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Topic 2.3: Newton's Third Law

Name: _______________________________ Date: _______________

Before We Start: Yesterday's Recap

Yesterday we said two forces on the same object that happen to be equal and opposite are NOT automatically a special pair. So what kind of relationship IS a genuine physics "pair"? Take your best guess before today's lesson.

Today's New Concepts

AP CED Alignment: Unit 2, Topic 2.3

Newton's Third Law

  • For every force one object exerts on a second object, the second object exerts an equal-magnitude, opposite-direction force back on the first
  • Symbol: $F_{A\text{ on }B} = -F_{B\text{ on }A}$
  • Units: newtons (N)
  • Always true, regardless of the two objects' relative mass, motion, or acceleration — NOT conditional on things being calm or balanced

Worked Example: A hammer strikes a nail. The hammer and nail are two different objects directly interacting, so the force the hammer exerts on the nail equals the force the nail exerts on the hammer — even though the nail is accelerating at that instant.

Telling a Genuine Third-Law Pair From Coincidentally-Equal Forces

  • A genuine third-law pair always involves exactly TWO different objects, one force from each acting on the other
  • Forces on the SAME object that happen to be equal (like gravity and normal force on a motionless box) are NOT a third-law pair — they're just two separate forces that happen to balance due to equilibrium (Newton's first law reasoning, not third)
  • Gravity's real third-law partner: the object pulling UP on the Earth with equal force — real, but unnoticeably small given Earth's mass

Worked Example: A box sits motionless on a table. Gravity and normal force are equal in size, but they act on the SAME object (the box) — not a third-law pair. The genuine pairs here are: (1) box pushes down on table / table pushes up on box, and (2) Earth pulls box down / box pulls Earth up.

Ideal vs. Real Strings and Ropes

  • An ideal (massless) string has the same tension at every point along its length
  • A real, heavy rope does NOT — tension varies along its length, and at any point it supports the weight of everything still hanging below that point
  • The higher up a real rope, the more weight is below, so the higher the tension

Worked Example: A heavy rope hangs from the ceiling. Tension at the very top supports the whole rope's weight. Tension exactly at the midpoint only supports the bottom half of the rope's weight — so the midpoint tension is half the top tension.

Keep This Sheet!

These sheets build into your semester study guide. Keep them in order in a binder or folder — you'll want to flip back through them before quizzes, unit tests, and when AP exam review starts in the spring.