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:
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 rearrangement of the equation before substituting any data
into the equation. It is easier to manipulate equations using
pronumerals rather than numerals. Having performed any required
rearrangement, 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, rearranging 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 velocitytime 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.
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