Accelerating an elevator A person is standing on a weighing scale in an elevator in upward acceleration.
Let $N$ be normal reaction force exerted by the weighing scale to the person (upward).
It is known that the person will experience a normal reaction force ($N$) larger than his own weight (larger reading on the weighing scale). While $N$ is equal, but in opposite direction, to the force that the person exerts to the weighing scale due to action-reaction pair (the person and the weighing scale). That means other than the person's weight, there should be an extra force exerting to the weighing scale downward ($A$).
So $-N$ (upward)$ = mg + A$ (downward). I can't figure out where does $A$ come from?
 A: Just don't start writing equations without a complete Free-Body-Diagram(may be rough diagram) according to the frame of reference..
1)Ground Frame

Now . Newtons law. $$\sum \vec{F_{ext}}=\frac{dp}{dt}=ma(for\ constant \ mass)$$
So, $$N-mg=\sum \vec{F_{ext}}=ma$$ Where system is boy in ground's frame.
Here we equate the net external force to the acceleration of body . $ma$ is not a force it is the measure of net force which causes body to accelerate.
2)In a accelerating frame(non-inertial)
here we have  to add a fictious force $-m\vec{a}$ where $\vec a$ is the acceleration of frame .

Here too $$N-mg-ma=\sum \vec{F_{ext}}=0(as \ in \ frame \ of \ elevator \ boy \ is  \ at \ rest)$$
Again you get $$N-mg=ma$$
A: Contrary to what the other answers seem to suggest, the force described in the question is not fictitious. Even in the inertial ground frame the person will exert a force of magnitude $m(g+a)$ on the scale. This force is real and not fictitious. (There is, however, no real downward force of magnitude $m(g+a)$ acting on the person.)
As to where the $ma$ component come from: The actual physical cause of normal forces are typically not given much thought in this type of calculations. Normal forces are introduced to uphold certain mechanical constraints that are assumed to hold. In this case, the constraints are that the elevator, the scale and the person should all remain intact, maintain their relative position to each other and move with the same speed and acceleration. We simply calculate the normal forces that must be present for this to occur. If the person and the scale could not exert this normal force on each other, our constraints would not hold. (The scale or the person would break or deform and at least for a while they would not travel with the same velocity and/or acceleration).
As to the physical cause of normal forces, I can rcommend reading some of the answers to this question.
