Normal Reaction force

In a frame with constant velocity it would be the same (the laws of physics work the same in all inertial reference frames). In an accelerating frame the force would be displaced by the acceleration.

The magnitude of the normal force is, F = mg + ma = m(g + a).

Here, a is vertical acceleration of the object. If the object is not in acceleration relative to the ground (observer's), then the vertical acceleration becomes zero and, therefore, F becomes equal to mg. If there is no acceleration then that means that the object is at rest or moving with constant velocity. By knowing this above-mentioned concept one can calculate the normal force correctly.