERGY is the CAPACITY to do work. Unit: Joule (J) — same as work. 'Energy and work are two faces of the same coin. Work DONE on an object INCREASES its energy. Work done BY an object DECREASES its energy.'
Kinetic Energy (KE) — Energy of Motion
KE = ½mv². Where m = mass (kg), v = speed (m/s).
Derivation Concept: Work done by a force accelerates an object from 0 to v. F = ma. s = v²/2a. W = F×s = ma × v²/2a = ½mv².
Worked Examples
Example: A car of mass 1000 kg moves at 20 m/s. KE = ½ × 1000 × 400 = 200,000 J = 200 kJ. If speed DOUBLES to 40 m/s: KE = ½ × 1000 × 1600 = 800 kJ. 'Speed DOUBLED → KE QUADRUPLED. This is why high-speed collisions are so much more destructive.'
Potential Energy (PE) — Energy of Position
Gravitational PE = mgh. Where h = height above reference level.
Derivation: To lift an object of mass m through height h, you apply force = mg (against gravity). Work done = F×s = mg×h. This work is STORED as PE.
Example: A 2 kg book lifted onto a shelf 1.5 m high. PE gained = 2 × 10 × 1.5 = 30 J.
3. Law of Conservation of Energy
Energy can NEITHER be created NOR destroyed. It can only be TRANSFORMED from one form to another. The total energy of an ISOLATED system remains CONSTANT.
Free Fall — KE and PE Exchange
A ball of mass m dropped from height h:
- At top: PE = mgh, KE = 0. Total = mgh.
- At height h/2: PE = mg(h/2), KE = mg(h/2). Total = mgh.
- Just before hitting ground: PE = 0, KE = mgh. Total = mgh.
'At EVERY instant, PE + KE = mgh = CONSTANT. The energy changes FORM but the TOTAL never changes.'
Applications
- Pendulum: At extremes — all PE. At lowest point — all KE. Total mechanical energy = constant (ignoring air resistance).
- Hydroelectric dam: PE of water behind dam → KE of falling water → KE of turbine → Electrical energy.
- Roller coaster: At top of hill — max PE. At bottom — max KE. Friction and air resistance convert some mechanical energy to HEAT.
4. Power
Power = Work done / Time taken = Energy transferred / Time. P = W/t. Unit: Watt (W). 1 W = 1 J/s.
Average power = Total work / Total time. Instantaneous power = F × v (force × instantaneous velocity).
Commercial Unit of Energy — Kilowatt-hour (kWh)
1 kWh = 1000 W × 3600 s = 3,600,000 J = 3.6 × 10⁶ J. 'kWh is a unit of ENERGY, not power. 1 unit on your electricity bill = 1 kWh.'
Example: An electric heater of 1000 W runs for 3 hours. Energy consumed = 1 kW × 3 h = 3 kWh = 3 units. Cost at ₹6/unit = ₹18.
5. Energy Transformation Chains
| Device | Input Energy | Output Energy |
|---|---|---|
| Electric motor | Electrical | Mechanical (KE) |
| Generator/Dynamo | Mechanical (KE) | Electrical |
| Solar cell | Light (solar) | Electrical |
| Microphone | Sound | Electrical |
| Loudspeaker | Electrical | Sound |
| Electric bulb | Electrical | Light + Heat |
| Battery (charging) | Electrical | Chemical |
| Battery (discharging) | Chemical | Electrical |
6. Common Mistakes
- 'Holding a heavy object is work': Zero displacement → zero work in physics. Muscles are working INTERNALLY, but no work is done ON the held object.
- Forgetting cos θ: Work = F×s×cosθ. When force and displacement are in the SAME direction (θ=0°), W=Fs. Otherwise, only the PARALLEL component counts.
- KE = mv² not ½mv²: The factor ½ is crucial. Missing it doubles the answer.
- 'Power and energy are the same': Power is the RATE of energy use. Energy is the TOTAL amount.
7. AP Exam Focus
| Topic | Marks |
|---|---|
| Work calculation (W=Fs cosθ) | 3-4 |
| KE and PE numericals | 4-5 |
| Conservation of energy | 4-5 |
| Power and kWh | 2-3 |
Quick Self-Test
- Work done when force of 10 N moves object 2 m at 60° to force? (Answer: 10×2×cos60° = 10 J.)
- KE of a 500 kg car at 10 m/s? (Answer: ½×500×100 = 25000 J = 25 kJ.)
- PE of 5 kg object at height 8 m? (Answer: 5×10×8 = 400 J.)
- A 60 W bulb runs for 5 hours. Energy consumed in kWh? (Answer: 60W×5h = 300 Wh = 0.3 kWh.)
- A ball dropped from height h. Speed just before hitting ground? (Answer: v = √(2gh). From ½mv² = mgh → v² = 2gh.)
