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Solving physics problems

What's a strategy for solving physics problems (using known physical laws)?

  1. Identify the relevant concepts, target variables (quantities we're trying to find), and known quantities (either given explicitly or implicitly in the problem)
  2. Set up the problem. Choose the tools that you will use to solve the problem and how you will arrange and connect these tools with one another. These tools are usually equations. Drawing a picture is sometimes helpful as well. Also try to make an estimate of the solution so you can have some intuition of where you're going.
  3. Execute (aka do the math).
  4. Evaluate the result. Is your answer close to your original estimate? If not, figure out whether your estimate was wrong or your answer was wrong. If there's a variable in the answer, think about whether the result of filling that variable would make sense for large and small values. Think about how you might solve more complicated or complex versions of the problem

Abstract away unnecessary details

If you were to take into account all of the possible details of a situation described in a problem, it would be hopelessly complicated and complex to solve. There's all sorts of details that exist but nonetheless stray far from what we're trying to solve for and the increased accuracy we would get from taking those details into account is simply not worth the cost. For example, if you were trying to find when a baseball would hit the ground after being thrown, you could take into account air resistance, how fast the ball is spinning, the fact that the ball isn't a perfect sphere (there's seams and manufacturing imperfections), etc. but really the only essential quantities we need to take into account are things like the initial velocity, the force gravity has on it, etc. What is considered "essential" depends on what the situation is you're trying to solve for. Are you an engineer trying to make a ball shooting machine that shoots x distance? Well you should probably take air resistance into account. But if we're just trying to figure out approximations, it's not necessary.

How valid predictions of a model for your situation are limited by the range of validity of the model. For example, Galileo's theory only works in the idealized case. But if you need to figure out how a feather is actually going to fall on Earth, it won't be useful. So which quantities are treated as essential changes the kinds of tools you can use.

Getting an estimate of an answer

Orders-of-magnitude calculations

Aka back-of-the-envelope calculations. Sometimes you don't know the exact data points for something you want to calculate but just using input values that are an order-of-magnitude off can give you a good idea of what the actual result might be like.