= Apparent weight
{title2=$N=m(g+a)$}
{wiki}
Apparent weight measures support rather than the gravitational <force> itself. In an ideal scale model, it is the magnitude $N$ of the <normal force> exerted on the body. A scale calibrated to display <mass> divides that support force by its calibration value of $g$.
Take upward as positive in a constant downward <gravitational acceleration> of magnitude $g$. If a body stays in contact with a horizontal scale and accelerates upward at $a$, <Newton's second law> gives $N-mg=ma$, hence $N=m(g+a)$. At rest, $N=mg$. In common <free fall>, $a=-g$, so $N=0$ despite the nonzero <gravitational weight> $mg$. If the formula would require $N<0$, ordinary supporting contact cannot realize it: the body loses contact instead.
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