Chapter 7: Newton's Third Law Notes

7.1 Interacting Objects

  • Interaction: Mutual influence between two objects.
  • Action/Reaction Pair:
    • Forces exerted on each other ($\vec{F}{A \text{ on } B}$ and $\vec{F}{B \text{ on } A}$).
    • Act on different objects.
    • Equal in magnitude, opposite in direction.
    • Same type of force.
  • System: Collection of objects being analyzed.
  • Environment: Objects external to the system.
  • Interaction Diagram: Shows system components and external forces.

7.2 Analyzing Interacting Objects

  • Propulsion: Internal energy source drives a system forward.

7.3 Newton’s Third Law

  • Every force is part of an action/reaction pair.
  • Action/reaction forces act on different objects.
  • Equal in magnitude, opposite in direction: F⃗<em>A on B=−F⃗</em>B on A\vec{F}<em>{A \text{ on } B} = -\vec{F}</em>{B \text{ on } A}.
  • Acceleration Constraint: Relationship between accelerations of multiple objects.

7.3.3 Strategy for Interacting-Objects Problems

  • Steps:
    1. Read the question carefully.
    2. Identify all forces acting on each system (omit internal forces).
    3. Draw a free-body diagram for each system.
    4. Apply Newton’s third law to equate action/reaction pairs.
    5. Include acceleration constraints and friction models.
    6. Apply Newton’s second law for each system ($\vec{F}_{\text{net}} = m\vec{a}$).
    7. Apply kinematics if needed.

7.4 Ropes and Pulleys

  • Tension in a massless string is constant along the string.
  • For massless ropes/strings and massless, frictionless pulleys:
    • Tension equals the pulling force.
    • Tension is the same at both ends of a rope connecting two objects.
    • Tension is unaffected by passing over a pulley.