Hello, everyone.
I’m Jesse Mason and in this installment of Teach Me we’re going to learn how to
solve any – YES, ANY!
– physics problem.
Now that’s a bold statement, I know.
But the method that we outline here is so useful that it can and should be used for
each and every physics problem that we encounter.
Okay.
So here’s a handy way (pause) to remember our problem solving method.
Yeah, it’s a little childish.
But as Eric Demaine said, “It’s not that little children are scientists; it’s that
scientists are big children.”
So our problem solving method comprises five steps.
First, draw a picture.
Second, knowns ‘n’ unknowns.
Third, equation.
Fourth, solve symbolically first.
And fifth, check your answer.
At the end of this video we’ll monkey around with a somewhat absurd but memorable mnemonic
device to remember these five steps so… stay with us.
Now before we elucidate each of these steps, it’s worth noting that there’s kind of
a zeroth step in our problem solving method and that’s to read the problem carefully.
Don’t forget to do that.
All right.
First official step: Draw a picture of the body or bodies in question.
Even if our artistic sensibilities have stagnated since second grade, we still need to draw
a picture in order to visualize the situation.
Be sure to include the surrounding environment in the picture, noting any motion that’s
occurring.
Are there forces at play?
If so, then we’ll need an additional depiction, namely a free body diagram.
Last but not least, we need to select a coordinate system and include it on all of our drawings.
Step two: List the knowns and unknowns relevant to the problem.
We will likely need all the numerical values given in the wording of the problem and possibly
a few more from an appendix or a Wikipedia entry.
These numerical values will be implemented in the eleventh hour of our problem solving.
Step three: Select the appropriate equation for the problem.
This step is the crux of physics problems and for green physics students – pardon
the etymological pun – the bane of their studies.
I can’t count the number of times that I’ve been asked, “Professor Mason, which equation
do I use?”
Alas, there is no silver bullet for equation selection.
One must first understand the conceptual underpinnings of the equations and their relevance to the
problem, which really only comes with practice.
Which is why “Practicing physics is so important to understanding physics!”
Of course, if a problem really has you flummoxed, a last ditch attempt at equation selection
can be made with trial and error.
Step four: Solve the equation symbolically first.
Numerical values should only be inserted once the equation has been solved for the unknown.
Terms will often cancel, simplifying solutions, and much physical insight about our world
can be gained from delaying the gratification that comes with plugging and chugging.
Oh!
And don’t forget the units when inserting numerical values.
Units are such an important and helpful aspect of problem solving that forgetting them is
practically an unpardonable sin.
It’s like I tell my students, “You take care of your units, and your units will take
care of you.”
Step five: Check your answer.
No, I don’t mean by looking in the back of the book or Googling for solutions.
I mean by asking yourself, “Does this answer make physical sense?”
Are the units what we’d expect?
Is the numerical value physically reasonable?
If the answer’s negative, does that make sense?
Asking – and answering – these questions are just as important as any other step in
the method and will put us on the path to a solid understanding of the material.
Now, you may be asking yourself, “How am I going to remember these five steps?”
Well, assuming that fingertip tattoos are out of the question, I proffer the following
mnemonic device: Donkey Kong Eats Stray Cats.
No, it’s not very humane.
Nor is it even accurate.
(Everyone knows that DK is a strict bananavore.)
But such a graphic mnemonic device is pretty hard to forget.
And that’s the mark of a good mnemonic device.
So there it is.
Draw a picture.
Knowns ‘n’ unknowns.
Equation.
Solve symbolically first.
And check your answer.
Donkey Kong Eats Stray Cats.
I’m Jesse Mason.
I hope you find this problem solving method as helpful as I do and that you employ it
with each and every problem that you encounter.
And until next time, happy learning!