Force and Motion

Key Concepts

• State of Motion: Represented by the velocity vector, which can be changed by acceleration.
• Velocity: Defined by two parameters: magnitude and direction.
• Force: Can change both the magnitude and direction of the velocity vector.
• Acceleration: Caused by a force, leading to a change in velocity.

Effects of Force

1. Force in the Direction of Motion

   • If an external force is applied in the direction of velocity:
     • The magnitude of velocity increases (speed up the body).
     • The direction remains unchanged.
   • Example: Body moving in a straight line with velocity vector (v) and force (f) applied in the same direction.

2. Force Perpendicular to Motion

   • When a force is applied perpendicular to the velocity:
     • The direction of the velocity changes (body bends in the direction of force).
     • Magnitude remains unchanged.
   • Effect depends on the mass of the body:
     • Light-weight body: Takes a turn quickly.
     • Heavy body: Turns gradually with a large radius of curvature.

Practical Illustration

• Coordinate System Example:
  • A particle starts from point A and moves along a path to point B.
  • As the particle moves in a curve, its direction changes (potentially magnitude as well).
  • At any point on the path, the velocity vector (v) is tangent to the curve.
  • Force (f) applied at an angle (\theta) to the direction of motion has two components:
    • Tangential Component ((f \cos \theta)): Acts along the direction of velocity. Responsible for changing the magnitude of the velocity vector.
    • Normal Component ((f \sin \theta)): Acts perpendicular to the direction of velocity. Responsible for changing the direction of the velocity vector.

Summary

• Parallel Force: Changes magnitude of velocity.
• Normal Force (Perpendicular): Changes direction of velocity.
• Understanding these effects helps in analyzing and predicting the motion of particles under different forces.