Is this formula for Fnet valid for various man-in-elevator scenarios?

[paulb203]

Is the following formula valid?

Fn-Fg=Fnet
(Fn being the normal force)
(And ignoring drag)

I've come across it several times while using ChatGPt but can't get it confirmed using Google.
The context; various man-in-elevator scenarios, (at rest; accelerating down; accelerating up)

 

[jbriggs444]

If there are only two forces acting on an object then the net force on the object is the sum of those two forces.

 

[paulb203]

If there are only two forces acting on an object then the net force on the object is the sum of those two forces.

Thanks.
So, to put that in a formula would it be, in this context;
Fnet=Fn+Fg?

If so, how does that compare to;

Fn-Fg=Fnet?

To rearrange the latter would give;

Fnet=Fn-Fg, yeah?

To 'reconcile' the two, for a novice like me, should I think of it as follows:

Fnet=Fn+Fg
is the same as, in this context (when up is +, and down is -),
Fnet=Fn+(-Fg)
Fnet=Fn-Fg?

Example;

90kg man in elevator. Gfs=10m/s/s. acc=2m/s UPWARDS

Fnet=Fn+Fg
Fnet=Fn+(-900)
Fnet=900+(-900)
Fnet=900-900
Fnet+0

Or,

Fn-Fg=Fnet
900-(-900)=Fnet
900+900=1800 ?!?!
That can't be right, obviously.

So should it be,

Fn-Fg=Fnet
900-(the magnitude of the Fg)=Fnet
900-900=zero ?

***

I think I'm just about beginning to grasp the physics of this, but the maths, the algebra, seems like a stumbling block. If I put the physics to one side for a moment and focus solely on the maths it seems that the formula is wrong (I'm not suggesting that it is wrong, just that it seems to me to be wrong).

If I was in a maths lesson (knowing nothing about physics) and was told that,

Fn-Fg=Fnet
And that n=900, Fg=-900, and was asked to find Fnet, I would do it as follows:

Fn-Fg=Fnet
900-(-900)=Fnet
Fnet=900+900
Fnet=1800

And I would think that was correct (when it wasn't).

 

[Ibix]

You are struggling with sign conventions, by the look of it.

You can define your forces as positive and then say that the net force is the total of upward-pointing forces minus the total of downward-pointing forces. That's what your $F_{net}=F_n-F_g$ is doing. Alternatively, you can define all forces as positive if they point upwards and negative if they point downwards, and then the net force is just the total of forces. That's what @jbriggs444 is doing, and gives $F_{net}=F_n+F_g$.

Neither is wrong. You get the same answer because in the second case $F_g$ is negative and the first case it's positive, so you end up with the same signs. Howrver, the second approach is much better, because it generalises to the case where forces are vectors in more than 1d and don't necessarily point in opposite directions. It also works better when you have unbalanced forces - if you say all forces are positive, the net force can still be negative, which is confusing. If you say positive means upwards, it's obvious what a negative force means.

So the smart thing to do is to pick a direction to call positive (typically upwards in this kind of case) and say that forces pointing in that direction are positive, then use $F_{net}=F_n+F_g$.

 

[Herman Trivilino]

I think I'm just about beginning to grasp the physics of this, but the maths, the algebra, seems like a stumbling block

That's because of the confusing way different authors and instructors use these symbols. $F$ is usually understood as the magnitude of $\vec{F}$ and thus it is never negative. On the other hand, when working in only one dimension, $F$ is often used as the component of $\vec{F}$. In this case $F$ can either be positive or negative.

The confusion is born in the mind of the student when the very first topic of one-dimensional motion is introduced. Equations like $v=v_o+at$ are introduced, but they really should be written as $v_x=v_{ox}+a_xt$. Because what we are dealing with here are the x-components of the velocity and acceleration vectors. But at that early stage of the course, vectors have not yet been introduced, so the author can't very well use vector components. This results in a lasting confusion in the students' minds. On the other hand, some authors first introduce vectors, so they can then use vector components when they treat one-dimensional motion. But the poor novice students then tend to get overwhelmed by the seemingly tedious use of subscripts.

The former approach is usually adopted, but then the instructor must be particularly conscientious about explaining the whole confusion, because most textbook authors don't even address it.

 

[paulb203]

Thanks, guys.