Force and Laws of Motion

• Introduction to Force

  • Definition: A push or pull on an object
  • Effects of Force:
    • Changes state of motion (rest to motion, motion to rest)
    • Changes speed
    • Changes direction
    • Changes shape/size
  • Types of Forces:
    • Balanced Forces: Net force = 0, no change in motion, can change shape
    • Unbalanced Forces: Net force $\neq$ 0, causes acceleration/change in motion

• First Law of Motion (Law of Inertia)

  • Statement: An object remains at rest or in uniform motion unless acted upon by an unbalanced force
  • Inertia:
    • Definition: Natural tendency to resist changes in the state of motion
    • Relation to Mass: Mass is a measure of inertia (more mass = more inertia)
  • Examples:
    • Falling forward when a bus stops suddenly
    • Coins falling into a glass when the cardboard is flicked

• Momentum

  • Definition: Product of mass and velocity ($p = mv$)
  • SI Unit: kg m/s
  • Vector quantity (has magnitude and direction)
  • Significance: Combined effect of mass and motion in causing impact

• Second Law of Motion

  • Statement: The rate of change of momentum is directly proportional to the applied unbalanced force
  • Mathematical Formulation:
    • $F \propto \frac{p_2 - p_1}{t}$
    • $F = ma$ (Force = mass $\times$ acceleration)
  • SI Unit of Force: Newton (N) or $\text{kg}\cdot\text{m/s}^2$
  • Applications:
    • Catching a cricket ball (pulling hands back increases time, reduces force)
    • High jump landing on foam/sand

• Third Law of Motion

  • Statement: To every action, there is an equal and opposite reaction
  • Key Points:
    • Forces act on different bodies, never on the same body
    • Action and reaction occur simultaneously
  • Examples:
    • Walking on the ground
    • Recoil of a gun
    • Propulsion of a rocket
    • Rowing a boat

• Conservation of Momentum

  • Law of Conservation: Total momentum of an isolated system of interacting objects is conserved (remains constant)
  • Formula: $m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$ (Before collision = After collision)
  • Application: Bullet fired from a gun, collision of balls