ICSE Class 10 Physics Chapter 2 covers foundational concepts of Work, Energy, and Power, focusing on definitions, formulas, and energy conservation. Key sub-topics include the definition/units of work, potential/kinetic energy, the work-energy theorem, conservation of mechanical energy, and power.
- Work:
- Definition, SI units (Joule), and CGS units (Erg).
- Conditions for work done (force and displacement).
- Expression for work ($W = Fs\cos\theta$).
- Positive, negative, and zero work (e.g., centripetal force).
- Energy:
- Definition and SI units.
- Mechanical Energy:
- Potential Energy (): Gravitational potential energy ($mgh$) and elastic potential energy.
- Kinetic Energy (): Formula $\frac{1}{2}mv^2$ and dependence on mass/velocity.
- Work-Energy Theorem: Work done equals the change in kinetic energy.
- Conservation of Mechanical Energy: Transformation of energy, specifically $P.E. \rightleftharpoons K.E.$ (e.g., a free-falling body).
- Different forms of energy (Heat, Electrical, Nuclear, Sound, Light) and conversions.
- Power:
- Definition: Rate of doing work.
- Units (Watt, Horsepower, kW, MW, GW).
- Relationship between Power, Force, and Velocity ($P = Fv$).
- Energy Sources and Sustainability:
- Renewable vs. Non-renewable sources.
- Energy degradation and conservation (e.g., greenhouse effect).
- Machines (Related Topic):
- Concepts of Mechanical Advantage, Velocity Ratio, and Efficiency ($\eta = \text{Work Output} / \text{Work Input}$).
1. Definition of Work
In physics, Work is defined as the product of the component of the force in the direction of the displacement and the magnitude of this displacement. It is not merely physical effort; for work to be "done," a force must cause an object to move.
Mathematical Expression
The general formula for work done ($W$) by a constant force ($F$) causing a displacement ($s$) at an angle ($\theta$) is:
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$W$: Work done
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$F$: Magnitude of the force applied
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$s$: Magnitude of the displacement
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$\theta$: The angle between the force vector and the displacement vector
2. Conditions for Work Done
For work to be non-zero, two primary conditions must be satisfied simultaneously:
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Application of Force: A net force must act on the body ($F \neq 0$).
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Displacement: The body must undergo a displacement in a direction that is not perpendicular to the force ($s \neq 0$).
When is Work Zero?
Work is considered zero ($W = 0$) in the following scenarios:
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No Displacement: Pushing against a solid wall. Even if force is high, $s = 0$, so $W = 0$.
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Perpendicular Force: When the force is acting at $90^\circ$ to the direction of motion ($\cos(90^\circ) = 0$).
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Example: A coolie carrying a load on his head while walking on a level road; the force of gravity is downward, but displacement is horizontal.
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Example: Centripetal Force acting on a body in circular motion.
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3. Units of Work
Work is a scalar quantity, meaning it has magnitude but no direction.
| System | Unit | Definition |
| SI System | Joule (J) | $1\text{ J} = 1\text{ Newton} \times 1\text{ Meter}$ |
| CGS System | Erg | $1\text{ erg} = 1\text{ Dyne} \times 1\text{ Centimeter}$ |
Conversion Factor: $1\text{ Joule} = 10^7\text{ ergs}$
4. Types of Work
The nature of work depends on the angle $\theta$ between force and displacement:
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Positive Work ($0^\circ \leq \theta < 90^\circ$): Force and displacement are in the same direction (e.g., a horse pulling a cart).
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Negative Work ($90^\circ < \theta \leq 180^\circ$): Force acts in the opposite direction of motion (e.g., Frictional force acting on a moving car).
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Zero Work ($\theta = 90^\circ$): As discussed, force is perpendicular to displacement.
1. Definition of Work
In physics, Work is defined as the product of the component of the force in the direction of the displacement and the magnitude of this displacement. It is not merely physical effort; for work to be "done," a force must cause an object to move.
Mathematical Expression
The general formula for work done ($W$) by a constant force ($F$) causing a displacement ($s$) at an angle ($\theta$) is:
-
$W$: Work done
-
$F$: Magnitude of the force applied
-
$s$: Magnitude of the displacement
-
$\theta$: The angle between the force vector and the displacement vector
2. Conditions for Work Done
For work to be non-zero, two primary conditions must be satisfied simultaneously:
-
Application of Force: A net force must act on the body ($F \neq 0$).
-
Displacement: The body must undergo a displacement in a direction that is not perpendicular to the force ($s \neq 0$).
When is Work Zero?
Work is considered zero ($W = 0$) in the following scenarios:
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No Displacement: Pushing against a solid wall. Even if force is high, $s = 0$, so $W = 0$.
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Perpendicular Force: When the force is acting at $90^\circ$ to the direction of motion ($\cos(90^\circ) = 0$).
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Example: A coolie carrying a load on his head while walking on a level road; the force of gravity is downward, but displacement is horizontal.
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Example: Centripetal Force acting on a body in circular motion.
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3. Units of Work
Work is a scalar quantity, meaning it has magnitude but no direction.
| System | Unit | Definition |
| SI System | Joule (J) | $1\text{ J} = 1\text{ Newton} \times 1\text{ Meter}$ |
| CGS System | Erg | $1\text{ erg} = 1\text{ Dyne} \times 1\text{ Centimeter}$ |
Conversion Factor: $1\text{ Joule} = 10^7\text{ ergs}$
4. Types of Work
The nature of work depends on the angle $\theta$ between force and displacement:
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Positive Work ($0^\circ \leq \theta < 90^\circ$): Force and displacement are in the same direction (e.g., a horse pulling a cart).
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Negative Work ($90^\circ < \theta \leq 180^\circ$): Force acts in the opposite direction of motion (e.g., Frictional force acting on a moving car).
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Zero Work ($\theta = 90^\circ$): As discussed, force is perpendicular to displacement.
1. Concept of Energy
Energy is defined as the capacity to do work. Like work, it is a scalar quantity.
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SI Unit: Joule (J)
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CGS Unit: Erg
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Relationship: $1 \text{ Joule} = 10^7 \text{ ergs}$
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Other Units: * Watt-hour (Wh): $1 \text{ Wh} = 3600 \text{ J}$
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Kilowatt-hour (kWh): The commercial unit of electrical energy ($1 \text{ kWh} = 3.6 \times 10^6 \text{ J}$).
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Electron volt (eV): Used in atomic physics ($1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$).
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2. Mechanical Energy
Mechanical energy is the energy possessed by a body due to its state of rest or state of motion. It exists in two forms: Potential Energy and Kinetic Energy.
A. Potential Energy (P.E.)
The energy possessed by a body by virtue of its specific position or changed configuration.
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Gravitational P.E.: Energy due to height above the earth's surface.
$$\text{P.E.} = mgh$$(Where $m$ = mass, $g$ = acceleration due to gravity, and $h$ = height)
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Elastic P.E.: Energy stored in a deformed body (like a compressed spring or a stretched rubber band).
B. Kinetic Energy (K.E.)
The energy possessed by a body by virtue of its state of motion.
(Where $m$ = mass and $v$ = velocity)
3. The Work-Energy Theorem
This theorem states that the work done by a force on a moving body is equal to the increase (change) in its kinetic energy.
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If work is done on the body, K.E. increases.
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If work is done by the body against a force (like friction), K.E. decreases.
4. Conservation of Mechanical Energy
According to the Law of Conservation of Energy, energy can neither be created nor destroyed; it can only be transformed from one form to another. In the absence of friction (conservative forces), the total mechanical energy (P.E. + K.E.) remains constant.
Example: A Free-Falling Body
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At the highest point: K.E. is zero, and P.E. is maximum ($mgh$).
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During the fall: P.E. decreases as it converts into K.E.
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Just before hitting the ground: P.E. is zero, and K.E. is maximum.
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At any point: $P.E. + K.E. = \text{Constant}$.
5. Forms of Energy and Conversions
Energy frequently changes forms to perform useful tasks:
| Device | Energy Conversion |
| Electric Motor | Electrical $\rightarrow$ Mechanical |
| Generator | Mechanical $\rightarrow$ Electrical |
| Photosynthesis | Light $\rightarrow$ Chemical |
| Battery/Cell | Chemical $\rightarrow$ Electrical |
| Electric Bulb | Electrical $\rightarrow$ Light & Heat |
6. Energy Sources and Sustainability
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Renewable Sources: Energy from sources that are naturally replenished (Solar, Wind, Hydro, Biomass).
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Non-renewable Sources: Sources that will eventually run out (Coal, Petroleum, Natural Gas).
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Energy Degradation: During energy transformation, a part of the energy is converted into non-useful forms (usually heat due to friction), which is called the degradation of energy.
1. Definition of Power
Power is defined as the rate of doing work or the rate at which energy is transferred or transformed. While work tells us how much energy is used, power tells us how fast it is being used.
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Mathematical Formula:
$$P = \frac{W}{t}$$(Where $P$ is Power, $W$ is Work done, and $t$ is Time taken)
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Quantity Type: Scalar quantity.
2. Power in Terms of Force and Velocity
Power can also be expressed in terms of the force applied to an object and the constant velocity at which it moves.
Since $W = F \times s$ (Force $\times$ Displacement), we can substitute this into the power formula:
Because $\frac{s}{t} = v$ (Velocity), the formula becomes:
Key Takeaway: For a machine to maintain a higher speed ($v$) while applying a specific force ($F$), it requires more power.
3. Units of Power
Power is measured in various units depending on the scale of the work being done:
SI Unit: The Watt (W)
One Watt is defined as the power of an agent which does work at the rate of 1 Joule per second.
Larger Units:
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Kilowatt (kW): $1 \text{ kW} = 10^3 \text{ W}$
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Megawatt (MW): $1 \text{ MW} = 10^6 \text{ W}$
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Gigawatt (GW): $1 \text{ GW} = 10^9 \text{ W}$
Engineering Unit: Horsepower (hp)
Historically used for engines and motors:
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1 hp = 746 W (approximately 0.75 kW)
4. Factors Affecting Power
The power spent by a source depends on two factors:
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The amount of work done by the source: Power is directly proportional to work ($P \propto W$).
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The time taken by the source: Power is inversely proportional to time ($P \propto \frac{1}{t}$).
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Example: If two people climb the same set of stairs, the one who reaches the top faster has spent more power, even though both performed the same amount of work.
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5. Difference Between Work and Power
| Feature | Work | Power |
| Definition | Measure of energy transfer. | Rate of energy transfer. |
| Time Factor | Independent of time. | Dependent on time. |
| SI Unit | Joule (J) | Watt (W) |
Quick Revision Table: Power Formulae
| To find... | Use Formula | Given Variables |
| Standard Power | $P = \frac{W}{t}$ | Work and Time |
| Mechanical Power | $P = F \times v$ | Force and Velocity |
| Electrical Power | $P = V \times I$ | Voltage and Current |
