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Real World Physics Problems Newsletter - Problem Solving, Issue #21
July 20, 2015
How To Solve Physics Problems
Over the years I have found that solving physics problems, especially tough ones, usually involves indirect methods. I never just "know" how to solve a tough physics problem. Instead, I know which techniques to use which will help me figure out how to solve it. Anything goes in this regard. If a technique helps you, use it.
My main technique is to think of an analogous problem that is simpler; which means, think of an easier problem that is similar and which you can relate the original problem to. For example, if a problem involves a ball skidding on a surface, first think of a block sliding on a surface, since it's easier to understand the physics of that. For a gyroscope experiencing complicated three-dimensional motion think of a simpler case of gyroscopic motion which you understand better and against which you can compare the original problem to. This helps you ground the problem to something you are more familiar with.
There is a true art and skill in learning how to use analogies to solve difficult physics problems. It means being able to consider the physics of something else that is simpler for you, and then extending that to the problem you're trying to solve.
So when analyzing a tough physics problem I often end up analyzing something else first, which is simpler for me, and then I use the insights gained from that to help me solve the problem at hand. Sometimes there are different smaller problems which can be analyzed and which are related to the main problem. The combination of these separate analyses will then help you solve the main problem at hand.
Comparisons of the physics between harder problems and simpler problems can be subtle and involves thinking visually and in terms of mathematics. And it need not be neat and tidy. It can be a complicated mishmash of cobweb laden confusion which you turn over and over in your head until eventually (and hopefully) some clarity starts to emerge and you begin to muscle the problem into submission.
Once again, anything goes. If it can help you use it. This includes using whatever physical objects you have lying around to help you understand the problem. For a physics problem involving a ball why not get an actual ball and play with it to get a sense of what's going on.
Another technique I use, which is common in physics problem solving, is to formulate a "worst", or most conservative case, which makes the problem simpler, and then use that to arrive at the answer. For example, let's say you have a car going around a turn really fast and you have to determine if it flips over. Imagine a "worst" case where the wheels on the inside of the turn produce no contact force with the ground (meaning the car is on the verge of flipping over). Then solve the problem and see what speed the car must be traveling at. If the car speed is less than this then the car won't flip over.
There's a term I use called "grounding yourself" in which you reduce the problem to its most simple form and then think about the problem variables in a step-wise fashion. For example, if you have a bunch of billiard balls moving around a pool table, that would be pretty complicated to analyze, so the first thing to do is imagine that time is slowed down and then look at what collides first, and then look at the resulting motion of the balls from that. You then look at what collides second, and so forth. So the problem is actually pretty simple. You just have to march the problem forward in small time increments and then analyze what happens bit by bit. Here's another example. Let's say you have a complicated set of forces acting on an object. Imagine taking all those forces away and then putting them back one by one. Think about the physics of what's happening as you do so. This can give you some insights into how each of the forces affect the object.
But some problems are so complicated, with so many interacting components, that you can't conceptualize the entire system in your head, no matter what techniques you use to wrap your mind around it. It's a nice luxury to be able to conceptualize a problem, since it makes things intuitive and helps you arrive at a solution faster, with added insight (plus you feel smarter). But unfortunately it's not always possible. So in this case you just have to go ahead and set up the governing equations, make sure they are correct, solve, and the resulting solution will be the correct one.
The main lesson here is that physics is something where you have to learn a handful of indirect tricks to solve problems, such as the use of analogies, looking at worst cases, reducing the problem to a simpler form, etc. And if all else fails just focus on getting the equations right, and the solution will be the correct one.
And always assume you could be wrong, or to put it differently, never assume you are automatically correct. Always assume that errors are just around the corner if you're not careful and don't bother double checking your work. You never reach a point in physics, no matter how much skill and experience you get, where you can confidently say that you are always right without giving it a second thought. It's usually a bit of a battle to solve physics problems, especially the ones that are not of a rote nature.
When double checking your solution be thorough. Look it over line by line, and for each bit of information ask yourself, "is this right?" And if there's anything which you're not totally sure of go back and recheck, and rework if necessary. Now, you can't do this on tests and exams because there's no time to do so, but you do it for problems in the real world where you have more time to solve them and getting the right answer is more important.
Until next time.
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