Newton's Third Law — Practice Problem Solutions

1. Yes — by Newton's third law, the force the person exerts on the wall and the force the wall exerts back on the person are always equal in magnitude (and opposite in direction), since they're a genuine action-reaction pair acting on two different objects.

2. No. Gravity and the normal force both act on the same object (the book), so equal magnitude alone doesn't make them a third-law pair — that's an equilibrium pair. Gravity's actual third-law partner is the book pulling up on the Earth; the normal force's partner is the book pushing down on the table.

3. $3F$ — Newton's third law guarantees the reaction force always matches whatever force is applied, no matter how large.

4. $\dfrac{2}{3}F_{top}$. The tension at any point in a hanging chain only has to support the weight of the chain below that point — one-third of the way down, two-thirds of the chain's weight still hangs beneath it.

5. Yes, the push forces are always equal in magnitude — Newton's third law guarantees this regardless of the skaters' masses. The lighter skater ending up moving faster doesn't contradict this; it's a second-law effect (the same force produces more acceleration on a smaller mass), not a violation of the third law.

6. a) Yes — the contact force the $3m$ block exerts on the $m$ block and the force the $m$ block exerts back are equal in magnitude, since Newton's third law applies to any two objects in contact regardless of their masses. b) The reasoning is wrong because Newton's third law doesn't care which object is heavier — contact forces between any two objects are always equal and opposite. Mass differences show up in each block's acceleration (Newton's second law), not in the size of the contact force itself.

7. a) Because the connecting string is massless, its own net force must be zero regardless of the system's motion — that requires the pull on each end to be equal in magnitude, making the tension the same throughout its length. b) Yes, it would change. A string with real mass also has its own weight to support; to keep every part of the system moving at constant velocity, the tension at the top of that connecting string would have to be slightly greater than the tension at the bottom, by an amount equal to the string's own weight.

8. (C) — none of these four forces are a Newton's-third-law pair, because all four act on the same object (the box). A true third-law pair always involves two different objects.