Two masses, one string, one number you cannot see.

Newton's second law is one line long. The art is choosing what to point it at — sometimes the whole system, sometimes a single particle, and the two choices tell you different things.

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$A$ is 5 kg, $B$ is 3 kg, joined by a light inextensible string over a smooth pulley and released from rest.

The string cannot stretch, so both have the same size of acceleration. The pulley is smooth, so the tension is the same on both sides.

Apply $F = ma$ once per particle, each in its own direction of motion: down is positive for $A$, up is positive for $B$.

Unwrap the pulley: one body of 8 kg, with $5g$ hauling one way and $3g$ the other.

The tension is internal — equal and opposite on $A$ and $B$ — so the whole system can never show it.

The system handed over $a$ and hid $T$. To get the tension, go back to a single particle — take the lighter one:

Three significant figures, because $g$ is only known to two.

The string pulls down on the pulley on both sides, so the force on the pulley is $2T = 73.5\text{ N}$ — not $T$, and not the combined weight.

And a tension is never just a weight. If $T$ were $3g$, $B$'s equation would give $a = 0$ and nothing would move at all.

Whole system first, then one body.

All three of Newton's laws, lifts and normal reactions, forces as vectors, cars and trailers, particles on tables, and twelve graded exam questions with full worked solutions are waiting.

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