Topic 2.3 Newton's Third Law: state Newton's third law, identify action-reaction force pairs, and explain why the paired forces act on different objects and so do not cancel.

What this topic is asking

The College Board (Topic 2.3) wants you to state Newton's third law, correctly identify action-reaction pairs, and explain why these paired forces, though equal and opposite, do not cancel. The crucial idea is that the two forces in a pair act on different objects, so they can never appear on the same free-body diagram and never cancel each other.

Newton's third law

Forces always come in pairs because a force is an interaction between two objects, and an interaction necessarily involves both. You cannot push on a wall without the wall pushing back on you with the same strength. There is no such thing as a lone, unpaired force.

Identifying an action-reaction pair

A reliable test: write each force as "X on Y." Its third-law partner is "Y on X." If you cannot swap the two object names like this, the forces are not a pair. The weight of a book (Earth on book) pairs with the book's gravitational pull on the Earth (book on Earth), not with the normal force.

Why the forces do not cancel

The single most important consequence is that the paired forces act on different objects, so they cannot cancel:

• The forces on one object are what determine its motion. A third-law partner acts on the other object, so it is irrelevant to the first object's acceleration.
• Two forces cancel only when they act on the same object (then they contribute to the same net force). Action-reaction forces never do.

This resolves the classic puzzle: if the forces are always equal and opposite, how does anything ever accelerate? The answer is that the two forces are on different bodies. When you push a cart, you exert a forward force on the cart (which accelerates the cart) while the cart exerts an equal backward force on you (which acts on you, not the cart). The cart accelerates because of the only third-law-relevant force acting on it, namely your push.

The third law versus the second law

A subtle point the exam loves to test is that equal forces do not produce equal accelerations. In a collision between a small car and a heavy truck, the car and truck push on each other with exactly equal forces (third law). Yet the car, having far less mass, suffers a much larger acceleration, because acceleration is $a = F/m$ (second law). This is why occupants of the lighter vehicle experience a more violent change in motion even though the forces are identical. Keeping the third law (about the forces between two objects) separate from the second law (about how one object responds to the net force on it) prevents a whole family of misconceptions. The third law also explains propulsion: a rocket pushes exhaust gas backward, and the gas pushes the rocket forward; you walk because you push the ground backward and the ground pushes you forward. In every case the useful force is the reaction acting on the object you care about.

Try this

Q1. A swimmer pushes water backward to move forward. Identify the force that propels the swimmer. [2 points]

• Cue. The water pushes the swimmer forward (the reaction to the swimmer pushing the water backward).

Q2. State whether the gravitational force the Earth exerts on the Moon equals the force the Moon exerts on the Earth. [1 point]

• Cue. Yes, they are equal and opposite (a third-law pair), despite the very different masses.