Answer
(a) The elevator is accelerating upward at a rate of $a = 0.603~m/s^2$.
(b) The elevator is accelerating downward at a rate of $a = 1.26~m/s^2$.
Work Step by Step
We can find the mass of the person.
$mg = 683~N$
$m = \frac{683~N}{9.80~m/s^2} = 69.69~kg$
Note that the normal force $F_N$ is equal to the reading on the scale.
(a) Let up be the positive direction.
$\sum F = ma$
$F_N - mg = ma$
$a = \frac{F_N-mg}{m}$
$a = \frac{725~N - (69.69~kg)(9.80~m/s^2)}{69.69~kg}$
$a = 0.603~m/s^2$ (upward)
The elevator is accelerating upward at a rate of $a = 0.603~m/s^2$.
(b) Let down be the positive direction.
$\sum F = ma$
$mg - F_N = ma$
$a = \frac{mg - F_N}{m}$
$a = \frac{(69.69~kg)(9.80~m/s^2) - (595~N)}{69.69~kg}$
$a = 1.26~m/s^2$ (downward)
The elevator is accelerating downward at a rate of $a = 1.26~m/s^2$.
