HOW TO SOLVE PHYSICS PROBLEMS
By its very nature Physics is the most fundamental of all Sciences. Physics attempts to describe and explain the universe as accurately and precisely as possible, from the tiniest entity and interaction to the largest. The predictive power of Physics allows us to design and build new structures, machines, devices and equipment to improve our quality of life. To successfully achieve all of the above, the Physicist must be an accomplished problem solver. That is the reason why every school and undergraduate Physics course contains its fair share of both experimental work and mathematical problem solving exercises. Both of these activities help students develop the key problem solving skills essential for all Physicists.
Although most students love experimental work (except perhaps for the Lab Reports), many students experience difficulty when first encountering Physics problem solving exercises. Often students lose confidence in themselves because of the difficulty they have with solving mathematical Physics problems. As it says on the front cover of the "Hitch Hiker's Guide To the Galaxy" – Don't Panic!
The following are suggested steps to help you become confident and proficient at solving mathematical Physics problems.
When solving a specific problem:
Read the problem carefully all the way through.
Go back through the problem. Draw a diagram of the situation. Write down the data you are given as you come across it and also what you are trying to find or do.
The data you are given and the quantity you are trying to determine should suggest to you the equation to use to solve the problem.
Select the appropriate equation (or in some cases equations) and perform any re-arrangement of the equation before substituting any data into the equation. It is easier to manipulate equations using pro-numerals rather than numerals. Having performed any required re-arrangement, substitute the data, making sure to use both appropriate units (usually SI Units) and appropriate signs (+ or -) for all vector quantities. For instance, if you are using v = u + at to determine the final velocity of a car, the signs of u and a are vital.
Solve the equation carefully and when you have an answer, think about it to check that it makes sense. Silly mistakes with algebra can often be corrected by having an idea of the approximate size and sign of the expected answer. Make sure you state the answer with its correct units.
Some general suggestions:
Learn all the formulas you are going to use. Yes that's right – learn them off by heart. I know all the formulas are supplied in exams but why waste your time constantly checking the Equations Sheet to find the right equation. Learn the equations. It will save you time and increase your confidence in yourself.
Know & use the correct units for all quantities.
Set out all solutions neatly and in a logical manner. State clearly what you are doing. That will not only help you, when you come back to study, it will develop a habit of neat, logical solutions that will impress examiners and make it easy for them to follow.
Draw diagrams to help visualise problems. Draw neat and tidy diagrams and graphs, as large as is practical and use a ruler to draw all straight lines – eg for vectors. Every vector must have an arrow and a label.
Practise as many problems as possible. There are lots of questions and worksheets on my site. There are many good question books around. Ask your teacher for guidance on what to buy and also for extra questions that he or she may be able to supply for you. Remember, nothing in this life is totally free. If you want to be the best problem solver you can be, you must practise on a regular basis.
Example Problems Using the Steps Above
The first example below is a simple kinematics problem. I have solved it explicitly pointing out the steps involved. This example is probably sufficient to enable you to get the idea of how to approach, set out and solve Physics problems.
The following four examples are more difficult problems. You may find them helpful to read through now or you may prefer to come back and have a look at these problems, as you encounter similar problems in the course.
Examples 2 to 5 are contained in the one Word document below. The solution to each problem is a separate pdf file. Note that I have not explicitly identified the individual steps in the solutions. As you read through the solutions you should try to identify the steps used to solve each problem.
Practice makes perfect. Stay calm and confident. Think things through physically. All the best in your problem solving. Keep having fun.