AS

09_ReadingWk_2023_PhysicsBookletUpToWk6 2

Resolving Vectors

  • A vector can be broken down into vertical and horizontal components.

  • Example of vector resolution: a vector can resolve into 2 right (horizontal) and 3 up (vertical).

  • Resolution of vectors is clearer on graph paper, but can be calculated using the vector's magnitude and direction.

    • To find components, know the vector's length and the angle to the horizontal or vertical axis.

Adding Resolved Vectors

  • Once vectors are resolved, their components can be added together.

  • Process of adding resolved vectors:

    • Resolve vector C into its components.

    • Calculate the resultant of the horizontal and vertical components.

    • Combine these results to find the overall resultant vector.

    • Find the resultant angle using trigonometry.

Equilibrium

  • Equilibrium occurs when all forces cancel, resulting in no motion or uniform motion.

  • As an example, the downwards forces (gravity) are balanced by upwards forces (normal force).

  • In equilibrium, vectors can be visualized as arrows connected head to tail, returning to the starting point indicating a resultant of zero.


Distance vs. Displacement

  • Distance:

    • Scalar quantity, representing total movement length.

  • Displacement:

    • Vector quantity, representing how far from starting position.

    • Example: Completing a 400m lap

      • Distance = 400m; Displacement = 0m.

Speed vs. Velocity

  • Speed:

    • Measure of distance covered with time, scalar in nature.

  • Velocity:

    • Measure of displacement with time, vector in nature.

    • Both are measured in m/s.

Time & Acceleration

  • Time: measured in seconds (s).

  • Acceleration:

    • Rate of velocity change, also a vector quantity, measured in m/s².

    • Depends on positive/negative directions:

      • Positive velocity with positive acceleration = increasing velocity.

      • Positive velocity with negative acceleration = decreasing velocity.

Uniform Acceleration

  • When acceleration is constant, velocity increases uniformly over time.

  • Example analysis of uniform acceleration at 2 m/s²:

  • Velocity (m/s) increases linearly: 0, 2, 4, 6, etc., over Time (s): 0, 1, 2, 3, etc.


Graphical Representation of Motion

Gradient

  • Calculated using the change in the y-axis over the change in the x-axis.

Area Under Graph

  • Area calculation for straight lines involves:

    • Rectangles: Area = base × height

    • Triangles: Area = ½ base × height

Displacement-Time Graphs

  • Graph A: Displacement constant, object stationary.

  • Graph B: Constant velocity, displacement increasing linearly.

  • Graph C: Accelerating, displacement increasing non-linearly.

Velocity-Time Graphs

  • Graph A: Constant velocity.

  • Graph B: Uniform acceleration, velocity increasing consistently.

  • Graph C: Non-uniform acceleration, velocity increases at an increasing rate.

  • Area under velocity-time graph indicates displacement.


Acceleration in Gravitational Fields

  • Objects fall freely, accelerating due to gravitational force, irrespective of mass (feather vs. bowling ball).

  • Near the Earth’s surface:

    • Gravitational field strength = 9.81 N/kg.

    • Acceleration of falling objects = 9.81 m/s².

Weight and Mass

  • Weight: Force due to gravity, calculated as:

    • Weight (W) = Mass (m) × Gravitational field strength (g)

  • Measured in Newtons (N).

Terminal Velocity

  • Objects accelerate due to weight until drag force equals weight, stopping acceleration at terminal velocity.

Projectiles

  • Parabolic path dictated by horizontal (u cos θ) and vertical (u sin θ) components of initial velocity.

  • Horizontal motion: constant velocity.

  • Vertical motion: acceleration due to gravity (9.81 m/s²).

  • Horizontal and vertical motions act independently.