So I've never posted here but I found your post on accident while searching for some other information...
Your debacle has so much related to what I did, I felt obligated to share. Bear in mind, that I am a student in the U.S. so some of our titles are different (A-level is like a freshman? First year?)
I am currently a senior (4th year) mechanical engineer who also joined the physics program (I am at my junior/3rd year in the physics program) at my university because the physics interested me so much. I am far from a perfect student, but am loving my classes and curriculum.
As a rule, engineers typically try to determine the maximum stuff that can be negated or ignored. Then we calculate forces & safety factors and usually all end up with different answers. So long as accurate assumptions are made and the margin of safety is large enough, it typically works and everyone is happy.
At the end of the day, your calculations lay the framework. Then you take the design and input it into a computer to perform finite element analysis (the computer chops everything up into a whole bunch of little pieces and performs the calculations at each point) and observe the results to ensure the project will work. If its overbuilt, you remove material/supports and try again until everything is optimized.
Physicist like to account for everything. The majority of the information is more theoretical. If designing an experiment, everything is taken into consideration and sometimes this leads to massive unnecessary equations. Furthermore, sometimes physicists end up creating equations that are unsolvable (mainly this is where the calculus comes into play) and you hit a stump. A lot of the models that are used do not depict the real life situations (I'm looking at you quantum wells) and have to be semi-visualized. When it comes to my physics work I tend to be in a constant state of confusion that somehow ends up clearing itself up, sometimes. It's fun, but the physics department at my university is also very light-hearted and easy to work with, so this comes into play a lot.
There is the debate that a physicist can do anything an engineer can. This is completely true; and if we waited for them to finish performing the calculations, we'd still be walking everywhere. Fortunately, we have engineers who are willing to fudge the numbers a bit, over build things, and by churning out some results the wright brothers made flight.
An example of the senior project I am currently working on. My team and I are to design & build an AUV for underwater missions. I am responsible for designing the heat transfer from the PC to the water.
From my engineering perspective;
I want to build it with atleast a safety factor of 2 (that is, it can remove 2x as much heat as the PC generates). Fortunately our hull has 2 end caps that are made of aluminum. => 2 end caps, safety factor of 2, each endcap needs to disperse the heat of the PC
The length of the hull is made of acrylic & offers little heat transfer => Ignore it.
One of the endcaps has wires coming out of it, this reduces the heat transfer across the endcap => Analyze this endcap
The water has a small current in it => too small of velocity worth considering, treat as stationary fluid of infinite medium
Now I just need to determine the thickness of the endcap (this has to do with the bolts that hold it together) and from there I can calculate the necessary fins for heat transfer.
From a physicist perspective;
The conductivity of the aluminum cap will need to be evaluated as the temperature changes (the change was so minimal, as an engineer the temp would be averaged and ignored)
Both endcaps would need to be analyzed together
Water current would need to be verified & calculated
The known fluid & heat transfer formulas that I use as an engineer would be scrapped, they are approximations.
The acrylic hull needs to be considered & analyzed.
Engineering perspective would take a week to do rough calculations (including time to figure out unknown information, such as thickness of cap).
Physics perspective would take a week to figure out what variables I still need to account for. Nevermind the calculations.