forcesfree-body-diagramnewtonian-mechanicsreference frames
If an upward force was applied on an object which was at rest, the magnitude of the normal force decreases,
whereas, in an elevator which is undergoing an upward acceleration, the magnitude of the normal force increases rather than decreasing.
Why does the magnitude of the normal force increase rather than decrease in the elevator?
Just don't start writing equations without a complete Free-Body-Diagram(may be rough diagram) according to the frame of reference..
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.
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 $$N-mg=ma$$
As you said correctly: as you accelerate upwards, the normal force acting on you will increase. Now look at the situation from the scale's "perspective" -- consider the forces acting on the scale:
Since the ground (i.e. the scale on which you stand) applies a normal force $F_N$ (upwards) on you, Newton's 3rd law says that you must also be applying a force $F_N$ (downwards) on the scale.
To summarize: the scale will measure the magnitude of the normal force acting on you; which is also the magnitude of the force you exert on the scale (by Newton's 3rd law).
Best Answer
Good Question 😊 !
Quick summary first
I like to visualise Normal force as a force whose magnitude depends on the intermolecular distances.
If the intermolecular distances increase, the repulsive force decreases and if the intermolecular distances are decreased then this repulsive force increases.
Knowing this, now you can apply this to the above two cases.
Case 1 :
In this case, you are actually separating the two surfaces in contact by pulling the block up and not moving the floor and due to this the intermolecular distances (between the two) increases and hence the normal force (between the two surfaces) decreases.
Case 2 :
In this case, initially the block was at rest but the floor accelerated upward which in a very short span get closer to the bottom surface of the block and the block get pressed to the floor (due to inertia) and thus the Normal force from the floor on that block increased and hence it also accelerates up with the floor quickly.
Hope it helps 🙂.