Lecture Notes on Newton's Laws of Motion

Introduction

• Discussed acceleration caused by a push or pull.
• Introduction of Newton's laws for a quantitative approach.

Newton's First Law

• Law of Inertia: A body at rest remains at rest, and a body in motion continues at constant velocity unless acted upon by an external force.
• Newton's formulation: "Everybody perseveres in its state of rest or uniform motion in a right line unless compelled to change that state by forces impressed upon it."
• Key Points:
  • Contradicts daily experiences due to gravity, friction, and air drag.
  • An object continues in straight line motion in the absence of forces.
  • Valid only in inertial reference frames (no acceleration).

Inertial Reference Frames

• 26.100 lecture hall is not an inertial frame due to:
  1. Earth's rotation.
  2. Earth's orbit around the sun.
  3. Sun's motion in the Milky Way.
• Estimated accelerations in 26.100:
  • Centripetal acceleration at equator: 0.034 m/s².
  • Much smaller than gravitational acceleration (300 times smaller).
  • Therefore, 26.100 can be considered a reasonable inertial frame.

Newton's Second Law

• Definition of Force: Force (F) is defined as the product of mass (m) and acceleration (A), or F = mA.
• Key Concepts:
  • Acceleration is in the direction of the force.
  • Units: Newton (1 N = kg·m/s²).
• Experimental validation:
  • Measured with spring extension.
• Mass can be defined without gravity by comparing relative sizes of objects.
  • Gravitational force: F = mg (linear relationship with mass).

Application of Second Law

• Example of a ball held in hand:
  • Force of gravity (mg) balanced by upward force from hand.
  • F_walter + F_gravity = 0, leading to F_walter = -mg.
• Valid for speeds much lower than the speed of light.

Newton's Third Law

• Action-Reaction Principle: For every action, there is an equal and opposite reaction.
• Key Examples:
  • Gravity: You push down on the seat; the seat pushes you up.
  • Baseball example: Ball pushes hand, hand pushes ball back with the same force.
• Example Problem:
  • Two objects (m1 = 5 kg, m2 = 15 kg) with a force acting on them results in a system acceleration.
  • Forces between the objects are equal and opposite (F12 = -F21).

Practical Examples of Third Law

• Balloon propulsion: Air pushes out, balloon moves in the opposite direction.
• Rocket propulsion: Exhaust gases push down, rocket moves up.

Detailed Example Problem: Mass on Strings

• Two strings hang a mass (M) at angles 60° and 45° with the vertical.
• Forces must balance (net force = 0).
• Decomposed forces into x and y components:
  • X-direction: T1cos(60°) - T2cos(45°) = 0
  • Y-direction: T1sin(60°) + T2sin(45°) - mg = 0
• Solving gives T1 and T2 in terms of m and g.

Experimentation with Tension in Strings

• Experimental setup with tension meters to validate calculations:
  • Observations showed discrepancies between expected and measured tensions due to inaccuracies in equipment.

Conclusion

• Engaged students in voting on which string would break under tension.
• Results demonstrated unexpected outcomes, reinforcing concepts of tension and forces.
• Encouraged students to think critically about physics principles in practical applications.

Key Takeaways

• Newton's laws provide a foundational understanding of motion and forces.
• Real-world applications and experiments demonstrate these principles in action.