Lecture Notes: Forces and Linear Movement

Introduction to Linear Movement

• Linear Movement: Movement of an object with no rotation.
• Examples:
  • Single electrons moving due to electric and magnetic fields.
  • A cart moving along a road (example of linear motion).

Forces and Motion

• Key Concepts:
  • Motion and force are closely linked.
  • Understanding motion requires identifying forces on an object.
• Main Forces on a Cart:
  • Weight: Gravity pulling downwards.
    • Formula: Weight = Mass x Gravitational Field Strength (constant on Earth).
    • Weight often confused with mass (should be in Newtons, not kilograms).
  • Thrust: Produced by the car engine.
  • Reaction Forces: Between cart and wheels, and wheels and road.

Resultant Force and Equilibrium

• Resultant Force: Sum of all forces as vectors.
  • Forces drawn from center of mass.
• Equilibrium:
  • Example: Stationary cart with weight downwards balanced by reaction forces upwards.

Acceleration and Velocity

• Accelerating Cart:
  • Produces a pulling force, breaking equilibrium.
  • Speed changes linearly with time.
  • Plot a straight line graph for speed vs. time.
• Calculating Acceleration:
  • Formula: ( \text{Acceleration} = \frac{\Delta V}{\Delta T} )
  • More general: ( \frac{dV}{dT} )
• Constant Acceleration Formulas:
  • Final velocity depends on starting velocity, acceleration, and time.
• Distance Calculation:
  • Integrating velocity to find distance.
  • Distance increases quadratically with time.

Factors Affecting Acceleration

• Mass:
  • Increased mass decreases slope (acceleration inversely proportional to mass).
• Force:
  • More powerful engine increases slope (acceleration proportional to force).
• Equation: ( F = ma ) (Force equals mass times acceleration).

Constant Velocity and Coasting

• Constant Velocity: No pulling force, car stays at the same speed.
• Distance when Coasting: Distance is linear with time (acceleration zero).

Deceleration and Stopping

• Breaking: Negative acceleration.
  • Use constant acceleration formula to show negative acceleration.
  • Quadratic speed-up and slow-down pattern.

Additional Forces and Real-World Considerations

• Air Resistance and Friction:
  • Depend on speed, complex to account for.
  • Not considered in simple constant force models.

Newton's Laws of Linear Motion

• Simplified Description of Object Behavior.

Energy Considerations

• Kinetic Energy:
  • Proportional to mass and square of velocity.
  • Energy is conserved, transformed into potential energy when going uphill.