Newton's Laws of Motion

Newton's First Law of Motion

• Definition: An object at rest will remain at rest unless acted on by an external, unbalanced force.
• Example:
  • A box on a surface remains at rest if no net force is applied.
  • Weight force calculation:
    • Weight force (W) = mass (m) × gravitational acceleration (g)
    • For a 10 kg box, W = 10 kg × 9.8 m/s² = 98 N
  • Normal force from the ground balances the weight force; thus, net force is zero.
• The law also states an object in motion will continue in motion unless acted on by an external, unbalanced force.
  • Example: A ball rolling on a carpet stops due to friction, whereas a puck on ice slides longer due to reduced friction.
  • In outer space, with virtually no friction, objects will continue in motion indefinitely (e.g., Earth's orbit around the Sun).

Application in Problems

1. Object at rest: Net force is zero.
2. Object in motion with constant velocity: Net force is zero.
3. Net force not zero: Object accelerates; use Newton's Second Law.

Newton's Second Law of Motion

• Equation: F = ma (Force = mass × acceleration)
  • Increasing mass while keeping acceleration constant increases force.
  • Increasing acceleration while keeping mass constant increases force.
  • If force is constant, increasing mass decreases acceleration and vice versa.
• Momentum and Impulse: terminology:
  • Momentum (p) = mass (m) × velocity (v)
  • Change in momentum (Δp) = mass × change in velocity (Δv)
  • Impulse = Force (F) × time (Δt) = Change in momentum (mΔv)

Newton's Third Law of Motion

• Principle: For every action, there is an equal and opposite reaction.
  • Example: A person throwing a ball in space will move in the opposite direction of the throw.
• Additional Example: Skaters pushing against each other exert equal and opposite forces, causing them to accelerate in opposite directions.

Additional Applications and Examples

1. Constant velocity problem:

   • Example: A car moving with constant velocity; net horizontal force and acceleration are zero.
   • Applied engine force equal to friction force for constant velocity (e.g., 1500 N).

2. Box on Frictionless Surface: Calculating Acceleration

   • F = ma; e.g., 200 N applied to 10 kg box gives acceleration of 20 m/s².
   • Use kinematic equations to find final speed and distance after a time duration.

3. Net Force and Acceleration Calculations

   • Example: Applied force minus friction force gives net force; calculate acceleration using F = ma.
   • Use kinematic equations to calculate distance traveled or final speed after a time duration.

4. Momentum Problems

   • Calculate momentum changes, impulse, and forces involved during collisions or actions like throwing objects in space.

Summary of Key Points

• Newton's First Law: An object will maintain its state of rest or constant motion unless acted on by an unbalanced force.
• Newton's Second Law: F = ma; the relationship between force, mass, and acceleration.
• Newton's Third Law: Each action force has an equal and opposite reaction force.

Additional Resources

• Useful Websites: Video-tutor.net for more physics tutorials and practice problems.
• Other Subjects: General Chemistry, Organic Chemistry, Algebra, Trigonometry, Pre-Calculus, Calculus.

Remember to practice problem-solving to master the application of Newton’s laws in different scenarios.