PHYSICS PROBLEM SOLVING HELP SHEET
INTRODUCTION
When starting any task it is important to have the right tools for the job. When cooking for example, you need a
knife, a cutting board, a pan, and an oven. You also need to follow the right steps, in the correct order, to be
successful (i.e. a recipe!). This also applies to solving physics problems. Over the years, you’ve been developing
the right tools, or more familiarly skills (math, visualization, logic, spatial skills etc.) to solve physics problems,
and by now you may have even become quite good at it. But if you haven’t, then it’s quite possible that you are
either missing a few tools (skills) or perhaps a recipe (proper procedure). And even if this is the case, you still
may be able to solve some problems. After all, you may be able to cook a great meal without a knife or even
without following recipe. But can you cook everything this way? No.
The good news is that it’s pretty easy to know where you fall short and what you need to work on:
If you have math problems, visualization problems, problems with reasoning etc., then you will probably
already know you do. This is the area you will have to focus on.
If you are able to solve math problems easily, are very visual, have no problem with reasoning etc., but still
have difficulty solving physics problems then you most likely need to work on mastering the problem solving
procedure. If you are able to solve problems, but your solution is very messy or it takes a long time to solve,
then you should work on this area as well.
MISSING SKILLS
“When Vince Lombardi took over the Green Bay Packers, he was asked if he was going to change the players,
the plays, the training, or other key aspects of the team. He replied, ‘I’m not going to change anything; we
are simply going to become brilliant on the basics.’
The Green Bay Packers had been doing poorly for some years.
In his first meeting with the team, he famously picked up a football and said, ‘‘Gentleman, this is a football.’’
From then on, Lombardi concentrated on the basics, running drills aimed at making his team faster and
more effective at executing plays than any other team. He took the Green Bay Packers to two Super Bowl
Championships and made football coaching history.”
– How the Best Leaders Lead, Brian Tracy
If you are missing a few skills, you need to identify which ones you are missing and work on them. In other
words, you need to go back to the basics. Even something as simple as refreshing a few bits of knowledge will
go a long way.
There is no secret to becoming a master at a skill. It just requires hard work and patience. Start with easy
exercises to build up your confidence and work your way up to harder problems. Practice lots and soon, the skill
you are working on will become second nature and you will wonder how you ever found some problems so hard.
MISSING PROCEDURE
“1. Write down the problem. 2. Think really hard. 3. Write down the answer.”
– How the Best Leaders Lead, Brian Tracy
The best way to solve a problem is to simplify the steps we use in solving it. Many people, when confronted with
a problem, don’t know where to start. Sometimes the problem seems overwhelming because of all the
information given. Sometimes people try to do too much too quickly when solving problems and end up with a
mess. The GRASP method has been developed to alleviate these problems. GRASP is an acronym for Given,
Required, Analysis, Solution, and Paraphrase.
Given: What is known about the problem?
In this step, we list what we know about the problem. We do this using variables and point form notes, going
sentence by sentence to extract the important details. We basically build a foundation for the problem with the
information we gather. You may think this step is pointless and say to yourself what’s the point of this?
Everything is already listed in the problem! But it is very important. Sometimes problems can be very complex
or they can be worded in a complicated manner. Writing what is known about the problem in variables makes
the problem easier to understand. It will also help us during the analysis stage of the problem.
Required: What do we need to find out?
Here, we write down what we need to find. Again, we do this, using variables. Sometimes, problems are broken
down into many parts. Therefore, this will make it clear as to exactly what we need to find. It will also help us
during the analysis stage.
Analysis: How will we find the solution?
Now that we have written down what is given and what is required, we can start thinking as to how to solve the
problem. With most textbook problems, the equations which we must use to solve the problem are usually within
the chapter. Having written down the given and required variables, we can simply try and find the equation that
relates them together. If we can’t correlate the variables with each other immediately, then we may need to use
a few different equations to relate them together. If we can almost correlate the variables to one another, but
have a few missing pieces of information, then perhaps we need to make some assumptions or look up some
reference values in a table. All in all, in this step we will have an outline of how we will solve the problem.
Solution: Find the solution.
We can now go through the motions of solving the problem through the steps we outlined in the analysis. It
should be straight forward from here since we have all our background material neatly listed and we have our
steps laid out.
List all the steps clearly. If we make a mistake, it will be much easier to go back and find out where it happened.
Remember, units are extremely important in physics and should NEVER be omitted. Make sure units are
consistent and make their cancellations clear. The units serve as a quick check of the final answer. If the units
do not match those of the required variable, then we made a mistake somewhere along the way.
Paraphrase: What is the answer?
This step is the simplest. We just write out the answer in a sentence. This makes our answer easy to find rather
than lost somewhere within the solution and keeps everything neat.
The GRASP method is great as it unclutters problems and keeps your solution elegant and organized. It will also
allow you to easily identify your mistakes much easier. If the problem you are solving is part of a homework
assignment, it makes the marker’s life so much easier.
CONCLUSION
You now know what you need to do in order to improve your physics problem solving. If you are missing the
proper skills, go and master them. If you aren’t using, the GRASP method, grasp it and you’ll be on your way. The
synergy of both will help you solve problems faster and allow you to approach larger more complicated
problems with confidence.
EXAMPLE OF THE GRASP METHOD
Problem:
Two UOIT physics students are at the southwest corner of the Polonsky commons discussing the fine nuisances
of physics, the universe, and all that is grand (because that’s what physics students do). They realize they don’t
understand a certain concept as well as they should, so they decide to race to the Student Learning Centre
(SLC) to book an appointment with the Physics/Engineering specialist. Student A chooses to run along path A
(diagonally across the grass) and Student B chooses to ride his bike along path B as shown in Figure 1. Both
students start from rest. Student A accelerates constantly until he reaches a distance of 10 m at which point he
runs at 6 m/s for 120 m. After this he decelerates constantly such that his velocity at the Student Learning
Centre is 0 m/s. Student B accelerates constantly for 5 s. During this interval he reaches a speed of 10 m/s. He
then travels at this speed for a total of x s. After which he decelerates constantly such that his velocity is 0 m/s
when he reaches the Student Learning Centre. Who will get to the Student Learning Centre first?
Given
70 m
10 m
U6
UL
60 m
U5
Library
Path B
(on bike)
Path A
UB
(on foot)
START
UA1
Student B
Segment 1
Segment 1
x A 1i = 0 m
x B 1i = 0 m
x A 1f = 10 m
V B 1i = 0 m /s
V A 1f = 6 m /s
t B1 = 5 s
V A 1i = 0 m /s
ERC
110 m
Student A
UA2
Figure 1: Physics Student Race
Note: We are also given the distances of the paths in
Figure 1, however, there is no need to relist it as
Figure 1 is very clear and easy to read.
a A1
= constant
V B 1f = 10 m /s
a B1
= constant
Segment 2
Segment 2
x A 2i = 10 m
v B 2i = 10 m /s
x A 2f = xA 2i + 120m
V B 2f = 10 m /s
V A 2f = 6 m /s
a B 2 = 0 m /s 2
V A 2i = 6 m /s
a A2
= 0 m /s 2
t B 2 = 10 s
Segment 3
Segment 3
x A 3i = xA 2i + 120m
V A 3i = 6 m /s
V B 3i = 10 m /s
V A 3f = 0 m /s @U6
a A 3 = - constant
V B 3f = 0 m /s @U6
a B 3 = - constant
The given material has been carefully extracted and is now organized in a neat and elegant manner which will
help us solve the problem. Notice how subscripts have been carefully used to easily identify variables.
Required:
How long does it take for Student A to get to the SLC?
How long does it take for Student B to get to the SLC?
( t Af = ?)
( t Bf = ?)
( Is t Af < , > or = t
Who got to the SLC first?
Bf ?)
As you can see, we have converted the word problem into mathematical form and now know exactly what
variables we are looking for.
Analysis:
Since we are required to find how long it takes Students A and B to get to the SLC and we are not given the
distance they travel in each segment directly, we should calculate the total distance each travels. The distance of
Student B’s path, x A , can be easily calculated as the distances of his route are specified. The distance of
Students A’s path, x B , will require us to use the Pythagorean theorem.
Student A
Student B
Segment 1
Segment 1
We know x i , x f , v i , v f , and we know that a is
constant, hence, we will use the following equation
to find the time, t :
xf = xi +
1
(v +v ) t
2 i f
We know the time Student B takes to travel during
this segment and this will help us determine who got
to the SLC faster. However, we want to find out how
far Student B travelled during this time so that it can
assist us in the Segment 3 calculation. We know x i ,
v i , v f , as well and we know that a is constant,
hence, we will use the following equation to find the
distance travelled, x B 1 f :
xf = xi +
Segment 2
We know x i , x f , v i , v f , and we know that a is
zero, hence, we will use the following equation to
find the time, t :
V=
x f - xi
t
1
(v +v ) t
2 i f
Segment 2
Again we know the time Student B takes to travel
during this segment and this will help us determine
who got to the SLC faster. However, we want to find
out how far Student B travelled during this time so
that it can assist us in the Segment 3 calculation.
We know v i , v f , t B 2 and we know that a is zero,
hence, we will use the following equation to find the
distance travelled during this segment, x B 2 :
V=
x
x f - xi
= B2
t
t
Student A
Student B
Segment 3
Segment 3
In this case, the distance and the time are not given.
We know the length of travel of the previous two
segments. We also are to initially calculate Student
A’s total path length, x A . This is equivalent to x A 3 f
We now know x i , x f , v i , v f , and we know that a is
constant, hence, we will use the following equation
to find the time, t :
xf = xi +
1
(v +v ) t
2 i f
The distance and the time are not given. We know
the length of travel of the previous two segments, as
we calculated them. We also are to initially calculate
Student B’s total path length, x B . Therefore, we can
find the total length of Segment 3, through:
x B3 = x B - x B2 - x B1
We now know x f - x i , v i , v f , and we know that a
is constant, hence, we will use the following equation
to find the time, t :
xf - x i=
1
(v +v ) t
2 i f
Once we have the time it takes Students A and B to complete their path, through the three segments of travel,
they will be summed up and compared to one another to determine who came to the SLC the fastest.
The groundwork for the solution has been laid out and now all we have to do is put in the values and solve.
Solution:
Student A Path Length
x A = ( 110 m) 2 + ( 70 m) 2 + 60 m + 10 m
x A = 200.38 m
x B = 110 m + 70 m + 60 m + 10 m
x B = 250 m
Student A
Student B
Segment 1
Segment 1
1
(v +v ) t
2 i f
1
x A 1 f = x A 1 i + (v A 1 i +vA 1 f ) t A 1
2
m
1 m
10 m = 0 m + ( 0 + 6 ) t A 1
2 s
s
m
1
10 m = ( 6 ) t A 1
s
2
t A 1 = 3.33 s
t A 1 = 3.33 s
x A 1 = 10 m
xf = xi +
Student B Path Length
1
(v +v ) t
2 i f
1
= x B 1 i + (v B 1 i +vB 1 f ) t B 1
2
m
1 m
= 0 m + ( 0 +10 ) ( 5 s)
2 s
s
m
1
= ( 10 ) ( 5 s)
s
2
t B1 = 5 s
= 25 m
x B 1 = 25 m
xf = xi +
x B1f
x B1f
x B1f
x B1f
Student A
Student B
Segment 2
Segment 2
x f - xi
t
x A2f - x A2i
=
t A2
V=
V A 2f + VA 2i
2
m
m
6 s +6 s
2
=
V B2f + VB2i
x A 2 i + 120 m - x A 2 i
m 120 m
6
=
s
t A2
t A 2 = 20 s
t A2
m
m x B2
10
=
s 10 s
x B 2 = 100 m
Student A
Student B
Segment 3
Segment 3
1
(v +v ) t
2 i f
1
x A 3 f = x A 3 i + (v A 3 i +vA 3 f ) t A 3
2
m
1 m
200.38 m = 130 m + ( 6 + 0 ) t
2 s
s A3
70.38 m = ( 3
A3
m
2
10 s + 10 s x B 2
=
2
10 s
t A 2 = 20 s
x A 2 = 120 m
xf = xi +
t
x f - xi
t
x B2f - x B2i
=
t
V=
m
s ) tA3
= 23.46 s
t B 2 = 10 s
x B 2 = 100 m
x B3 = x B - x B2 - x B1
x B 3 = 250 m - 100 m - 25 m
x B 3 = 25 m
xf - x i= +
1
(v +v ) t
2 i f
1
(v +v ) t
2 B3i B3f B3
m
m
1
25 m = ( 10
+0 ) t B 3
s
s
2
x B3 =
t A 3 = 23.46 s
x A 3 = 70.37 m
25 m = ( 5
t B3 = 5 s
m
)t
s B3
t B3 = 5 s
x B 3 = 25m
Student A
Student B
Total time to get to the SLC
Total time to get to the SLC
t A = t A 1+ t A 2 + t A 3
t A = 3.33 s + 20 s + 23.46 s
t A = 46.79 s
t B = t B1 + t B2 + t B3
t B = 5 s + 10 s + 5 s
t B = 20 s
The solution was easy to solve as the “thinking” was completed in the analysis section. Make note of how
elegant the presentation is. Finding an error or mistake would be very easy.
Paraphrase:
Student B, the one who rode his/her bike to the Student Learning Centre, got there first. He/she got to the SLC
in 20 s, while Student A got to the SLC in 46.79 s.
This was an easy example and you could have probably done the question without using the GRASP method.
However, it proves to illustrate how the GRASP method keeps the problem and solution organized and easy to
follow. Getting into the habit of using the GRASP method will help you solve more difficult problems later on in
the future.
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Email: [email protected]
Website: uoit.ca/studentlearning
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CENTRE