⚡ Fast Revision: Work & Energy Fundamentals
- Definition: Work is said to be done only when a force applied on a body produces displacement in the direction of the force.
- Zero Work: If displacement is zero or perpendicular to the force (e.g., carrying a load on head while walking).
- Energy Link: Energy is the capacity to do work. Work done = Energy spent.
Work/Energy: W/E | SI Unit: Joule (J)
CGS Unit: erg | Conversion: $1\ J = 10^7\ erg$
$W = F \times S$
($F$ = Force, $S$ = Displacement in the direction of force)
Assuming work is done by just holding a heavy box. Fix: Even if you feel tired, Work = 0 if the box doesn't move ($S = 0$).
⚡ Fast Revision: Kinetic & Potential Energy
- Potential Energy (P.E.): Energy possessed by a body due to its position (height) or configuration (stretched spring).
- Kinetic Energy (K.E.): Energy possessed by a body due to its state of motion.
- Conservation: In the absence of friction, Total Mechanical Energy (P.E. + K.E.) remains constant.
$P.E. = m \times g \times h$
$K.E. = \frac{1}{2} m v^2$
| Feature | Potential Energy | Kinetic Energy |
|---|---|---|
| Dependency | Height and Mass | Mass and Velocity |
| State | Energy at rest | Energy in motion |
| Example | Water in a dam | Flowing water |
Thinking K.E. doubles if velocity doubles. Fix: Since $K.E. \propto v^2$, if velocity doubles, Kinetic Energy becomes 4 times ($2^2$) greater.
⚡ Fast Revision: Power & Efficiency
- Definition: The rate of doing work or the rate at which energy is transferred.
- Time Dependency: Unlike work, power depends on the time taken to complete the task.
- Horsepower: A larger unit of power often used for engines ($1\ hp = 746\ W$).
$Power (P) = \frac{Work (W)}{Time (t)}$
$Efficiency (\eta) = \frac{\text{Output Energy}}{\text{Input Energy}} \times 100\%$
Power: P | SI Unit: Watt (W) or $J/s$
Commercial Unit: Kilowatt-hour (kWh) | Used for: Electrical Energy
| Feature | Work | Power |
|---|---|---|
| Definition | Force $\times$ Displacement | Work / Time |
| Time factor | Independent of time | Dependent on time |
| SI Unit | Joule (J) | Watt (W) |
Confusing Kilowatt (kW) with Kilowatt-hour (kWh). Fix: kW is a unit of Power; kWh is a unit of Energy ($1\ kWh = 3.6 \times 10^6\ J$).
⚡ Fast Revision: Energy Sources & Conversion
- Renewable: Sources that can be replenished naturally (e.g., Solar, Wind, Hydro, Biomass).
- Non-Renewable: Sources that cannot be replaced once used (e.g., Coal, Petroleum, Natural Gas).
- Conservation of Energy: Energy cannot be created or destroyed, only transformed from one form to another.
| Device | Energy Transformation |
|---|---|
| Electric Motor | Electrical $\rightarrow$ Mechanical |
| Generator | Mechanical $\rightarrow$ Electrical |
| Photosynthesis | Light $\rightarrow$ Chemical |
| Battery | Chemical $\rightarrow$ Electrical |
Definition: Solar energy received per unit area per unit time at the earth's surface.
Approx Value: $1.4\ kW/m^2$ (or $1.4\ kJ/s/m^2$)
Labeling "Nuclear Energy" as renewable. Fix: While low-carbon, Uranium is a finite resource, so Nuclear energy is technically non-renewable.