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.