If the elevator was stationary, the scale would read exactly the weight of the person:
However, the elevator is moving with an acceleration a, so the scale reads a new value of the weight, which we call W'. Newton's second law becomes
where a' is actually the total acceleration of the person, so it's the sum of the acceleraion of the elevator and of the gravitational acceleration:
Taking the direction of g (downward) as the positive direction, we can find the value of a:
So, the acceleration of the elevator is
, with same sign of g, so it's directed downward as well.
However, the elevator is moving with an acceleration a, so the scale reads a new value of the weight, which we call W'. Newton's second law becomes
where a' is actually the total acceleration of the person, so it's the sum of the acceleraion of the elevator and of the gravitational acceleration:
Taking the direction of g (downward) as the positive direction, we can find the value of a:
So, the acceleration of the elevator is