Work and Energy (NCERT Std 9)

Cheatsheet Content

### Work Done by a Force - **Definition:** Work is done when a force causes a displacement. - **Formula:** $W = F \times s$ - $W$: Work done (Joules, J) - $F$: Force applied (Newtons, N) - $s$: Displacement (meters, m) - **Conditions for Work:** 1. A force must act on an object. 2. The object must be displaced. 3. The force must have a component along the direction of displacement. - **Units:** The SI unit of work is Joule (J). - $1 \text{ Joule} = 1 \text{ Newton} \times 1 \text{ meter}$ (1 J = 1 N m) - **When is work zero?** - When $F=0$ (no force). - When $s=0$ (no displacement). - When the force is perpendicular to the displacement (e.g., a person carrying a load on their head and walking on a horizontal road, or a satellite orbiting Earth). - **Positive, Negative, and Zero Work:** - **Positive Work:** Force and displacement are in the same direction (e.g., pulling a trolley). - **Negative Work:** Force and displacement are in opposite directions (e.g., work done by friction, or an object moving upwards against gravity). - **Zero Work:** Force is perpendicular to displacement, or no displacement occurs. ### Energy - **Definition:** Energy is the capacity to do work. - **Units:** The SI unit of energy is also Joule (J). - $1 \text{ kJ} = 1000 \text{ J}$ - **Forms of Energy:** - Mechanical Energy (Kinetic Energy + Potential Energy) - Heat Energy - Chemical Energy - Electrical Energy - Light Energy - Nuclear Energy ### Kinetic Energy - **Definition:** The energy possessed by an object due to its motion. - **Formula:** $E_k = \frac{1}{2}mv^2$ - $E_k$: Kinetic energy (Joules, J) - $m$: Mass of the object (kilograms, kg) - $v$: Velocity of the object (meters/second, m/s) - **Examples:** A moving car, a flying bird, flowing water. ### Potential Energy - **Definition:** The energy possessed by an object due to its position or configuration. - **Gravitational Potential Energy:** - **Definition:** Energy stored in an object due to its height above the ground. - **Formula:** $E_p = mgh$ - $E_p$: Potential energy (Joules, J) - $m$: Mass of the object (kilograms, kg) - $g$: Acceleration due to gravity (approx. $9.8 \text{ m/s}^2$) - $h$: Height above the ground (meters, m) - **Examples:** Water stored in a dam, a stone held at a height, a stretched bowstring (elastic potential energy). ### Law of Conservation of Energy - **Statement:** Energy can neither be created nor destroyed; it can only be transformed from one form to another. - **Total Energy:** The total energy before and after transformation remains constant. - **Example:** A falling object: - At height 'h': Max $E_p$, Min $E_k$ - During fall: $E_p$ decreases, $E_k$ increases - Just before hitting ground: Min $E_p$, Max $E_k$ - $E_k + E_p = \text{constant}$ (Mechanical Energy) ### Power - **Definition:** The rate at which work is done or energy is transferred. - **Formula:** $P = \frac{W}{t}$ or $P = \frac{E}{t}$ - $P$: Power (Watts, W) - $W$: Work done (Joules, J) - $E$: Energy transferred (Joules, J) - $t$: Time taken (seconds, s) - **Units:** The SI unit of power is Watt (W). - $1 \text{ Watt} = 1 \text{ Joule/second}$ (1 W = 1 J/s) - **Commercial Unit of Energy:** - Kilowatt-hour (kWh) - $1 \text{ kWh} = 3.6 \times 10^6 \text{ J}$ - This is the energy consumed by a device of 1 kW power in 1 hour.