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Newton's Third Law
Action and Reaction

Every force in nature comes in pairs: when one object pushes or pulls another, the second object pushes or pulls back with a force that is equal in magnitude and opposite in direction.

AP Physics 1

What Is a Force Pair?

In physics, forces never exist alone. Whenever object A exerts a force on object B, object B simultaneously exerts a force back on object A. These two forces form what we call an interaction pair (also known as an action-reaction pair).

Forces Are Everywhere

Ground You You push ground Ground pushes you

When you walk, your foot pushes backward on the ground. The ground pushes forward on you. Without this reaction force, you could not accelerate forward.

Why Does This Matter?

Rockets
Exhaust gases are pushed downward; the rocket is pushed upward by the reaction force.
Swimming
Your hands push water backward; the water pushes you forward through the pool.
Car Tires
Tires push the road backward via friction; the road pushes the car forward.

The Formal Statement

$$ \vec{F}_{A \to B} = -\vec{F}_{B \to A} $$

1
Equal magnitude: \( |\vec{F}_{A \to B}| = |\vec{F}_{B \to A}| \). The two forces are always the same size.
2
Opposite direction: The forces point in exactly opposite directions along the same line of action.
3
Different objects: Each force acts on a different object. They are never on the same free-body diagram.

Visualizing the Interaction

A
(mass \(m_A\))
B
(mass \(m_B\))
\(\vec{F}_{A \to B}\)
\(\vec{F}_{B \to A}\)
\(|\vec{F}_{A \to B}| = |\vec{F}_{B \to A}|\)

Third Law Pairs vs. Balanced Forces

Third Law Pair Balanced Forces
Objects involved Two different objects Same object
Direction Opposite Opposite
Magnitude Always equal Equal only when \( a = 0 \)
Cancel out? Never Yes: net force = 0
Example Earth pulls you down / you pull Earth up Weight down + normal force up on a book at rest

A hand and wall force pair

This separate illustration shows forces on different objects: the hand pushes the wall and the wall pushes the hand with equal magnitude and opposite direction.

A hand exerts 100 N on a wall and the wall exerts 100 N on the hand in the opposite direction. These third-law forces act on different bodies and are not a net-force balance on one body.
A hand exerts 100 N on a wall and the wall exerts 100 N on the hand in the opposite direction. These third-law forces act on different bodies and are not a net-force balance on one body.

How to Identify a Third Law Pair

1
Name two objects. A valid pair always involves exactly two distinct objects (e.g., "book" and "table").
2
Swap the roles. Write the force as "A on B" then reverse it to "B on A." Both sentences must describe real physical contact or gravitational interaction.
3
Check the type. Both forces must be the same type: if one is gravitational, the other is gravitational. If one is contact/normal, the other is contact/normal.
4
Confirm magnitude and direction. Equal magnitude, opposite direction. They exist simultaneously: one cannot exist without the other.

Example 1: Book on a Table

Table Book
Force of Table
on Book (\(F_N\))
Force of Book
on Table

Example 2: Falling Ball and the Earth

Earth Ball
\(F_{E \to B}\)
\(F_{B \to E}\)

Example 3: Two Ice Skaters Push Off

A 50 kg B 80 kg
\(F = 60\text{ N}\)
\(F = 60\text{ N}\)
\(a_A = 1.2 \text{ m/s}^2\)
\(a_B = 0.75 \text{ m/s}^2\)

Same Force, Different Acceleration

A common misconception is that a heavier object exerts a larger force. It does not. The forces are always equal. What differs is the acceleration each object experiences, because of Newton's Second Law:

$$ a = \frac{F_{\text{net}}}{m} $$

Small mass
Same force, larger acceleration. The lighter object moves more.
Large mass
Same force, smaller acceleration. The heavier object moves less.

Third Law in Ropes and Tension

Block
Rope
Rope pulls
Block (\(\vec{F}_{R \to B}\))
Block pulls
Rope (\(\vec{F}_{B \to R}\))

The Normal Force as a Third Law Pair

When you stand on the floor, two distinct third-law pairs are at play. Many students confuse them:

1
Gravitational pair: Earth pulls you down (\( F_g \)) and you pull Earth up (\( F_g \)). Both are gravitational forces.
2
Contact pair: The floor pushes you up (normal force \( F_N \)) and you push the floor down. Both are contact forces.

Common Mistakes

✕ Forces cancel out
Third-law forces act on different objects, so they never cancel. Only forces on the same object can produce zero net force.
✕ Heavier object pushes harder
The forces are always equal regardless of mass. A truck and a mosquito exert equal forces on each other during a collision.
✕ Weight and normal force are a pair
Weight (Earth on you) and normal force (floor on you) both act on you: same object. They are balanced forces, not a third-law pair.

Summary of Newton's Third Law

Property Details
Statement \(\vec{F}_{A \to B} = -\vec{F}_{B \to A}\)
Magnitude Always equal
Direction Always opposite
Objects Always two different objects
Force type Both forces are the same type
Timing Simultaneous: one cannot exist without the other
Acceleration Differs based on each object's mass (\(a = F/m\))

Question 1 of 5

A hammer strikes a nail with a force of 500 N. What force does the nail exert on the hammer?

Question 2 of 5

A book sits at rest on a table. Which pair of forces is a Newton's Third Law pair?

Question 3 of 5

A 1000 kg car collides with a 2000 kg truck. During the collision, which statement is correct about the forces?

Question 4 of 5

Two ice skaters push off each other. Skater A has mass 60 kg and skater B has mass 90 kg. If skater A accelerates at \( 3 \text{ m/s}^2 \), what is skater B's acceleration?

Question 5 of 5

A person stands still in an elevator moving upward at constant velocity. The normal force from the elevator floor on the person is \( F_N \), and the person's weight is \( W \). Which is true?