Weight in an elevator? Free body diagrams

[Henrybar]

A 60kg student is standing on a scale in an elevator that measures weight in Newtons. Calculate the reading on the scale if the elevator is accelerating down at 4 m/s^2...when the elevator is accelerating up at 4 m/s^2... and in free fall.

Not sure if my work/answer is correct

accelerating down (up is positive)
Fnet= Fn - Fg
ma = Fn - mg
(60)(-4)= Fn - (60)(-9.8)
-240 = Fn +588
Fn = -828
∴ Fn = 828 N(Down)

accelerating up (up is positive)
Fnet = Fn - Fg
240 = Fn +588
Fn = -348
∴Fn = 348 N(down)

Free fall: the weight of the student is the same as if he/she were standing on the ground(588N) since gravity is still present and the student's mass remains constant.

 

[guitarphysics]

You did it incorrectly, because the Fg should be added to the Fn, not subtracted. You take care of its direction by making its acceleration, g negative (so it points downwards). Also think about it intuitively- the student should press down on the scale "harder" if the elevator is accelerating upwards instead of downwards, but you got a lower value. In free fall, it's also incorrect. Imagine if you're falling and the elevator is falling as well. You feel "weightless", so what would the scale reading be?