General: How do you approach/think of a problem?

[Drk2]

This is a general question, so I hope you don't mind the lack of specificity.

How do you guys approach or think through any given problem? It's my first semester in undergrad physics and I find that, while I'm capable of doing the math, I'm bogged down or get side tracked in the process of A to B to C to the answer. This becomes particularly frustrating on examinations when I have a time limit.

Do you visualize the answer and work backwards with general equations or vice versa or what?

Any input would be great, thanks!

 

[mfb]

That depends so much on the type of problem that I don't even know how an answer could look like.

Some tasks can be so easy that you just see the result, sometimes you get an idea just by working a bit with the things you know, sometimes working backwards can help, sometimes you need many consecutive steps, ...

 

[Delphi51]

Great question! I have struggled with this over 30 years of teaching high school physics. How come I knew what to do from just reading the question but the students struggled? I thought about how I understood problems and taught this approach:
Take your list of formulas and write them all using the word "causes".
F = ma becomes "a force causes a mass to accelerate, a = F/m"
Vf = Vi + at becomes "an acceleration causes a change in velocity"
and so on. Note that the causes statement shows understanding of the physics so you have more than just math.

When faced with a problem such as "Find the speed of a car after a force is applied for 30 seconds" you first think about the causes statements involved. I use → in place of the word "causes". And I see this as I read the problem: F → a → ΔV. Then I write the formula for each → . The causes chain is the understanding of the whole situation. Questions may start from the end and work backwards or whatever, but that's just manipulation of the formulas in the chain.

Many students have trouble finding the right formulas because they are thinking mathematically instead of physically and will use an E for energy formula when they should be using an E for electric field one. Looking for the causes in a problem eliminates that trouble.

Consider the problem of a potential across parallel plates causing an electron between the plates to speed up. How fast does it go? It is quick and easy to explore two causes routes:
1) V → Electric field → force on electron → acceleration → ΔV
this is a chain of four formulas
2) Thinking of the definition of electric potential as energy per charge V = ΔU/q as V → ΔU it is easy to come up with a shorter chain of causes: V → ΔU kinetic → ΔV (referring to Uk = ½mv² in the second →)
this is a chain of only two formulas
And you see instantly that if you want the acceleration rather than the change in velocity, you'd better use the first route.

 

[Enigman]

Better problem solving comes from more problem solving.
At the beginning of any new topic I have always found that trying out some solved examples without looking at the solutions just the concepts required and then comparing your solutions and the book's really helps.
And there is always the usual advice for better problem solving. For those see here: http://www.utm.utoronto.ca/asc/Handouts/A%20Problem%20Solving%20Technique%20for%20Physics.pdf [Broken]
-the things given might seem laborious at first but over time they will come naturally not to mention they make seeing what the problem actually requires much easier.

 

[Drk2]

Thanks for the suggestions! Delphi51, that is some wonderful advice! It's such a simple, detailed and well laid-out approach. Many thanks!

 

[bowlbase]

Although I am far from being a great physics student (I come here often with questions) I do one thing that really helps me understand difficult problems that seems a no brainer in retrospect. When I'm at my whits end with a question I come to this forum and type out my issue as clearly and concisely as I can. Quite literally 50% of the time I find my error or misunderstanding in the process of doing this.

Actually, using LaTeX helps out tremendously with this. On paper you simply pencil in quickly what you think and that's it. On here I have to think about exactly how I want to show, in LaTeX, my problem.

It comes down to taking your time and explaining yourself in a way where you can go back and understand your own argument as it were. The biggest problem I have is rushing my problems or getting a mental block and just giving up. Coming here and typing out my issues actually focuses my argument into something I can go back and pick through myself without anyone else's help. It just takes time (as it should.. physics isn't generally easy for anyone).

I find this to be a thousand times better than actually sitting with a TA or professor and discussing problems. They know the problems, normally, inside and out and can just talk through them a lot faster than I can understand what they're saying. This goes for teaching in general, I think, most students just can't sit through a lecture and soak it up. I learn almost nothing from lectures for the sciences, personally.

tl;dr
Simply write out your problem or issue for someone else to read. Disassociating yourself so you can critique your own methods/logic.

 

[Chestermiller]

The question you are really asking is "how do you develop a mathematical model to describe the behavior of a physical system." I've been doing modeling for about 50 years, and have evolved to an approach that is in some ways similar to that of Delphi51. I don't start out by writing any equations. Instead, I start out by articulating in words the basic physical mechanisms that are playing a role in the system under investigation. I also sometimes start out very simply by looking at reduced versions of the problem, which may not include all the detail and mechanisms. Why? Because if I can't solve the simpler problem, I certainly won't be able to do the more complicated version. Plus, once I solve the simpler problem, I will already have some results under my belt to provide better understanding of what is happening, and to build upon. After I have articulated the fundamental physical mechanisms involved, I then translate this articulation of the mechanisms into the language of mathematics using equations. So there is an Articulation stage in attacking a problem, and then there is a Formulation stage. At this point, the hard part is over. The next stage is the equation Solution Stage (which in practice is often easier than the formulation stage). After the Solution Stage, you enter the Results and Interpretation Stage in which you look at the quantitative solution to the equations, and make physical sense out of them. Then, finally, there is the Reporting Stage in which you package what you found in a way that is simple and concise enough for your audience to understand.