## Section 1.4 Problem Solving

###### Key Questions

What are some strategies to practice selecting a tool from your problem-solving toolbox?

What is the basic problem-solving process for equilibrium?

Statics may be the first course you take where you are required to decide on your own how to approach a problem. Unlike your previous physics courses, you can't just memorize a formula and plug-and-chug to get an answer; there are often multiple ways to solve a problem, not all of them equally easy, so before you begin you need a plan or strategy. This seems to cause a lot of students difficulty.

The ways to think about forces, moments and equilibrium, and the mathematics used to manipulate them are like tools in your toolbox. Solving statics problems requires acquiring, choosing, and using these tools. Some problems can be solved with a single tool, while others require multiple tools. Sometimes one tool is a better choice, sometimes another. You need familiarity and practice to get skilled using your tools. As your skills and understanding improve, it gets easier to recognize the most efficient way to get a job done.

Struggling statics students often say things like:

“I don't know where to start the problem.”

“It looks so easy when you do it.”

“If I only knew which equation to apply, I could solve the problem.”

These statements indicate that the students think they know how to use their tools, but are skipping the planning step. They jump right to writing equations and solving for things without making much progress towards the answer, or they start solving the problem using a reasonable approach but abandon it in mid-stream to try something else. They get lost, confused and give up.

Choosing a strategy gets easier with experience. Unfortunately, the way you get that experience is to solve problems. It seems like a chicken and egg problem and it is, but there are ways around it. Here are some suggestions which will help you become a better problem-solver.

Get fluent with the math skills from algebra and trigonometry.

Do lots of problems, starting with simple ones to build your skills.

Study worked out solutions, however don't assume that just because you understand how someone else solved a problem that you can do it yourself without help.

Solve problems using multiple approaches. Confirm that alternate approaches produce the same results, and try to understand why one method was easier than the other.

Draw neat, clear, labeled diagrams.

Familiarize yourself with the application, assumptions, and terminology of the methods covered in class and the textbook.

When confused, identify what is confusing you and ask questions.

The majority of the topics in this book focus on equilibrium. The remaining topics are either preparing you for solving equilibrium problems or setting you up with skills that you will use in later classes. For equilibrium problems, the problem-solving steps are:

Read and understand the problem.

Identify what you are asked to find and what is given.

Stop, think, and decide on an strategy.

Draw a free-body diagram and define variables.

Apply the strategy to solve for unknowns and check solutions.

Write equations of equilibrium based on the free-body diagram.

Check if the number of equations equals the number of unknowns. If it doesn’t, you are missing something. You may need additional free-body diagrams or other relationships.

Solve for unknowns.

Conceptually check solutions.

Using these steps does not guarantee that you will get the right solution, but it will help you be critical and conscious of your chosen strategies. This reflection will help you learn more quickly and increase the odds that you choose the right tool for the job.