AP Physics: Problem solving strategy

How to avoid making physics seem like this:

When solving any physics problem (or any problem in life) it is best to:

1. Read the problem completely!
2. Identify what the problem is asking.
3. Identify the model you likely will use to solve the problem: Is it a simple kinematics problem, an energy problem, a collision problem, a wave problem, etc.
4. Define your system.
   • What are the objects that you are studying.
   • Are there any objects that interact with your system that are not part of it.
5. Sketch the situation
   • In your sketch, identify coordinate system: Where is your axis, and which way is positive for both horizontal and vertical.
   • Even if an image is provided, manually sketching it has two benefits:
     • You have to think about and notice all the information provided, some of which may be in the problem and not in the image provided.
     • You activate another part of your brain, and the more of your brain you activate, the better your problem solving skills are.
   • While not all of us are sketch artists, do your best to be neat.
     • Give yourself plenty of space. In general, larger images are easier to see and divide into different sections.
6. List all the information that is given.
   • Write all of the information in the form ‘variable = value units’
     • e.g. velocity initial = 3.2 m/s or kinetic energy = 6.3 J
   • Remember, some variables may be ‘hidden’ without numbers, e.g. “the car comes to a stop” implies that the final velocity is zero.
   • If the problem is on a sheet of paper you can mark up, it’s OK to circle the information provided, then label each with an arrow.
7. Write out a sentence/equation that your final solution will look like. For example:
   • “The gravitational energy at the top of the second hill is ____ Joules.”
   • “The final velocity of Cart A will be _______ m/s and the final velocity of Cart B will be ____ m/s.”
8. Look at your diagram, given data, and final solution, and find an equation that has all those variables in it.
   • In some cases, you may need to combine two equations.
   • In other cases, it may appear that you are missing a variable, but that variable may ‘cancel out’ in Step 9 (e.g. mass often is not needed in gravity problems).
9. Write down the standard form of the equation.
10. Rearrange the problem to solve for the unknown.
11. Plug and chug!
12. Re-write your sentence you wrote in Step 7 with the final answer included.
13. Check: Does this answer make sense? Is it in a reasonable range; does positive/negative directions make sense?

Special case add-ons

One dimensional collision strategy

1. After completing the general steps above:
2. Write a general express for the total momentum of the system before and after the collision. This should look something like:
   • m₁ v₁ x m₂ v₂ = m₁ v_1f x m_2f v_2f
   • Remember that some velocity values are likely negative, but not necessarily.
   • Read the problem carefully: In most cases the mass of the objects does not change.
3. If the collision is elastic, write a general express for the total kinetic energy of the system before and after the collision.
4. Solve the equation. In elastic collisions, it is helpful to remember that, if the masses don’t change, combining the energy and momentum equations results in the following ‘shortcut’ equation. You will need to memorize this one if you want to use it.
   • v_1i – v_2i = negative ( v_1f– v_2f)