When I asked our real engineer he never once mentioned that he actually did this, leading me to believe he doesn't and just used math.
Which could be for any number of reasons.
Did you ask a question which would have gotten that response?
Given the fact that you say "leading me to believe" I assume your questions were poor and didn't get the full scope.
You can visualize wrong and you can do math wrong. But humans are visual creatures. It is far more easy to enter the wrong number in the equation than it is to not see something right due to repeated experiences.
And you can check the numbers.
The distinction is the accuracy.
Yes, humans are visual creatures, but their visual abilities are far from perfect.
This means if you are just relying upon vision, you don't know the limits of something.
You don't know if the ramp is too steep or shallow.
You don't know if the iron beam is strong enough to hold the weight, or just only close to that. You wont have any idea for the safety margin.
But with math, the numbers can be checked and that can be calculated, without any destructive or potentially lethal testing.
We are told that order of operations should ALWAYS be done. This is a faulty premise. A school teacher doing grade averaging will average like nine grades:
24+34+56+75+85+12+98+99+94/9
No, they won't.
They might use a simple calculator where what they really do is:
24+34
58+56
114+75
189+85
274+12
286+98
384+99
483+94
577/9
Or they might us a computer, or a better calculator.
Either way, they will still be following the correct order of operations.
So what if your premise pertaining to gravity is wrong?
Then it almost certainly would have been discovered by now.
If I am able to accurately visualize where things will fall and roll, does it make any difference if I have an engineering degree or not?
But can you accurately visualize? And if so, how precisely?
Because that makes the difference.
You can use numbers to clearly show just how accurate and precise you are.
But when you are just "visualising" then you have very little idea.
But again, none of this explains why a load cell measures weight.