Newton's Third Law and Applications

Newton's Third Law

Statement: For every action, there is an equal and opposite reaction.

More precisely: When object A exerts a force on object B, object B exerts an equal magnitude force on object A in the opposite direction.

$\vec{F}_{A \text{ on } B} = -\vec{F}_{B \text{ on } A}$

Or more compactly: $\vec{F}_{AB} = -\vec{F}_{BA}$

Key Characteristics of Action-Reaction Pairs

1. Equal magnitude: $|F_{AB}| = |F_{BA}|$
2. Opposite directions: One points one way, the other points the opposite way
3. Same type of force: If one is gravitational, both are gravitational
4. Different objects: Each force acts on a different object
5. Simultaneous: Both forces exist at the same time

Identifying Action-Reaction Pairs

Template

"Object A exerts force on object B" ⟺ "Object B exerts force on object A"

Examples

Example 1: Book on table

• Action: Earth pulls down on book (weight)
• Reaction: Book pulls up on Earth

NOT action-reaction:

• Weight (Earth on book) and Normal force (table on book) - these act on the same object!

Example 2: Hammer hits nail

• Action: Hammer exerts force on nail (to the right)
• Reaction: Nail exerts force on hammer (to the left)

Example 3: Rocket propulsion

• Action: Rocket pushes gas backward
• Reaction: Gas pushes rocket forward

Common Mistakes

❌ Wrong: Normal force and weight are action-reaction pairs ✓ Correct: They act on the same object, so they can't be action-reaction

❌ Wrong: Action happens first, then reaction ✓ Correct: Both happen simultaneously

❌ Wrong: The heavier object exerts more force ✓ Correct: Forces in a pair are always equal magnitude

Why Don't Action-Reaction Forces Cancel?

Action-reaction forces act on different objects, so they don't cancel!

Example: Push a wall

• You push wall to the right with force $F$
• Wall pushes you to the left with force $F$
• Net force on you: $F$ to the left (you accelerate backward)
• Net force on wall: $F$ to the right (but wall doesn't move—it's also attached to Earth!)

Forces only cancel if they act on the same object.

Applications of Newton's Third Law

Walking

• Your foot pushes backward on ground
• Ground pushes forward on your foot (you accelerate forward)
• Without friction, you can't push on ground → can't walk (like ice skating!)

Swimming

• You push water backward with your hands
• Water pushes you forward
• More water displaced → greater forward force

Rocket Propulsion

• Engine expels gas backward (action)
• Gas pushes rocket forward (reaction)
• Works in space (doesn't need air to "push against")

Tension in Ropes

If rope has negligible mass:

• Tension is the same throughout the rope
• Forces at both ends of rope segment are equal and opposite (third law)

Normal Force

• Object pushes down on surface
• Surface pushes up on object (normal force)
• Perpendicular to surface

Internal vs. External Forces

Internal Forces

• Forces between objects within a system
• Come in action-reaction pairs
• Cancel out when considering the system as a whole
• Example: Tension between two connected blocks

External Forces

• Forces from outside the system
• Don't have reaction partners within the system
• Cause acceleration of the system
• Example: Friction from ground on a car

For a system: Only external forces affect the motion of the center of mass.

Problem-Solving with Third Law

1. Identify the two objects in the interaction
2. Name both forces:
   • Force object A exerts on object B
   • Force object B exerts on object A
3. Remember: Equal magnitude, opposite direction
4. Draw separate FBDs for each object if needed
5. Apply Second Law to each object separately

Connected Objects

When objects are connected (ropes, contact, etc.):

1. Draw separate FBDs for each object
2. Apply Newton's Second Law to each object
3. Use Third Law to relate interaction forces
4. Solve the system of equations

Example: Two blocks connected by rope

• Tension force on block 1: $T$ (pulls block 1)
• Tension force on block 2: $T$ (pulls block 2)
• If rope is massless: same tension throughout

Misconceptions Clarified

Q: If forces are always equal and opposite, how does anything accelerate?

A: Action-reaction forces act on different objects! The net force on each object determines its acceleration.

Q: When a horse pulls a cart, doesn't the cart pull back equally hard on the horse? How does the cart move?

A: Yes, cart pulls on horse (backward) and horse pulls on cart (forward) with equal forces. But these act on different objects!

• For the cart to accelerate: Forward force from horse > Backward friction on cart
• The horse accelerates forward because: Ground pushes horse forward > Cart pulls horse backward

Q: If I push a wall and it pushes back equally hard, why do I move but the wall doesn't?

A: The wall is attached to the Earth (huge mass!). The force accelerates you: $a = F/m$. Same force on Earth: $a = F/M_{Earth} \approx 0$ (negligible).