State Newton's third law, identify action-reaction force pairs, and explain why the two forces in a pair act on different objects and therefore do not cancel (MA STE Introductory Physics, Motion and Forces).

What this topic is asking

Newton's third law is short to state but easy to misuse, and the Massachusetts Introductory Physics MCAS targets exactly that confusion. You must state the law, identify the action-reaction pair in a situation, and explain the subtle but crucial point that the two forces act on different objects, which is why they do not cancel. The standard is built around constructing explanations: propulsion, walking, and rockets all come down to the third law.

Newton's third law

The law says forces always come in pairs. There is no such thing as a lone force; if A pushes B, then B pushes A. The pair is equal in magnitude and opposite in direction, no matter the masses involved. When you push on a wall, the wall pushes back on you with exactly the same force. When the Earth pulls a falling ball down (its weight), the ball pulls the Earth up with an equal force, though the Earth's huge mass means its acceleration is unnoticeable.

Why the pair does not cancel

This is the heart of every MCAS third-law question. It is tempting to think that if the forces are equal and opposite, they should cancel and nothing should move. They do not cancel, because they act on different objects.

Consider a swimmer. She pushes the water backward (action); the water pushes her forward (reaction). The backward force acts on the water; the forward force acts on the swimmer. They are a pair, but because they act on different things, the forward force on the swimmer is free to accelerate her. The same logic explains walking (you push the ground back, it pushes you forward) and a rocket (it pushes gas down, the gas pushes it up).

Telling the third law from the first

A frequent trap mixes up a third-law pair with balanced forces on one object. A book on a table has:

• Balanced forces on the book: its weight down and the normal force up. These act on the same object (the book), are equal, and balance, so the net force on the book is zero (first law) and it stays at rest.
• A third-law pair: the book pushes down on the table, and the table pushes up on the book. These act on different objects.

The weight of the book and the normal force on the book are not a third-law pair, even though they look equal and opposite, because the third-law partner of the book's weight is the book's pull on the Earth, not the normal force.

Try this

Q1. A rocket expels gas downward. State the reaction force that lifts the rocket. [1]

• Cue. The gas pushes the rocket upward with a force equal to the downward force the rocket exerts on the gas.

Q2. Explain why the equal and opposite forces when you push a wall do not stop you exerting a force. [2]

• Cue. The two forces act on different objects (your hand on the wall, the wall on your hand), so they do not cancel; each object feels only the force acting on it.