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General Physics and Mechanics (Unit 1)

Jun 4, 2024

General Physics and Mechanics (Unit 1)

Topics Covered

  • Measurements
  • Density
  • Mass and Weight
  • Gravity
  • Motion
  • Forces
  • Momentum

Quantities and Measurements

  • Checklist for Revision: Read each sentence from the syllabus, understand it, and mark it as confident, unsure, or not okay.
  • Measuring Length: Use rulers, measuring cylinders, and other instruments. Know how to determine average values for small distances and time intervals.
  • SI Units:
    • Length: meters (m)
    • Time: seconds (s)
    • Mass: kilograms (kg)
    • Temperature: Kelvin (K)
    • Electric Current: ampere (A)
  • Prefixes: Kilo (×1000), Centi (÷100), Milli (÷1000). Ability to convert between units.

Measuring Length and Volume

  • Length: Ruler for up to a meter, measuring tape for long distances, micrometer for thin objects.
  • Volume for Regular Solids: Use geometric equations.
  • Volume for Irregular Solids: Displacement method (use measuring cylinder, record initial and final volume).

Measuring Time

  • Time Intervals: Use stopwatches, clocks, and timers. Convert between hours, minutes, and seconds.
  • Pendulum: Measure the time of multiple oscillations and divide by the number of cycles to get the time for one oscillation.

Mass and Weight

  • Mass: Amount of matter in an object. Use a balance to measure.
  • Weight: Gravitational force on an object. Calculated as W = mg (mass × gravitational field strength).
  • Earth's Gravitational Field Strength: 9.8 N/kg, equivalent to the acceleration of free fall.
  • Measuring Mass of Liquids: Use an empty container, measure it, fill the liquid, and subtract the container's mass.

Density

  • Definition: Mass per unit volume (ρ = m/V).
  • Units: kg/m³ or g/cm³.
  • Measuring Density:
    • Regular solids: Measure mass and volume part by part.
    • Liquids: Using a measuring cylinder.
    • Irregular solids: Displacement method.
  • Floating and Sinking: Compare densities; if less dense than the liquid, it floats, and if denser, it sinks.
  • Effect of Temperature: Increasing temperature generally decreases density due to thermal expansion.

Scalars and Vectors

  • Scalars: Only magnitude (e.g., distance, speed, time, mass, energy).
  • Vectors: Magnitude and direction (e.g., force, weight, velocity, acceleration).
  • Resultant Vectors: Calculated using the Pythagoras theorem for right-angled vectors: [ R = \sqrt{(A^2 + B^2)} ].
  • Direction: Use trigonometric functions to find the angle (e.g., tan θ = opposite/adjacent).
  • Graphical Method: Vector diagrams to scale.

Motion and Speed-Time Graphs

  • Speed: Distance over time (d/t).
  • Velocity: Speed with a given direction.
  • Speed-Time Graphs:
    • Constant speed (horizontal line)
    • Acceleration (sloped line)
    • Deceleration (curved line downwards)
    • Calculate distance as the area under the graph.
  • Acceleration: Change in velocity over time, including both positive (acceleration) and negative (deceleration).

Newton’s Laws of Motion

  • First Law: Objects at rest remain at rest, and objects in motion remain in motion at a constant velocity, unless acted upon by an external force.
  • Second Law: Force is equal to mass times acceleration (F = ma).
  • Third Law: For every action, there is an equal and opposite reaction.

Circular Motion and Free Fall

  • Circular Motion: Force (centripetal force) acts towards the center, depends on speed, mass, and radius of the circle.
  • Free Fall: In absence of air resistance, objects fall at constant acceleration due to gravity (9.8 m/s²). With air resistance, objects can reach terminal velocity.
  • Skydivers and Parachutes: Accelerate until air resistance equals weight, after which they fall at terminal velocity.

Forces

  • Types of Friction: Solid friction (between two surfaces) and drag (air/water resistance).
  • Solid Friction: Depends on the roughness of surfaces, produces heat.
  • Drag: Increases with speed and surface area.
  • Hooke’s Law: Force in a spring is proportional to the extension until the limit of proportionality (F = kx).

Momentum

  • Definition: Mass times velocity (p = mv).
  • Impulse: Force times time (Ft), equal to change in momentum (Δp).
  • Conservation of Momentum: The total momentum before a collision is equal to the total momentum after the collision, in a closed system.
  • Calculations: Use momentum and impulse equations to solve real-world problems.

Important Equations:

  • Speed: v = d/t
  • Acceleration: a = Δv/Δt
  • Force: F = ma
  • Hooke’s Law: F = kx
  • Momentum: p = mv
  • Impulse: Ft = Δp