Writing Problem Solutions in Physics Exam

Present your work so that the grader knows what you are thinking.

Just giving “the answer” to a problem without any work will earn you no credit, even if you are correct.

Style

Your problem solution should be written in technical style.

When helpful, present information in the form of idealized diagrams, tables, lists, mathematical derivations, and so forth.

Solution Structure

Diagram

Begin your solution by presenting the situation it describes and all of the information it gives you, i.e., by presenting your understanding of the problem definition. Drawing a picture is usually the most effective (and time efficient — very important on exams) way to do this; incorporate the given information into the picture by labeling it. Turn your picture into a technical diagram reducing the situation to only the physically relevant parts. For example, if our problem were about forces, draw a free-body diagram.

Given and target data

Describe the Physics. Convert the problem that you have described into physics terms.

Define physical variables. Write down given data and target quantity, using variable symbols.

Equations

Write down related equations that you think will be useful. Concretely, it often helps to classify your problem by its method of solution.

Math

Use mathematics to find a symbolic expression giving the target quantity in the terms of the given information.

I don’t ask you to provide textual commentary as you go, narrating what you are doing and explaining anything, as often it is very difficult to read hand-written texts, however you should write out all your steps of mathematical transformations in correct mathematical expressions.

Use logical symbols or short phrases (one - two words) to explain the sequence and the logic of your work. Make your logic clear.

You should use the conventions of physics and mathematics to communicate much information implicitly.

For example, don't explain that g is the acceleration due to gravity, because it is conventional and because of the context.

Solve with symbols first. Do not substitute numerical values into your expressions as you go. Work with symbols.

Substitution

When you have your symbolic solution giving the target quantity in the terms of the given information (expressed by symbols), you can substitute any given (or generally known ones, like g) numerical values with appropriate measurement units into your symbolic solution to find a numerical solution with measurement units. 

Show transformations with measurement units. Give prove that your symbolic solution give correct units of the target quantity. 

This part will not be present for problems that don’t provide numerical values.

Report

Write separately and highlight final numerical value. Report numbers with units specified and with reasonable significant figures.

Main Sections

So, main sections of your solution:

1. Diagram

2. Given and target data

3. Equations

4. Math (Math transformations to find a symbolic solution)

5. Substitution (Substitutions of numerical physical values into the symbolic solution)
6. Report

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