PROBLEM SOLVING IN PHYSICS
INTRODUCTION
The general goal of physics is to provide a quantitative understanding of the laws in our Universe. Problem solving
within physics is the means to applying the fundamental laws of the universe to real world applications and experimental observations. Learning and applying problem solving techniques early in your physics career is the key to
PROBLEM SOLVING
IDENTIFY CONCEPTS
1.) Read and re-read the problem. Conceptualize
and understand the problem by visualizing it in your
mind and drawing a diagram.
To help you categorize the concepts used in the problem, look for keywords or code words that signal what
principles and related equations apply to the problem.
2.) What is goal of the problem? Determine the
final outcome the problem is asking for and write it
down. Then write down all of the given information.
Make a table to list the known and unknown values/
quantities.
3.) Draw pictures. Draw as many pictures as you
need and label the given and unknown information.
Pictures include force diagrams, graphs, coordinate
systems, conceptualize diagram, etc.
Word
Meaning
At rest, starts from rest
Velocity or initial velocity is zero
Constant velocity, constant
speed, object at rest or
doesn’t move
Acceleration is zero. Net force acting
on object is zero.
Smooth, icy, slippery surface Friction is zero
Rough, bumpy, un-even
surface
Friction is NOT zero
4.) Categorize the problem. Write down what concepts and principles are related to the problem. Write
down any related formulas that may be useful in solving the problem.
Is accelerated, pushes,
moves
Net force acting on object is not zero.
Free body diagram.
Crashes, bumps, collide,
bounces, impact
Momentum and Impulse
5.) Simplify and breakdown. Can the problem be
broken down into smaller sub-problems? Write down
the steps or sub-problems that you will need to solve
before obtaining the final answer.
Free-fall, slides down, inclined plane
Acceleration due to gravity.
Particle with a speed and
mass
Kinetic Energy, Work
Rotate, spin, pulley, torque
Angular and rotational kinematics
Oscillation, restoring force,
resonance
Simple Harmonic Motion, Hooke’s Law
Tension, cable, string
Forces, Newton’s 2nd Law
6.) Solve Algebraically. Solve each equation for the
unknown variable algebraically. Use those answers to
substitute into the other sub-problems if required.
7.) Complete the problem numerically. Convert
all known data to equivalent units prior to substituting
the values into t algebraic answers from step six.
8.) Check your answer. Does it have the correct
units? Is it the right order of magnitude? Does it
make sense? Does it have the correct number of significant figures?
DRAWING PICTURES
Pictures and diagrams help to understand problems
in more detail. Pictures used in physics are simplified
sketches. The most common form of diagrams used
in physics are called Free Body Diagrams. Free body
diagrams are used to break down the various forces
acting on objects and show only those forces acting
on the object in question. In addition, when constructing your free body diagrams, always include
your coordinate system in the picture.
Free Body Diagrams
PROBLEM SOLVING IN PHYSICS
DIMENSIONAL ANALYSIS
ESTIMATING PROBLEMS
Dimensions are what describe the nature of quantities,
they are not units. Dimensions can be multiplied and
divided, but not added or subtracted. The three fundamental quantities are length [L], time [T], and mass
[M].
- Quick Figuring. This technique is great for simple problems. By
replacing the actual numbers in a problem with simpler, but similar
numbers, you can then calculate an approximate answer in your
head.
Example: What is the dimension of velocity?
- Scaling. Scaling is a technique used to help understand what
principles and concepts need be used to solve a problem. This is
done by selecting one of the values in the problem and changing its
scale to observe how other aspects of the problems react.
Velocity is given by change in position divided by change in time.
v 
x
t
- Order of Magnitude. Divide the problem up into manageable
pieces and then make an educated guess or rough estimate as to its
value. Combine all of these guesses into the final answer.
ANALYSIS TECHNIQUES

Sub Goals—break the problem into smaller manageable problems.

Decompose Vectors-treat each vector component
independently.

Work Backwards-start with the final goal and work
backward toward the given values algebraically.

Use subscripts to label and track multiple variables:
- mass of car 1 = m c1
- mass of car 2 = m c2
- mass of truck = m t
Reduce the problem to simplest form and solve
first. Then add the extras like friction and energy
transfer.

Label and organize your work as you progress to
prevent repeating work already completed.
Breakdown Vectors into Components:
- a = a x î + a y ĵ + a zǩ
SIGNIFICANT FIGURES
Common notation symbols:


So to find the dimensions for the quantity of velocity we see that we have
length [L] divided by time [T]. This tells us our final answer should be
something like m/s or km/h.
L
[v ] 
T
NOTATION
v
velocity
G gravitational
force between
two bodies
I moment of inertia
a
acceleration
g acceleration
due to gravity
E electrical field
F
force
L angular momentum
R resistance
Fw weight
T period
I current
Fn force normal
θ angle
B magnetic field
W work
α angular acceleration
c speed of light
P
ω angular speed
e electron charge




All non-zero digits are considered significant.
Zeros appearing anywhere between two non-zero digits are
significant.
Leading zeros are not significant.
Trailing zeros in a number containing a decimal point are significant.
For multiplication and division, the result should have as many
significant digits as the measured number with the smallest
number of significant digits.
For addition and subtraction, the result should have as many
decimal places as the measured number with the smallest number of decimal places.
Examples (Digits in bold are significant):
Decimal Version
power
U
potential energy
λ wavelength
K
kinetic energy ƒ frequency
p linear momentum
Scientific Notation
4
34000
3.4 x 10
102.34
1.0234 x 102
345
3.45 x 10
No. Sig. Figures
2
5
2
45.6700
4.56700 x 10
0.0001234
1.234 x 10-4
3
1
6
4