Process for Problem Solving

 

Below is a summary of the suggested steps when solving a standard end-of-the-chapter textbook problem.  These won't apply exactly to standard AP 1 problems which are often conceptual, but the ideas may still be helpful.

 

1. Read and understand the problem.  This may seem obvious, but it’s a good idea take a minute to thoroughly visualize what's happening.  If you can't, reread the situation until you can.

 

2. Draw a picture of what's happening. Even if a diagram is there, drawing-out what is happening and labeling all of the given values will reinforce the sense of what’s happening.  In the same diagram, write down the goal and draw a box around it.

 

3. Make a list of the stages of motion.  For each stage, define the system and decide what model or principle can best be applied (Newton’s second law, work-energy theorem, impulse-momentum theorem, etc.)

 

4. Write-out the full model(s) or principle(s) that will be used.  Write the plan that will be used to find the solution.

 

5. Follow the plan.  Write-out or draw all aspects of the solution (equations, free-body-diagrams, graphs, motion maps, energy pie charts, kinematics boxes).  If a given method or model doesn't work (say F = ma doesn't seem to get the answer), try another model (like work-energy).  If stuck in this step, try solving a simpler version of the given problem.  Let this suggest the solution to the original problem.

 

6. Check the solution.  If the solution is numeric, you can check that the value is reasonable.  If the solution is algebraic, you can check that the units on both sides of the equation are equal (dimensional analysis).  You can also check if the result makes sense if zero is inserted for a given variable or check that it makes sense if one value increases, a second value correspondingly increases or decreases.

 

7. Review the problem.  How did you know what models or principles to apply?  Are there other methods of solution?

 

Principles or models

 

1. Motion with constant acceleration: a =

 

2. Newton’s second law of motion: The acceleration of a system is equal to the net external force on the system divided by the inertial mass of the system.

 

3. Work-energy theorem: The net external work on a system is equal to the change in energy of the system.

 

4. Impulse-momentum theorem: The net external impulse on a system is equal to the change in momentum of the system.