In a stationary situation, the weight of person is
[tex]W=mg=(62 kg)(9.81 m/s^2) = 608.2 N[/tex]
This is the weight "felt" by the scale, which is basically the normal reaction applied by the scale on the person, and which uses the value of g (9.81) as reference to convert the weight (602.8 N) into a mass (62 kg).
When the person is in the elevator, the scale says 77 kg. The scale is still using the same value of conversion (9.81), so the apparent weight "felt" by the scale is
[tex]W' = m'g=(77 kg)(9.81 m/s^2)=755.4 N[/tex]
This is the normal reaction applied by the scale on the person, and which is directed upward. Besides this force, there is still the weight W of the person, acting downward. So, if we use Newton's second law:
[tex]\sum F = ma[/tex]
[tex]W-W'=ma[/tex]
where a is the acceleration of the elevator. If we solve for a, we find
[tex]a= \frac{W-W'}{m}= \frac{608.2N-755.4N}{62 kg}=-2.37 m/s^2 [/tex]
The negative sign means the acceleration is in the opposite direction of g (which we take positive), so it means the elevator is going upward.
