Dynamics - Grade IX Physics

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Mass vs. Weight Property Mass Weight Definition Amount of matter in an object Force exerted on an object due to gravity Symbol $m$ $W$ SI Unit Kilogram (kg) Newton (N) Formula Does not change with location $W = mg$ (Depends on gravity) Measured By Beam balance or digital scale Spring balance Effect of Gravity Same everywhere in the universe Changes depending on gravitational field strength Mass and Inertia Mass is a measure of inertia. Inertia: Property of an object to resist changes in its state of motion (rest or uniform motion). Greater mass = greater inertia = harder to start/stop motion. Gravitational Field Strength ($g$) Definition: Force per unit mass experienced by an object in a gravitational field. Also called acceleration due to gravity . Formula: $g = W/m$ SI Unit: N/kg or m/s$^2$ Values: Earth: $g = 9.8 \text{ N/kg}$ or $9.8 \text{ m/s}^2$ Moon: $g = 1.6 \text{ N/kg}$ Jupiter: $g = 24.8 \text{ N/kg}$ Force A force is a push or pull. It can change or tend to change an object's motion (move, stop, change direction, accelerate, decelerate) or shape. Force is a vector quantity (magnitude and direction). SI Unit: Newton (N) $1 \text{ Newton (N)}$ is the force required to accelerate a $1 \text{ kg}$ object at $1 \text{ m/s}^2$. So, $1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2$. Types of Forces Contact Forces Act when objects are in physical contact. Examples: Friction, tension, normal force, air resistance, drag, thrust. Non-Contact Forces Act without physical contact. Examples: Gravitational force, magnetic force, electrostatic force. Fundamental Forces of Nature Force Relative Strength Range Effect Example Strong Nuclear Force 1 (Strongest) Short-range (within atomic nuclei) Holds atomic nuclei together Binding protons and neutrons in a nucleus Electromagnetic Force $10^{-2}$ Infinite Acts between charged particles Electric and magnetic field Weak Nuclear Force $10^{-5}$ Very short-range Responsible for radioactive decay Beta decay in atomic nuclei Gravitational Force $10^{-39}$ (Weakest) Infinite Attraction between masses Earth's gravity Relative strength: Strong Nuclear > Electromagnetic > Weak Nuclear > Gravitational. Dr. Abdus Salam contributed to the unification of weak nuclear and electromagnetic forces (Electroweak Theory). Free-Body Diagrams (FBD) Simplified sketch showing all forces acting on an object. Steps: Represent object as a dot or box. Draw arrows for forces. Label each force with its type and direction. Newton's Laws of Motion 1st Law (Law of Inertia) An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Inertia is the tendency of an object to resist changes in its state of motion. 2nd Law (Law of Acceleration) The acceleration ($a$) of an object is directly proportional to the net force ($F_{net}$) applied and inversely proportional to its mass ($m$). Formula: $F_{net} = ma$ Units: $F$ in Newtons (N), $m$ in kilograms (kg), $a$ in m/s$^2$. 3rd Law (Action-Reaction Law) For every action, there is an equal and opposite reaction. Forces always occur in pairs. Limitations of Newton's Laws Valid only in inertial frames (non-accelerating reference frames). Fails at very high speeds (requires Einstein's Theory of Relativity). Fails at atomic level (requires Quantum Mechanics). Effect of Force on Velocity Force Direction Effect on Velocity Examples Same Direction Increases velocity Car accelerating Opposite Direction Decreases velocity Brakes applying force Perpendicular Direction Changes direction but not speed (e.g., circular motion, projectile motion) Ball on a string, gravity in projectile motion Resultant Force (Same Straight Line) Definition: The single force that has the same effect as all individual forces acting together. Same direction: Add magnitudes ($F_{resultant} = F_1 + F_2 + ...$). Opposite directions: Subtract magnitudes ($F_{resultant} = F_1 - F_2$). Terminal Velocity Definition: The maximum constant velocity reached by a falling object when the force of gravity is balanced by the resistive force (e.g., air resistance). When falling through a fluid, two forces act: Gravity (downward) Air resistance (upward) Initially, gravity $>$ air resistance, object accelerates. As velocity increases, air resistance increases. When air resistance = gravity, net force = 0, and the object falls at constant velocity (terminal velocity). Momentum Definition: Product of an object's mass and velocity; quantity of motion. Formula: $p = mv$ Units: kg$\cdot$m/s Momentum is a vector quantity ; its direction is the same as velocity. Greater mass or velocity means greater momentum. Force and Momentum Relationship Newton's Second Law: Force is the rate of change of momentum. Formula: $F = \Delta p / \Delta t = (mv_f - mv_i) / t$ $\Delta p$ = change in momentum, $t$ = time over which force acts. A larger force changes momentum faster. A longer time period reduces the force needed (safety features like airbags, seatbelts). Impulse Definition: Change in momentum of an object when a force is applied over time. Formula: Impulse ($J$) $= F \times t = \Delta p$ Units: Newton-seconds (N$\cdot$s) or kg$\cdot$m/s. A shorter impact time leads to greater force. A longer impact time reduces force, making collisions safer (e.g., airbags, cushioned helmets). Law of Conservation of Momentum The total momentum of a system remains constant if no external force acts on it. Total momentum before collision = total momentum after collision. Applies to collisions and explosions. Momentum is conserved in both elastic and inelastic collisions. Formula: $m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$ $m_1, m_2$: masses of objects $u_1, u_2$: initial velocities $v_1, v_2$: final velocities Collision Safety Design Principles Increase Collision Time ($\Delta t$): Use materials that deform or compress (e.g., foam, airbags) to spread out the impact over a longer time. Reduce Impact Force ($F$): Spread the force over a larger area (e.g., helmets with padding). Examples: Helmets: Cushioned interiors increase impact time, reducing force on skull. Airbags: Inflate to cushion impact, increasing time of impact. Parachutes: Increase air resistance, slowing descent and reducing impact force. Crumple Zones in Cars: Designed to absorb energy by controlled deformation. Friction Definition: A force that opposes the motion of an object when it comes into contact with a surface. Acts parallel to the contact surface and opposite to the direction of motion. Caused by surface roughness and intermolecular forces. Two types: Rolling friction and sliding friction. Rolling Friction vs. Sliding Friction Aspect Rolling Friction Sliding Friction Definition Friction when an object rolls over a surface Friction when an object slides over a surface Cause Caused by deformation of surfaces at contact points Caused by interlocking of rough surfaces Magnitude Smaller compared to sliding friction Larger because more surface contact creates resistance Practical Use Wheels, ball bearings reduce friction Brakes in vehicles create sliding friction to stop Rolling friction is weaker than sliding friction, which is why wheels and ball bearings are used to reduce friction. Methods to Reduce Friction Method How It Works Example Lubrication Oils/grease create a thin layer, reducing direct surface contact Lubricating motorbike chains, door hinges Polishing Surfaces Smoother surfaces reduce interlocking of rough surfaces Polishing floors, car bodies Using Ball Bearings Converts sliding friction into rolling friction Bicycle wheels, conveyor belts Using Air Cushioning Creates a layer of air to reduce contact Hovercrafts, air hockey tables Streamlining Objects Reduces air resistance (fluid friction) by reducing surface area Aerodynamic design in cars, airplanes Using Magnetic Levitation (Maglev) Eliminates contact by using magnets Maglev trains Using rollers or wheels Converts sliding friction into rolling friction Using trolleys with wheels to move heavy objects Reduce weight Less forces between surfaces reduces friction Lightweight materials in machinery Centripetal Force Definition: The force required to keep an object moving in a circular path, always directed toward the center of the circular motion. It continuously changes the direction of the object's velocity (without changing its speed). Formula: $F_c = \frac{mv^2}{r}$ $F_c$: centripetal force (N) $m$: mass of the object (kg) $v$: speed of the object (m/s) $r$: radius of the circular path (m) The centripetal force is always perpendicular to the velocity vector, pointing to the circle's center. Sources of Centripetal Force Source How it Provides Centripetal Force Examples Tension A pulling force through a string/cable that directs an object inward Pendulum, twirling a stone on a string Friction A resistive contact force that can redirect motion inward on a curve Car rounding a bend, bicycle turning a corner Gravity An attractive force between masses that pulls objects toward each other (center of orbit) Planetary orbits (Sun pulling on planets), Moon orbiting Earth