## Solving Problems in Physics

1.7 Solving Problems in Physics

### Learning Objectives

By the end of this section, you will be able to:

- Describe the process for developing a problem-solving strategy.
- Explain how to find the numerical solution to a problem.
- Summarize the process for assessing the significance of the numerical solution to a problem.

### Strategy

*Examine the situation to determine which physical principles are involved*.*Make a list of what is given or can be inferred from the problem as stated (identify the “knowns”)*.*Identify exactly what needs to be determined in the problem (identify the unknowns)*.*Determine which physical principles can help you solve the problem*.

### The I.S.E.E. Solution Method

Often students believe the important thing when solving a problem is to get the right answer, no matter how you get there. While this can be useful for some students in the short term, it only encourages sloppy thinking, and can sometimes lead to the issue that you get to the right end-point without really understanding how you got there, or what the implications of getting there are.

A well-written physics solution is akin to a well-written short essay in a humanities class. It has an introduction, a body, and a conclusion. Following the I.S.E.E. method will help hone your “thinking-like- a-scientist” skills and will better prepare you for dealing with an unfamiliar problem in, say, an exam situation. Furthermore, your solutions will form a useful archive for you to return to when reviewing – you will be much better able to decipher what you were thinking when you wrote it. (You’ll also remember better what you did the first time.)

The I.S.E.E. method consists of four parts: **I**dentify, **S**et Up, **E**xecute, and **E**xplain/**E**valuate.

**Identify** – What information is given and what will you need to find?

- Explicitly state what the problem is asking including clarifying the problem statement.
- Identify the target variables of the problem – that is, the quantities whose values you’re trying to find.
- Identify the known quantities, as stated or implied in the problem.
- Identify applicable concepts/laws and assumptions/simplifications. Think what physics concepts/laws are involved and what assumptions you can make about the physical situation in order to apply those concepts/laws.

**Set Up** – Represent the problem physically and mathematically

- Represent physically. Translate the text of the problem into an appropriate type of physical representation (This may be a picture, a free-body diagram, an energy bar chart, a ray diagram …).
- Represent the concepts/laws mathematically. Use the physical representation to construct a mathematical representation. You should have a symbolical mathematical statement that clearly shows what concept/law you are starting with to solve the problem. For example, a 1-d kinematics equation could start with x
_{f}= x_{0}+ v_{0}t + 1/2at^{2}. - As best you can, estimate what your results will be and predict what the physical behavior of a system will be.

**Execute** – Work through the mathematics.

- Use the mathematical relationships you identified earlier to clearly solve for the unknown quantity (quantities). Make sure you include enough steps that someone can follow your work and that you use consistent units.
- Keep symbols in your solution as long as possible and only put numbers in at the final step. Make sure you include appropriate units in your final answer.

**Explain/Evaluate** – Was your answer as expected, does it make physical sense?

- Is the final value you found reasonable? Are the units appropriate? Compare your answer with your estimate(s), and reconsider things if there’s a discrepancy.
- If your answer includes an algebraic expression, assure yourself that it correctly represents what would happen if the variables in it had very large or very small values. Does the result make sense in limiting cases?
- Does the result make physical sense? Include an explanation for why your result makes sense and what it tells you about what happens in the physical situation.

The I.S.E.E. method must be used for all problem solutions, quizzes, and exams. The figure above shows the weighting of each part of an I.S.E.E. method solution. Notice how the correct answer is only worth 1/10 of the total score. Every part of the I.S.E.E. solution is important, necessary, and critical for communicating scientifically.