⚡Newton's Third Law
Action-Reaction Pairs
Newton's Third Law: For every action force, there is an equal and opposite reaction force.
F_AB = −F_BA
When object A exerts a force on object B, then object B exerts an equal and opposite force on object A. These are called Newton's Third Law pairs (or action-reaction pairs).
Critical point: Third law pairs ALWAYS act on DIFFERENT objects. This is why they don't cancel each other out!
Example: You push on a wall with 50 N to the right. The wall pushes back on you with 50 N to the left. These forces act on different objects (you vs. the wall), so they don't cancel.
Think About It
A truck collides with a small car. Which experiences the greater force — the truck or the car?
Identifying Third-Law Pairs
To identify a Newton's Third Law pair, ask: "Object A pushes on Object B → Object B pushes back on Object A."
The pair must: 1. Be equal in magnitude 2. Be opposite in direction 3. Act on DIFFERENT objects 4. Be the same TYPE of force
Example: A book rests on a table. - Earth pulls book down (gravity) ↔ book pulls Earth up (gravity) ← This IS a 3rd Law pair - Book pushes table down (contact) ↔ table pushes book up (normal force) ← This IS a 3rd Law pair
The "weight down and normal force up" on the book are NOT a 3rd law pair — they're both on the same object!
✏️ Worked Example
Problem: A horse pulls a cart with 500 N. By Newton's 3rd Law, the cart pulls the horse with 500 N in the opposite direction. Why does the horse-cart system move forward?
📐 Key Equations
Newton's Third Law
F⃗_A \to B = -F⃗_B \to A|F⃗_A \to B| = |F⃗_B \to A|⚠️ Common Mistakes
Misconception: Third-law forces cancel, so the net force on a system is always zero and nothing can accelerate.
✓ Correct thinking: Third-law forces act on DIFFERENT objects. When analyzing one object, you include only forces acting ON that object. The reaction force on the other object is irrelevant to the first object's acceleration.
Why: Third-law pairs never appear together in a single free body diagram. Cancellation only occurs if two equal-and-opposite forces act on the SAME object.
Misconception: The heavier object exerts a greater force in a collision than the lighter object.
✓ Correct thinking: By Newton's Third Law, both objects exert equal and opposite forces on each other, regardless of their masses. The lighter object experiences a greater acceleration because F = ma.
Why: The confusion arises from mixing up force and acceleration. Equal forces + different masses = different accelerations.
Misconception: A book on a table: the weight of the book and the normal force from the table are a Third-Law pair.
✓ Correct thinking: They are not a Third-Law pair. Both act on the same object (the book). The actual Third-Law pair of the book's weight is the gravitational pull the book exerts on Earth.
Why: A Third-Law pair must involve two objects each pushing/pulling on the other. "Weight" and "normal force" are different types of force from different sources.
📝 Practice Problems
Try these problems. Check your answer when ready.
You push a 2 kg book against a wall with 20 N. What force does the book exert on your hand?
A 60 kg person stands on a 1 kg bathroom scale inside an elevator. The elevator accelerates upward at 3 m/s². What does the scale read? (g = 10 m/s²)
A 1000 kg car rear-ends a stationary 2000 kg truck. During contact they exert forces on each other. (a) Which experiences the greater force? (b) Which experiences the greater acceleration?
Identify the Newton's Third Law partner for each force: (a) Earth pulls the Moon downward with gravity. (b) A bat hits a ball with 500 N to the right. (c) Air pushes a rocket exhaust downward with 30,000 N.
A 3 kg block sits on top of a 7 kg block, which sits on a frictionless floor. A 50 N horizontal force is applied to the bottom block. The two blocks accelerate together. (a) Find the acceleration. (b) Find the friction force the bottom block exerts on the top block.
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