In my physics book the equation for apparent weight is given as FN = mg + ma where FN is the normal force, m is the mass of the object, g is the gravitational acceleration of the object (= 9.8 m/s2) and a is the acceleration of the system. For example the system could be someone standing on a scale inside an elevator. Let's for simplicity's sake say this person weighs 100 kg. Let's also for simplicity's sake only consider the cases where the elevator goes from rest and accelerates either upwards or downwards, and not the cases when it is already moving and slows down. When the elevator is standing still then, the acceleration a of the system is 0, so the normal force will be FN = 100*9,8 = 980 N. The normal force is the apparent weight that is shown on the scale and when the elevator is standing still it's equal to the true weight. Now if the apparant weight is, let's say a) 700 N and b) 1100 N, how large is the acceleration a of the system? According to the equation above it will be a = FN/m - g so we will get a) a = 700/100 - 9.8 = -2.8 m/s2 b) a = 1100/100 - 9.8 = 1.2 m/s2 Now what puzzles me here is the sign of the acceleration. We know that the apparent weight is larger when the elevator goes from rest and accelerates upwards, and less when it goes from rest and accelerates downwards. Hence, the negative sign in a) implicates an elevator going from rest accelerating downwards. But if a = -2.8 m/s2 implicates something accelerating from rest DOWNWARDS, then why shouldn't the formula have g = -9.8m/s2, when g being gravitation obviously also means acceleration from rest downwards. It doesn't, in the equation we used a positive value for g! If we had used g = -9.8m/s2, both case a) and b) would have given the same sign which is incorrect. Where is the error? Why doesn't g and a, when both are going in the same direction (from rest to acceleration downwards) have the same sign?