This MCQ module is based on: Conservation of Energy and Power
TOPIC 24 OF 50
Conservation of Energy and Power
🎓 Class 9
Science
CBSE
Theory
Ch 7 — Work, Energy, and Simple Machines
⏱ ~13 min
🌐 Language: [gtranslate]
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7.7 Law of Conservation of Energy
If you watch a pendulum carefully, it slows at the top of each swing, speeds up at the bottom, slows again, speeds again. A bouncing ball rises a little less each time. A torch battery dims after long use. Yet through all these changes, careful experiments show that energy is never created or destroyed. It is only transferred from one body to another or transformed from one form into another.
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.
A demonstration — the freely falling ball
Suppose a ball of mass \(m\) is dropped from a height \(H\) above the ground. Take \(g = 10\) m s⁻². At the start (point A) the ball is at rest, so its kinetic energy is zero and all the mechanical energy is potential:
\[ \text{At A:}\quad \text{PE}_A = mgH,\quad \text{KE}_A = 0 \]
While falling, suppose it has dropped a distance \(x\) and reached point B at height \((H-x)\) with speed \(v\). Using \(v^2 = 2gx\):
\[ \text{KE}_B = \tfrac{1}{2} m v^{2} = \tfrac{1}{2} m (2gx) = mgx \]
\[ \text{PE}_B = mg(H-x) \]
\[ \text{Total}_B = \text{KE}_B + \text{PE}_B = mgx + mg(H-x) = mgH \]
Just before striking the ground (point C, height = 0), all the PE has converted to KE: \(\text{KE}_C = mgH,\;\text{PE}_C = 0\). At every point along the fall the sum (KE + PE) is the same — proving conservation of mechanical energy in the absence of air resistance.
🍎 Free Fall — Step through the energy conversion L3 Apply
An apple falls from height \(H\). Click positions A → B → C in turn and apply conservation of mechanical energy: at every height, PE + KE = constant.
Click position A, B, or C above to step through the conversion of PE into KE.
7.8 Forms of Energy
Energy comes dressed in many forms. Each form can convert into another under suitable conditions, but the total amount stays fixed.
| Form | Source / Description | Everyday Example |
|---|---|---|
| Mechanical | Kinetic + potential energy of moving or raised bodies | Flowing river, stretched bow, swinging hammer |
| Heat (Thermal) | Energy due to random motion of molecules | Hot tea, an electric iron, friction-generated warmth |
| Light | Electromagnetic energy our eyes detect | Sunlight, glowing bulb, candle flame |
| Sound | Energy carried by vibrations through a medium | Drumbeat, human voice, ringing bell |
| Electrical | Energy of moving charges | Current in wires, lightning, dry cell |
| Chemical | Energy stored in chemical bonds | Food, petrol, coal, dry cell electrolyte |
| Nuclear | Energy locked in atomic nuclei | Sun's core, nuclear power plants, nuclear bombs |
Energy transformations in everyday devices
- Electric bulb: electrical → light + heat
- Loudspeaker: electrical → sound
- Battery torch: chemical → electrical → light + heat
- Solar cell: light → electrical
- Hydroelectric plant: gravitational PE of water → KE → electrical
- Burning candle: chemical → light + heat
- Eating food: chemical (food) → mechanical (muscle work) + heat (body warmth)
7.9 Activity — Tracking Energy Through Forms
Activity 7.2 — Trace the EnergyL4 Analyse
Predict first: When you switch on a battery torch and shine it on a wall, what is the original source of the light energy you see?
- List the form of energy stored inside a torch when it is off.
- Switch the torch on. Identify the new forms of energy now appearing.
- Now think backwards: where did the chemical energy in the cell come from in the first place?
- Draw an energy-flow chart from the original sunlight all the way to the light hitting the wall.
Observations: (1) Stored as chemical energy in the cell. (2) Chemical → electrical (current) → light + heat (in bulb). (3) The chemicals were manufactured using energy ultimately obtained from sunlight (solar → electrical → chemical during cell manufacture). (4) Sunlight → electricity in factory → chemical energy in cell → electrical (when used) → light + heat at bulb.
Conclusion: Almost every form of energy on Earth is traceable to the Sun. Energy keeps changing form, but the total never changes.
Conclusion: Almost every form of energy on Earth is traceable to the Sun. Energy keeps changing form, but the total never changes.
7.10 Power — Rate of Doing Work
Two students each lift a 10 kg suitcase to a height of 2 m. The first does it in 2 seconds; the second takes 10 seconds. Both did the same amount of work (W = mgh = 200 J). But the first student is clearly more powerful — she did the work faster. To compare such situations, we define power.
Definition. Power is the rate at which work is done (or energy is transferred). Mathematically,
\[ P = \frac{W}{t} = \frac{\text{Energy used}}{\text{Time taken}} \]
SI unit and other units of power
- Watt (W): 1 watt = 1 joule per second. Named after James Watt.
- Kilowatt (kW): 1 kW = 10³ W = 1000 W. Used for household appliances and motors.
- Megawatt (MW): 1 MW = 10⁶ W. Used for power-station outputs.
- Horsepower (hp): a non-SI unit, 1 hp ≈ 746 W. Often quoted for vehicles and motors.
An alternative form of P
If a constant force \(F\) moves a body with constant velocity \(v\) along its line of action, then in time \(t\) the work done is \(W = F\,(v\,t)\), and so
\[ P = \frac{W}{t} = \frac{F\,v\,t}{t} = F\,v \]
This form is useful for vehicles moving at steady speed against friction or air drag.
7.11 Worked Numericals on Power
Example 1 — Lifting a load L3
A 50 kg girl runs up a flight of stairs of vertical height 4 m in 5 s. Find the power she develops. (g = 10 m s⁻²)
Work done against gravity: W = mgh = 50 × 10 × 4 = 2000 J.
P = W/t = 2000 / 5 = 400 W.
Example 2 — Power of a pump L3
A water pump lifts 600 kg of water through a vertical height of 15 m in one minute. Find its power.
W = mgh = 600 × 10 × 15 = 90,000 J.
t = 60 s. P = 90,000 / 60 = 1500 W = 1.5 kW.
Example 3 — From P = Fv L3
A car moves at a steady 20 m s⁻¹ against a total resistive force of 600 N. Find the power developed by its engine.
P = F v = 600 × 20 = 12 000 W = 12 kW.
In horsepower: P ≈ 12 000 / 746 ≈ 16 hp.
Example 4 — Comparing two motors L4
Motor A does 600 J of work in 5 s; motor B does 1200 J of work in 8 s. Which motor is more powerful?
P(A) = 600 / 5 = 120 W.
P(B) = 1200 / 8 = 150 W.
Motor B is more powerful.
7.12 The Commercial Unit of Energy — Kilowatt-hour
The joule is convenient for laboratory problems but far too small for billing electricity. Your home consumes millions of joules every day. Electricity boards therefore use a much larger unit — the kilowatt-hour (kWh), often called simply a "unit" on the bill.
Conversion:
\[ 1\;\text{kWh} = 1\;\text{kW} \times 1\;\text{h} = 1000\;\text{W} \times 3600\;\text{s} = 3.6\times 10^{6}\;\text{J} \]
Example 5 — Reading the meter L3
A family uses a 100 W bulb for 10 hours, a 1500 W heater for 2 hours and a 60 W fan for 8 hours in a day. Find total energy consumed in kWh, and the bill at ₹6 per unit.
Bulb: 100 × 10 = 1000 Wh = 1 kWh.
Heater: 1500 × 2 = 3000 Wh = 3 kWh.
Fan: 60 × 8 = 480 Wh = 0.48 kWh.
Total = 1 + 3 + 0.48 = 4.48 kWh. Bill = 4.48 × 6 = ₹26.88.
Example 6 — kWh to joules L2
Express 5 kWh in joules.
5 × 3.6 × 10⁶ = 1.8 × 10⁷ J.
Quick Recap
| Concept | Key relation / fact |
|---|---|
| Conservation of energy | Total energy of an isolated system stays constant; energy only changes form. |
| Free fall | KE + PE = mgH at every point. |
| Power | P = W/t = F v ; SI unit watt (W). |
| 1 kW | 10³ W |
| 1 hp | ≈ 746 W |
| 1 kWh | 3.6 × 10⁶ J |
Competency-Based Questions
A 2 kg ball is dropped from a height of 5 m above the ground. Take g = 10 m s⁻² and ignore air resistance. The ball falls freely.
Q1. What is the total mechanical energy of the ball at the moment it is released? L3
(c) Initially KE = 0 and PE = mgh = 2 × 10 × 5 = 100 J → Total = 100 J.
Q2. What is the kinetic energy of the ball just before it hits the ground? Justify. L3
By conservation of energy, all PE converts to KE: KE = 100 J. Equivalently v² = 2gh = 100, so v = 10 m s⁻², KE = ½ × 2 × 100 = 100 J.
Q3. A 60 W ceiling fan runs for 5 hours. Find the energy consumed in kWh and joules. L3
Energy = P × t = 60 × 5 = 300 Wh = 0.3 kWh = 0.3 × 3.6 × 10⁶ = 1.08 × 10⁶ J.
Q4. Identify the energy transformations in: (a) electric heater (b) microphone (c) photosynthesis. L2
(a) electrical → heat + light. (b) sound → electrical. (c) light (solar) → chemical (stored in glucose).
Q5. True or False: "1 kWh and 1 watt-hour represent the same amount of energy." L1
False. 1 kWh = 1000 Wh — they differ by a factor of 1000.
Assertion–Reason Questions
Options: (A) Both A and R are true and R is the correct explanation of A. (B) Both true but R is not the correct explanation. (C) A true, R false. (D) A false, R true.
A: The total mechanical energy of a freely falling body remains constant in the absence of air resistance.
R: The kinetic energy gained at any instant equals the loss in potential energy at that instant.
(A) Both true and R correctly explains A. Conservation: ΔKE = −ΔPE, so KE + PE = constant.
A: A more powerful machine necessarily does more work.
R: Power is the rate of doing work.
(D) Assertion is false — a powerful machine does work faster, not necessarily more in total. Reason is true.
A: 1 kilowatt-hour equals 3.6 million joules.
R: 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J.
(A) Both true; R is the direct calculation that justifies A.
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