HOW TO SOLVE PHYSICS PROBLEMS

                                                 Samantha Carter - serious problem solver in StarGate SG1

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: 

1.      Read the problem carefully all the way through.
 

2.      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.
 

3.      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.
 

4.      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.
 

5.      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: 

1.      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.
 

2.      Know & use the correct units for all quantities.
 

3.      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.
 

4.      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.
 

5.      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

Example 1: 

A Ford Falcon is travelling at a constant velocity of 30 ms^-1 east along a straight, flat road.  The driver applies the brakes to produce a uniform deceleration of magnitude 10 ms^-2 to bring the car to rest.  Determine the time taken by the car to come to rest.

Solution: 

Having read the problem through once, we go back, draw a diagram and write down what we know & what we are looking for.  This produces the following.

u = 30 ms^-1 East =  + 30 ms^-1 (note that we have decided that East is positive)

a = 10 ms^-2 West =  - 10 ms^-2

v = 0 ms^-1

t = ? (we are looking for the time)

The data clearly suggest using the equation v = u + at.  So, re-arranging this equation before entering the data we have

           t = (v – u) / a.

Substituting into this equation we have

               t = (0 – 30) / (-10) = 3 s.

Clearly, the time taken by the car to come to rest is 3 seconds.

In Examples 2 to 5 below, I have not overtly 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.

Example 2:

A train travels from one station, A, to the next station, B, at a constant speed of 100 km/h and returns at a constant speed of 150 km/h.  Compare the average speed and the average velocity for this journey.

Warning: The average speed is NOT 125 km/h.  Why not?  The reason is that the acceleration is not constant over the whole journey.  This is not one continuous trip where a train accelerates uniformly from 100 km/h to 150 km/h and we want to calculate its average speed over that period of time.  The train in this question must accelerate and decelerate albeit briefly on each leg of its journey.

Go to Solution - this is a pdf file.  You will require an appropriate reader such as Adobe Acrobat.

Example 3:

A stone is thrown vertically upwards with a velocity of 29.4 m/s from the edge of a cliff 78.4 m high.  The stone falls so that it just misses the edge of the cliff and falls to the ground at the foot of the cliff.  Determine the time taken by the stone to reach the ground.  Assume the acceleration due to gravity is 9.8 ms^-2.

Note that this question is probably harder than you would expect to get under the current Syllabus.

Go to Solution - this is a pdf file.  You will require an appropriate reader such as Adobe Acrobat.

Example 4:

A police car is parked at the side of a highway with its engine running.  A car speeds past the police car at 30m/s.  The police immediately give chase, moving with a constant acceleration until they catch the speeding car after 50 s.  The speeding car maintains a constant speed of 30 m/s throughout the chase. 

(a)   Sketch the motion of both the speeding car and the police car on a velocity-time graph.
 

(b)   Calculate the speed of the police car at the instant it reaches the speeding car.
 

(c)   Use the graph to determine the acceleration of the police car.

Go to Solution - this is a pdf file.  You will require an appropriate reader such as Adobe Acrobat.

Example 5:

Two cars have a collision at a 90^o intersection.  Car A of mass 500 kg was travelling west at 20 ms^-1 before the collision.  Car B of mass 650 kg was travelling north at 25 ms^-1 before the collision.  After the collision the cars were locked together.  Find: 

(a)   the momentum of car A before the collision;
 

(b)   the momentum of car B before the collision;
 

(c)   the total momentum before the collision;
 

(d)   the total momentum after the collision;
 

(e)   the loss in kinetic energy during the collision.

Go to Solution - this is a pdf file.  You will require an appropriate reader such as Adobe Acrobat.

Practice makes perfect.  Stay calm and confident.  Think things through physically.  All the best in your problem solving.  Keep having fun.

Top of Page