GOAL Problem Solving Steps
Gather information
The first thing to do when approaching a problem is to understand the situation. Carefully read the problem statement, looking for key phrases like “at rest,” or “freely falls.” What information is given? Exactly what is the question asking? Don’t forget to gather information from your own experiences and common sense. What should a reasonable answer look like? You wouldn’t expect to calculate the speed of an automobile to be 5 106 m/s. Do you know what units to expect? Are there any limiting cases you can consider? What happens when an angle approaches 0 or 90 or a mass gets huge or goes to zero? Also make sure you carefully study any drawings that accompany the problem.
Organize your approach
Once you have a really good idea of what the problem is about, you need to think about what to do next. Have you seen this type of question before? Being able to classify a problem can make it much easier to lay out a plan to solve it. You should almost always make a quick drawing of the situation. Label important events in your sketch. Indicate any known values, perhaps in a table or directly on your sketch. Some kinds of problems require specific drawings, like a free body diagram when analyzing forces. Once you’ve done this and have a plan of attack, its time for the next step.
Analyze the problem
Because you have already categorized the problem, it should not be too difficult to select relevant equations that apply to this type of situation. Use algebra (and calculus, if necessary) to solve for the unknown variable in terms of what is given. Substitute in the appropriate numbers, calculate the result, and round it to the proper number of significant figures.
Learn from your efforts
This is actually the most important part. In the real world, you would use this as an opportunity to consider what experience you have gained by successfully solving this particular problem. In the more artificial academic world, try to put yourself in your instructor’s place. Why did he or she assign this specific problem? You should have learned something by doing it. Can you figure out what?
Examine your numerical answer. Does it meet your expectations from the first step? What about the algebraic form of the result before you plugged in numbers? Does it make sense? (Try looking at the variables in it to see if the answer would change in a physically meaningful way if they were drastically increased or decreased or even became zero.) Think about how this problem compares to others you have done. How was it similar? In what critical ways did it differ?
For complex problems, you may need to apply these four steps of the GOAL process recursively to subproblems. For very simple problems, you probably don’t need this protocol. But when you are looking at a problem and you don’t know what to do next, remember what the letters in GOAL stand for and use that as a guide.
GOAL Problem Solving Steps
Gather information
- What is the question asking for?
- Write down the relevant known and unknown quantities with units.
- Predict a reasonable range for the answer based on your own common-sense experiences.
- Consider how the answer could vary for limiting cases. (e.g. What happens when an angle approaches 0 or 90 or when a mass goes to zero?)
- Look for key phrases like “at rest,” or “falls freely” for clues about relevant physics principles.
Organize your approach
- Draw a diagram labeled with the variables assigned from the G step above to help visualize the situation.
- Draw any additional diagrams or graphs needed to visualize the physics of what’s going on.
- Classify the problem according to the general physics principles that apply. (e.g. Newton's second law, conservation of energy)
- Describe how you will solve the problem.
Analyze the problem
- Write down relevant general equations (express general physics principles in equation form).
- Add equations of constraint that specify special conditions that restrict the problem. (e.g. two objects have the same mass: m1 = m2) Make sure that you have enough equations to solve the problem (the same number of independent equations as variables).
- Solve for the desired unknown variable (on the left of the equation) in terms of the known variables (on the right). This may require manipulating and combining several equations without substituting numbers.
- Substitute known values, calculate a numerical answer, and round the answer to the appropriate number of significant figures based on the precision of the input data.
Learn from your efforts
- Check your answer.
Does the answer agree with the prediction in the G step?
Are the units correct?
Does the result have the correct sign or direction?
Does the algebraic result make sense for limiting cases as predicted in the G step?
- If the problem were modified, how would the result change? (e.g. What if air resistance or friction were significant factors?)
- Why was this particular problem assigned?
What is the key point or critical issue in this problem?
How is this problem similar or different from other problems you have examined?
GOAL Problem-solving Template
Gather information: (2 pts.)
What is known? What are you looking for?
Predict a reasonable answer with units. (Consider limiting cases.)
Organize your approach: (2 pts.)
Draw a diagram(s) labeled with variables from G step.
Classify the problem according to the general physics principle(s) used.
Describe how you will use the general principle(s) to solve the problem.
Analyze the problem: (3 pts.)
Identify and show general physics equations.
Add constraints that specify condition that restrict the problem.
Solve for the unknown variable in terms of the known variables.
Substitute known values, calculate answer, round appropriately.
Learn from your efforts: (3 pts.)
Check your answer. Does the answer agree with the prediction in G step? Correct units?
Does the algebraic result make sense for limiting cases?
If the problem were modified, how would the result change?
Why was this particular problem assigned?