Physics · Class 9-10 · CBSE
Work, Energy, Power and Conservation Laws
Understand scientific definition of work (positive, negative, zero), kinetic energy, gravitational potential energy, law of conservation of mechanical energy, and power in commercial units.
1Scientific Definition of Work
In physics,Workis done only when a force produces displacement along the direction of the force. If displacement is zero, work done is strictly zero regardless of muscular effort.
Work Done Formula
- W = Work done in Joules (1 J = 1 N·m)
- F = Applied force in Newtons
- s = Displacement produced in metres
- θ = Angle between force and displacement vectors
Sign of Work Done & Real Life Scenarios
| Type of Work | Angle (θ) | Physical Meaning | Real-World Example |
|---|---|---|---|
| Positive Work | 0° ≤ θ < 90° | Force accelerates the body in displacement direction | Pulling a toy car across the floor |
| Negative Work | 90° < θ ≤ 180° | Force opposes motion and retards velocity | Braking force stopping a car; friction |
| Zero Work | θ = 90° or s = 0 | Force perpendicular to motion or no movement | Coolie carrying luggage on head walking horizontally |
Positive Work
- Angle (θ)
- 0° ≤ θ < 90°
- Physical Meaning
- Force accelerates the body in displacement direction
- Real-World Example
- Pulling a toy car across the floor
Negative Work
- Angle (θ)
- 90° < θ ≤ 180°
- Physical Meaning
- Force opposes motion and retards velocity
- Real-World Example
- Braking force stopping a car; friction
Zero Work
- Angle (θ)
- θ = 90° or s = 0
- Physical Meaning
- Force perpendicular to motion or no movement
- Real-World Example
- Coolie carrying luggage on head walking horizontally
2Forms of Mechanical Energy: Kinetic & Potential
Kinetic Energy (KE)is energy possessed due to motion, whereasPotential Energy (PE)is stored energy due to position or deformed configuration.
Kinetic Energy vs Gravitational Potential Energy
| Parameter | Kinetic Energy (KE) | Potential Energy (PE) |
|---|---|---|
| Formula | KE = (1/2) · m · v² | PE = m · g · h |
| Source | Velocity of moving mass | Position above reference plane against gravity |
| Velocity Dependence | Quadratically dependent (doubling v quadruples KE) | Independent of velocity (depends purely on height h) |
| Sign | Always positive (since v² ≥ 0) | Can be positive, zero, or negative depending on datum |
Formula
- Kinetic Energy (KE)
- KE = (1/2) · m · v²
- Potential Energy (PE)
- PE = m · g · h
Source
- Kinetic Energy (KE)
- Velocity of moving mass
- Potential Energy (PE)
- Position above reference plane against gravity
Velocity Dependence
- Kinetic Energy (KE)
- Quadratically dependent (doubling v quadruples KE)
- Potential Energy (PE)
- Independent of velocity (depends purely on height h)
Sign
- Kinetic Energy (KE)
- Always positive (since v² ≥ 0)
- Potential Energy (PE)
- Can be positive, zero, or negative depending on datum
Conservation of Mechanical Energy of a Freely Falling Ball
- 1
1. At highest point H: Velocity v = 0 ⇒ KE = 0, PE = mgH ⇒ Total Energy E = mgH
- 2
2. At midpoint h: Part of PE has converted to KE ⇒ Total Energy = (1/2)mv² + mgh = mgH
- 3
3. Just before striking ground: Height h = 0 ⇒ PE = 0, striking speed v = √(2gH) ⇒ KE = (1/2)m(2gH) = mgH
- 4
4. Conclusion: Mechanical Energy is strictly conserved at every instant in the absence of air friction.
3Power and Commercial Units of Energy
Poweris the rate of doing work or rate of energy transfer: P = W / t. Its SI unit is theWatt (W), where 1 Watt = 1 Joule/second.
Everyday Power & Commercial Electricity Units
| Unit | Standard Value | Common Application |
|---|---|---|
| 1 Kilowatt (kW) | 1,000 Watts | Appliance power ratings (AC, heater, geyser) |
| 1 Horsepower (hp) | 746 Watts | Electric motors and automotive engine power |
| 1 Kilowatt-hour (kWh) | 3.6 × 10⁶ Joules | 1 Board of Trade Unit on household electric meter |
1 Kilowatt (kW)
- Standard Value
- 1,000 Watts
- Common Application
- Appliance power ratings (AC, heater, geyser)
1 Horsepower (hp)
- Standard Value
- 746 Watts
- Common Application
- Electric motors and automotive engine power
1 Kilowatt-hour (kWh)
- Standard Value
- 3.6 × 10⁶ Joules
- Common Application
- 1 Board of Trade Unit on household electric meter
Real-life example · Electricity Bill Calculation Example
A 100 W bulb runs 10 hours daily for 30 days. Energy consumed = (100 W / 1000) × 10 h × 30 = 30 kWh (30 units). At ₹6 per unit, monthly cost = 30 × 6 = ₹180.
4Exam Corner: Tips, Mistakes & Board Questions
Critical Formulas for Exam Numericals
- Work-Energy Theorem: Net Work Done = Change in Kinetic Energy = (1/2)m(v² - u²).
- 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ Joules.
- When a satellite orbits Earth in circular path, gravitational force is perpendicular to velocity at every instant, so work done by gravity is zero.
Exam question · CBSE Class 9/10 Board
- A.3 times
- B.6 times
- C.9 times
- D.Remains unchanged
- Kinetic energy is proportional to the square of velocity: KE = (1/2) m v².
- When velocity becomes 3v: KE_new = (1/2) m (3v)² = 9 × [(1/2) m v²] = 9 × KE_initial.
- Therefore, kinetic energy becomes 9 times.
Answer: C. 9 times
Remember
- Work is done only when displacement occurs along force direction: ==W = F·s·cosθ==.
- Kinetic energy ==KE = (1/2)mv²and Potential energy
- In an isolated system, total mechanical energy ==KE + PE = constant==.
- Commercial electrical unit: ==1 kWh = 3.6 × 10⁶ Joules==.
Check yourself
Question 1
How much work is done by a porter carrying a 50 kg load on his head walking 100 m on a level road?