Your mass is how much of you there is. Your weight is how hard gravity pulls on it — a force, and therefore newtons. $W = mg$, read aloud W equals m g: $W$ is the weight in newtons, $m$ is the mass in kilograms, and $g$ is the acceleration gravity hands out, $9.81\ \mathrm{m/s^2}$ on every paper in this chapter. Solve it for $W$ going down, or for $m$ coming back.

Every kilogram is charged 9.81 newtons, like a tax nobody voted for. A 100 kg motor does not weigh “100” — it weighs 981 N, and the lug it hangs from is rated in newtons, not kilograms. Bathroom scales are cheerful liars about this: they FEEL a force and print kilograms, silently dividing by g on your behalf. In this room nobody divides on your behalf.

Units guide, they do not confess. Push them through your rearrangement every time: $\mathrm{kg} \times \mathrm{m/s^2}$ is exactly a newton, so $W = mg$ survives the check. If the units refuse to cancel into the answer's units, the rearrangement is wrong, no appeal — but units that do work out never prove you right. The check runs one way only.