How many times have you come across a homework problem like this:
And have promptly followed by filling your paper with this:
Let’s be honest with ourselves: most of the time our first stab at a physics problem is like Dick Cheney at a shooting contest – scattered and badly off the mark.
Now, despite how little you think you understand about how to solve practice problems, don’t short-change yourself. You probably know enough to get most of the way there, and with a small tweak to how you approach the problem itself, you can set yourself up for a much more successful attempt at a solution (and for professors who aren’t evil curmudgeons, you’ll earn yourself partial-credit in the process).
Step (1): The problem statement
First, before anything else, get your head around the problem.
As you’re already too familiar, practice problems are typically presented in hieroglyphic-like jargon like this one below.
How many times did you just read those 4 sentences? Don’t lie…
What you should do though, is put it into your own words, as simply as possible.
In this case I’ve written out the problem statement as one bullet point to cover the specifics of the situation (initial speed, height, and speed constraint), and one bullet point to cover the actual question.
(Check out my Hacking Physics Guide for the problem solving template I’m using.)
Now that we’ve got the problem in a slightly more understandable form, let’s move on to figuring out what exactly we’re supposed to do here.
Step (2): What’s it asking for?
This is the single most important step in solving any Physics problem.
Done incorrectly, you can send yourself down a rabbit-hole of convoluted and irrelevant equations, algebra, and nonsensical answers that will have you pulling out your hair while simultaneously fighting off the urge to flip over your desk in a hulk-like rage. This is, in large part, one of the main reasons we freak out on exams.
Done correctly, and it will ease your nerves and will virtually guarantee at least 50% credit on the problem (assuming you’re at least vaguely familiar with the material).
To do the job, we need to probe a little deeper into what the question is asking for in our plain-English problem statement from Step (1).
“Are you going to get a speeding ticket?”
When do people get speeding tickets?
When their speed is greater than the limit shown on the road. Here that’s 70 km/hr at the bottom of the hill.
Okay, we need to figure out how fast the car will be going at the bottom of the hill, and then compare that speed to the 70 km/hr limit.
If it’s over 70, we’ll get a ticket (assuming in this case the cop is a total ass). If it’s under, we’re good to go.
Step (3): Draw it yourself
Now let’s break down the problem even further and convert words into a sketch.
It’s important here not to just use or copy the picture provided with the problem statement. Drawing it yourself helps to personalize the information, and better solidify the lay-of-the- land (again helping to build experience for your “Physics Intuition”).
Images also contain a significant amount more information than text, and are much more easily processed in the brain. If you’ve ever said, “Nah I’ll just wait for it to come out as a movie,” you know what I’m talking about.
Now keep in mind, this is not art class. We’re looking for a purely functional picture of the situation. So don’t spend time making it “pretty,” just get it done.
1. A representation of the physical action
As you can see below, taken from Step (1) I’ve drawn my awesome hot-rod starting at the top of the hill moving to the right, descending down the hill and coasting at the bottom.
Along with the car and hill, I’ve included the important variables (vi, h, vf) again pulled from my statement in Step (1), along with their actual values if given by the problem.
3. Assumptions and constraints
Last, I threw in a 70 kph speed limit sign to represent the constraint I need to check my final answer against.
Variables, Equations, and the Solution
Now we’ve got the whole picture, and we can start defining variables and pulling out some of our knowledge of what equations we might use to get our answer.
(Note: Don’t worry if this seems like a jump here. I’ll be covering much more on setting up variables, creating more in-depth diagrams to tease out relationships, and generating the equations you need in future posts.)
Granted, you have to have at least a basic understanding of the underlying concepts and equations related to the problem (conservation of energy, kinetic energy, etc.). But by breaking the problem down properly, it starts to point you in the right direction.
From here, if you know the material, it’s smooth sailing.
And even if you’re not sure what to do next, you’ve demonstrated knowledge of what the problem is asking, and the relevant relationships – which in most cases (again, depending on the class/professor) will earn you some credit on the problem.
For more on how to break down and solve any mechanics problem, check out my free problem solving template and guide here – and stop pulling your hair out trying to finish that next problem set before midnight on Friday.