Problem solving is one of the areas physics education research (PER) focuses on.
Before I look at the aspects of physics problem solving that PER has reported, I would like to put down my thoughts on physics problems after being a physics learner and now a physics educator for 10+ years.
Physics problems can be separated into different levels. For simplicity, I will just do 3 categories: Easy, Medium, Hard. Note: my categorization is based on students at the pre-university level.
Easy problems are the plug-and-chug problems. In my opinion, these problems are meant to get students to use the formula students learned in the chapter. For example, suppose students learned the formula for Newton’s 2nd law, , easy problems looked like this:
The car has a mass of 800 kg and an acceleration of 1.0 m/s2. What is the net force acting on the car? (Answer: 800 N)
These problems only require the usage of 1 formula. The numbers to be substituted in the formula can be found in the question directly without any additional calculations.
For problems of Medium difficulty level, they require the use of 2-3 formulae on average. Such problems can be about a single topic or multiple concepts.
A single-topic (projectile motion) Medium difficulty level problem looks like this:
A pipe discharges storm water into a creek. Water flows horizontally out of the pipe at 1.2 m/s, and the end of the pipe is 3.0 m above the creek. How far out from the end of the pipe is the point where the stream of water meets the creek? [Answer: 0.94 m]
Here are the steps to solve the above question:
(1) Find the time taken for the water to fall 3.0 m vertically first by using .
(2) Find the horizontal distance traveled by the water by using .
A Medium difficulty level problem involving multiple concepts looks like this:
The car has a mass of 800 kg and an acceleration of 1.0 m/s2. What is the kinetic energy of the car after it travels 10 m from rest? [Answer: 8000 J]
Here are the steps to solve the above question:
(1) Find the net force acting on the car using .
(2) Find the work done by net force on the car by using .
(3) Using the fact that work done by net force on the car = change in kinetic energy of the car.
Alternative approach:
(1) Find the final speed of the using .
(2) Find the kinetic energy of the car using .
To solve Medium level physics problems, one needs to have good familiarity of the formula learned from the different physics chapters. In general, the later chapters in physics tend to require certain ideas learned in the earlier chapters, such as Newton’s laws and conservation of energy. Some interpretation of the numbers obtained may be necessary.
In Hard problems, students need to demonstrate that they can solve quadratic equations or simultaneous equations, and interpret the numbers calculated along the way to express the answer in the appropriate manner. These question tend to involve multiple concepts and be more mathematical in nature.
One example would be motion of charged particle in a parallel plate setup. In the diagram below, a positively charge particle is moving into a region of uniform electric field with an initial velocity . Find the direction of velocity of the particle if the particle emerges from the plate at the bottom right end.
To solve these question, here are the steps:
(1) Find the x-component of the velocity.
(2) Find the acceleration along the vertical direction using the electric force and Newton’s second law.
(3) Find the y-component of the velocity using the kinematics equation.
(4) Find the magnitude of velocity using Pythagoras theorem.
(5) Find the direction of velocity using .
This example is pretty involved an many steps are needed. Students need to be familiar with the ideas from electric field, Newton’s laws, and 2D-kinematics.
In my opinion, all three levels of problems are necessary for students. However, students should not expect that physics problems in exams to be in the Easy and Medium level of difficulty. Some problems will be in the Hard difficulty. The exams need to differentiate students who are really good from the group.
How to get better in solving physics problems?
- Practice. Physics problems are not too far from applied mathematics problems. It involves the use of formula and apply them in appropriate situations. It is not easy to remember how and when to use a formula without using it in different situations on your own.
- Reflect. This is a necessary step. After solving problems using a particular method a few times, one needs to reflect on why that method works. It will help to reinforce conceptual understanding and problem solving ability.
- Teach. If you have the chance to help others, teach your friends or other people how to solve physics problems. Teaching gives you more opportunities to revise your physics knowledge and sometimes you may discover different ways to approach the same problem.
Everyone would agree that physics teachers do these 3 things all the time. For beginners, you will start from the Practice stage. When you revise for exam, that is when most people perform their Reflect stage. After that, it is rinse and repeat. Usually after a few exams, you will know who the better ones are. Some of them may end up becoming the little teachers in the class, reaching the Teach stage. However, teaching is not restricted to students who are really well in physics. If you have something to contribute and are proper physics, you can teach as well!
That’s all from me for now. If you have any comments, please let me know.
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