Force, Work, Power, Energy

Cheatsheet Content

### Force - **Definition:** An external agent that changes or tends to change the state of rest or uniform motion of a body, or changes its size/shape. - **Unit:** Newton (N) - **Types of Forces:** - **Contact Forces:** Frictional, Normal, Tensional, Applied. - **Non-Contact Forces:** Gravitational, Electrostatic, Magnetic. - **Turning Effect of Force (Moment of Force / Torque):** - $\tau = F \times d$ (Force $\times$ perpendicular distance from pivot) - **Unit:** Newton-metre (Nm) - **Clockwise Moment:** Tends to turn body clockwise (negative). - **Anticlockwise Moment:** Tends to turn body anticlockwise (positive). - **Principle of Moments:** For a body to be in rotational equilibrium, the sum of clockwise moments must be equal to the sum of anticlockwise moments. - $\sum \tau_{clockwise} = \sum \tau_{anticlockwise}$ - **Couplet:** Two equal and opposite parallel forces, not acting along the same line, producing only rotational motion. - **Moment of Couplet:** $F \times d$ (Force $\times$ perpendicular distance between forces). ### Centre of Gravity - **Definition:** The point where the entire weight of the body appears to act, irrespective of its orientation. - **Stability of Bodies:** - **Stable Equilibrium:** CG is lowest, base of support is wide. Returns to original position if slightly displaced. - **Unstable Equilibrium:** CG is highest, base of support is narrow. Topples over if slightly displaced. - **Neutral Equilibrium:** CG remains at the same height if displaced. ### Uniform Circular Motion - **Definition:** Motion of a body with constant speed along a circular path. - **Key Characteristics:** - **Speed:** Constant. - **Velocity:** Changes continuously (due to change in direction). - **Acceleration:** Present (centripetal acceleration), directed towards the centre. - **Force:** Centripetal force, $F_c = \frac{mv^2}{r}$ (directed towards the centre). - **Centrifugal Force:** Fictitious force experienced by an observer in a rotating frame of reference, directed away from the centre. ### Work - **Definition:** Work is done when a force causes a displacement in the direction of the force. - **Formula:** $W = F \times d \cos\theta$ - If force and displacement are in the same direction, $W = F \times d$. - If force and displacement are perpendicular, $W = 0$. - If force and displacement are in opposite directions, $W = -F \times d$. - **Unit:** Joule (J) - **Conditions for Work Done:** 1. A force must act on the body. 2. The body must be displaced. 3. The component of force must be in the direction of displacement. ### Energy - **Definition:** The capacity to do work. - **Unit:** Joule (J) - **Forms of Energy:** - **Mechanical Energy:** - **Potential Energy (PE):** Energy possessed by a body due to its position or state. - $PE = mgh$ (gravitational potential energy) - **Kinetic Energy (KE):** Energy possessed by a body due to its motion. - $KE = \frac{1}{2}mv^2$ - **Other Forms:** Heat, Light, Sound, Electrical, Chemical, Nuclear. - **Conservation of Energy:** Energy can neither be created nor destroyed, but can be converted from one form to another. The total energy in an isolated system remains constant. - For a freely falling body: $KE + PE = \text{constant}$ ### Power - **Definition:** The rate at which work is done or energy is transferred. - **Formula:** $P = \frac{W}{t} = \frac{F \times d}{t} = F \times v$ (if velocity is constant) - **Unit:** Watt (W) - 1 Watt = 1 Joule/second - **Commercial Unit:** kilowatt-hour (kWh) - $1 \text{ kWh} = 3.6 \times 10^6 \text{ J}$ - **Relation between Power and Speed:** $P = F \times v$ ### Machines - **Definition:** A device that helps to do work easily and quickly. - **Terms related to Machines:** - **Load (L):** The resistance to be overcome. - **Effort (E):** The force applied to the machine. - **Mechanical Advantage (MA):** $MA = \frac{\text{Load}}{\text{Effort}} = \frac{L}{E}$ - **Velocity Ratio (VR):** $VR = \frac{\text{Distance moved by effort}}{\text{Distance moved by load}} = \frac{d_E}{d_L}$ - **Efficiency ($\eta$):** The ratio of work output to work input. - $\eta = \frac{\text{Work Output}}{\text{Work Input}} \times 100\% = \frac{\text{MA}}{\text{VR}} \times 100\%$ - **Ideal Machine:** $\eta = 100\%$ (MA = VR) - **Types of Machines:** - **Levers:** - **Class I:** Fulcrum between effort and load (e.g., see-saw, crowbar). MA can be >1, 1. - **Class III:** Effort between fulcrum and load (e.g., fishing rod, human forearm). MA always