Newton's Third Law — Action-Reaction Examples Explained

Newton's Third Law sounds obvious until CBSE or JEE asks you to identify the correct action-reaction pair from four options — and two of them look almost right. The law itself is clean. The confusion comes from not applying the two key conditions: same magnitude, opposite direction, and most importantly, acting on different bodies.

Question

(Part A) State Newton's Third Law of Motion. Give three real-life examples.

(Part B) Identify the action-reaction pair when a book rests on a table.

(Part C) Explain the horse-and-cart paradox: If the cart pulls the horse backward with the same force the horse pulls the cart forward, how does the system ever accelerate?

Solution — Step by Step

Part A: The Law and Examples

Newton's Third Law: When body A exerts a force on body B, then body B simultaneously exerts an equal and opposite force on body A.

In equation form: $\vec{F}_{AB} = -\vec{F}_{BA}$

Three real-life examples:

1. Walking: Your foot pushes the ground backward (action). The ground pushes your foot forward (reaction). That forward push from the ground is what moves you.

2. Rocket propulsion: The rocket engine pushes hot gases downward (action). The gases push the rocket upward (reaction). No air is needed — rockets work in the vacuum of space.

3. Swimming: A swimmer pushes water backward with their hands (action). Water pushes the swimmer forward (reaction).

Part B: Book on Table — Identifying the Correct Pair

Forces on the book:

• Weight of book = $mg$ downward (Earth pulls the book)
• Normal force from table = $N$ upward (table pushes the book)

These two forces are equal and opposite, but they are NOT an action-reaction pair. They are both acting on the same body (the book) and they balance each other — that's why the book is in equilibrium.

The actual action-reaction pairs here:

Part C: The Horse-and-Cart Paradox

The confusion arises from analyzing the wrong system.

When we say action-reaction forces are equal and opposite, we mean they act on different bodies. So to analyze whether the cart moves, we look at forces on the cart alone. To analyze whether the horse moves, we look at forces on the horse alone.

Forces on the horse:

• Horse pushes ground backward (action)
• Ground pushes horse forward — call this $F_{ground}$ (reaction to horse's push on ground)
• Cart pulls horse backward — tension $T$ (reaction to horse pulling the cart)

For the horse to accelerate forward: $F_{ground} > T$

Forces on the cart:

• Horse pulls cart forward — tension $T$
• Road friction on cart wheels — call this $f_{cart}$ (backward)

For the cart to accelerate forward: $T > f_{cart}$

So the system accelerates when: $F_{ground} > T > f_{cart}$

The horse's legs generate enough friction from the ground to overcome both the cart's resistance and move the whole system. This is why horses can't pull carts on ice — $F_{ground}$ becomes negligible, and no forward motion is possible.

Why This Works

Newton's Third Law always involves two different bodies. The moment you see a question about "action-reaction pairs," check: are the two forces acting on two different bodies? If yes, they could be an action-reaction pair. If both act on the same body, they're not — they're just balanced forces (or unbalanced, if the body is accelerating).

The second check: action-reaction pairs are always the same type of force. The Earth's gravity on the book and the table's normal force on the book are different types — they cannot be action-reaction with each other.

Alternative Method — Identifying Pairs Systematically

Use this algorithm for any problem:

1. Pick body A.
2. Identify a force that some body B exerts on A. Call this the "action."
3. The reaction is: A exerts the same magnitude force on B, in the opposite direction.

Example: Earth exerts gravity on Moon (action). Moon exerts gravity on Earth (reaction). Same magnitude — which is why Earth also wobbles slightly (though imperceptibly, given the mass difference).

Common Mistake