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AP Physics Rapid Learning Series - 03
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 1
Rapid Learning CenterChemistry :: Biology :: Physics :: Math
Rapid Learning Center Presents …Rapid Learning Center Presents …
Teach Yourself AP Physics in 24 Hours
1/42 *AP is a registered trademark of the College Board, which does not endorse, nor is affiliated in any way with the Rapid Learning courses.
Problem Solving in ob e So gPhysics
Physics Rapid Learning Series
Rapid Learning Centerwww.RapidLearningCenter.com/© Rapid Learning Inc. All rights reserved.
Wayne Huang, Ph.D.Keith Duda, M.Ed.
Peddi Prasad, Ph.D.Gary Zhou, Ph.D.
Michelle Wedemeyer, Ph.D.Sarah Hedges, Ph.D.
AP Physics Rapid Learning Series - 03
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 2
Learning Objectives
When to follow problem-solving techniques
By completing this tutorial, you will learn:
solving techniques
A general problem-solving technique
How to solve word problems
How to prepare for an exam
Tips for taking exams
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Tips for taking exams
Concept Mapexperimental science
Physics is an experimental science
Requires
Previous content
New content
ExperimentationExperimentation ConclusionsResults &
Conclusions
CalculationsCalculations
Leads to
Often requires
Problem SolvingRequires
Requires
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General problem-solving
strategyKUDOS method
Exam prep & Exam prep & Exam taking
TipsFor word
problems
Use On Exams
AP Physics Rapid Learning Series - 03
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Problem-Solving
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What is Problem Solving?
You are here
A “problem” is when you don’there
Problem Solving Strategy
when you don t know how to get from here…
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You need to get there
to there
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Why is it Important?
Problem solving is needed in every aspect of physics:
Labs & investigationsPractice problemsExamsAnytime you apply concepts
to different situations
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Knowing how to break a problem down into steps is the key to solving any kind of problem!
General Problem Solving Strategy
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5-Step Problem Solving Strategy
Identify what is being given1
General steps for solving any type of problem in physics:
Identify what is being given.
Clarify what is being asked.
Select a strategy
1
2
3
If unclear, try to rephrase it.
Trial & error, search, deductive reasoning, working backwards or knowledge-based.
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Solve using the selected strategy
Review
4
5
backwards or knowledge based.
Check for reasonableness, units and significant figures.
Applying the “General” Strategy
This general strategy will work for any type of problem in physics, not just “math” problems.y j
Calculations, concepts, diagrams, etc.
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Problem Solving Example #1
StepId tif h t’ i 10201
Description Information
Example: How many significant digits are in 1020 g?
Identify what’s given
Identify what’s being asked
Strategy: Knowledge based
Apply strategy: Count the
1020 g
? Significant digits
Use your knowledge of significant digits to count.There is no decimal point—count digits between the first and last non-zero number.
1
2
3
4 1020 g 3 significant digits
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significant digits4
Review5
1020 g 3 significant digits
The rule without a decimal place is count between the non-zero numbers. There are 3 “102” significant figures.
Problem Solving Example #2
StepIdentify what’s given Force & acceleration1
Description Information
Example: What is the relationship between force and acceleration?
Identify what s given
Identify what’s being asked
Strategy: Deductive reasoning
Force & acceleration
What is the relationship? Is it direct (as one increases, the other does also) or indirect (as one increases, the other decreases)
Force is the push on an objectAcceleration is the rate of change of velocityLook for any mathematical equationsForce = m * a
1
2
3
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Apply the strategy: Deduce the relationship4
Review5
If force increases, the “push” increases. Therefore the acceleration will increase.
The harder you push on an object, the greater the change of velocity
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Word Problem Solving Strategy
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Word Problem Woes
Many people are intimidated by word problems…they don’t know where to begin.
Instead of seeing them as word problems, use the KUDOS method to
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turn them into simple calculation problems.
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The KUDOS Method
KnownUnknownDefinitionO t t
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OutputSubstantiation
Step “K”
Identify what is known.K
“Known”
Tip Example
A car travels 15.2 m
A car travels 15.2 m
“m” (meters) is a distance unit. The statement is giving distance (“d”)
d = 15.2 m
Use units to identify information
Write information symbolically
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A book is accelerating across a table
Therefore there is a net force
Look for implied information
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Step “U”
Identify what is unknownU
“Unknown”
Tip Example
How many Newtons…
How many Newtons…
Newtons is a force unit
F = ? N
What is the problem looking for?
Write information symbolically
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This helps you focus on the “goal”
Step “D”
Define needed informationD
“Definition”
Tip Example
Velocity needs to be converted to m/s
Solve for distance knowing velocity and time
1 km/h = 0.27 m/sFind equalities to convert
Choose & re-arrange equations t
dV = So tVd ×=
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There’s a constant in the equation, such as “g”
You’re missing a piece of information and cannot find it elsewhere
Look on a cheat-sheet of constants
Look for another equation or approach
Look other places for missing info
Re-evaluate your approach if needed
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Step “O”
Find the output of your informationO
“Output”
dtV =×
gmW ×= “g” is acceleration due to gravity
Tip Example
12.5m/s × 1.25s = dPlug values into equations
Use fundamental constants if needed
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12.5m/s × 1.25s = d
12.5m/s × 1.25s = d 15.6 m =d
needed
Check unit cancellation
Perform the calculation
12.5m/s × 1.25s = d
Step “S”
Substantiate your results with a 1-2-3 check:S
“Substantiation”
Are the units remaining after cancellation appropriate?
Are the results reasonable & possible?
When solving for mass, you should get a mass unit
Tip Example
Is it 10,000 when it should be 10?1. Check Validity
2. Check Units
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× or ÷ use least # of s.f in problem+ or - use least # of decimal places in problem
Are the significant figures in the answer correct?
3. Check Significant Figures
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Connecting the Known and Unknown
One of the hardest things for students is determining how to get from the known to the unknown…
?Known UnknownDefinition
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The “Definitions” (Step “D”) shows the connections!
Using Symbols EffectivelyPhysics uses so many symbols that are similar that it can quickly become confusing.
Try to label symbols with something meaningful and y y g gmnemonic to help you sort them out.
To symbolize this… Don’t use this…
m1 & m2
Instead use this…
mp & mnMass of proton & mass of neutron
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p1 & p2
V1 & V2
pl & pq
Vc & Vt
Momentum of linebacker and momentum of quarterback
Velocity of car & velocity of truck
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KUDOS Example #1Example:
Step Source Information Write down
What is the net force if a girl pulls with 27 N and a boy pulls with 14 N in the other direction?
Force of girl
What is the net force?
Net force is the sum of all forces
Fg= 27 N
Given forces in “N”Fnet = ? N
Fnet = Fg + Fb
K
U
D
Force of boy Fb = -14 N (opposite direction, so “-”)
Fnet = Fg + Fb
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O
validity, units & significant figures
13N is a reasonable answer“N” is a force unit0 decimal places given 0 in
answer
S
Calculate Fnet
g
Fnet = (27 N) + (-14 N)Fnet = 13N
KUDOS Example #2Example: Find the focal length of a mirror if a 2.0 cm tall object is 5.0 cm
from the mirror appears with a 4.0 cm tall image.
Step Source Information Write down2.0 cm tall object
What is the focal length
Equation to find focal length
ho = 2.0 cm
f = ? cm
K
U
D
Object is 5.0 cm from the lens do = 5.0 cm
Distances of image and object are related to heights
do1
di1
1f+
=
dodi
hohi −
=
4.0 cm tall image hi = 4.0 cm
But “di” is not known
dihohido =×−
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O
validity, units & sig figs
10 cm is a reasonable answer“cm” is the unit used for other
lengths2 s.f. given 2 s.f. in answer
S
Calculate di and then calculate f
g
10cmdi2.0cm4.0cm5.0cm −==×−
10cm
5.0cm1
10cm1
1f =+
−
=
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KUDOS Example #3Example:
Step30.0 V
V = 30 0 V
Source Information Write down
Find current in a circuit with a 30.0 V battery and a 10.0Ωresistor.
“V” is a voltage unit
Find current (which is measured in Amps)
V 30.0 V
I = ? A
K
U
D
10.0Ω“Ω” is a resistance unit
R = 10.0 Ω
Define resistance & solve for currentIVR = So
RVI =
RVI =
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O
validity, units & sig figs3.0 A is reasonable for current“A” is a valid unit for current3 s.f. given 3 s.f. in answer
S
Solve for currentR
I = 30.0 V / 10.0 Ω
I = 3.00 A
Connecting the “General” Strategy & KUDOS
Problem Solving
5-Step General problem-solving
strategy
For any type of problem, use
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KUDOS method
For word problems, the 5-step process becomes
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Physics Exams
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Help for Physics Exams
So now that you know how to attack individual problems using th P bl S l i St tthe Problem-Solving Strategy, or the KUDOS method for word problems…
How do you attack the big problem…the exam?
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Types of Exams
Short answer exams Assessing
First, understand the two types of exams:
Short answer exams – Assessing knowledge of physics facts.
Long answer exams Assessing
Fill in the blank, True/False, Multiple-choice, matching
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Long answer exams – Assessing critical thinking, application of concepts, problem-solving.Essay, calculation problems
Exam-Prep Tips
Stay ahead of the game1
Here are some helpful hints for preparation
Begin preparing early…the night before should be for
Make a cheat sheet2Even if you can’t use it on the test, creating a cheat-sheet is an excellent way to review the important information.
brief overview after studying for several night, not cramming as your only preparation!
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Know the format & what information is “test-able”3Focus your energy…know what you will tested on and how they will test it.
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Exam-Prep Tips (Con’t)
Make a mock-exam4Try choosing the 5 most important topics and writing
Attend the review session5Even if this session is optional, GO! Instructors often give extra help and hints of what will be on the exam at these sessions.
questions about them.
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Get help early6Don’t wait until the last minute to ask questions…do so well in advance (at least 2 days before the exam so that you have time to apply the information and make sure you understand it).
Exam Taking Tips
Arrive early and prepared1
Here are some helpful hints for taking your exam
Rushing or searching for supplies builds anxiety
Listen & read instructions carefully2Don’t assume you know the instructions…read them carefully.If the instructor gives any last-minute changes or instructions, be sure to pay attention and write them down!
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Memory dump first3down!
Write down any equations or facts that you’ve been remembering on the top or back of the test first thing. Once you have them to refer to, you’ll be calmer taking the test. Do this on the test, not scratch paper to avoid accusations of cheating!
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Exam Taking Tips (Con’t)
Skim the test and make a plan4Budget your time according to length and difficulty of
Answer questions sequentially5Often the answer to or information from a previously problem is re-used.
questions.
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Apply the guessing rule6Don’t just randomly guess. Use your information and understanding to eliminate wrong answers. Eliminate as many as you can and then guess from the remaining if you’re not sure.
Multiple-Choice Tip #1
Scan all the choices1
Here are some helpful hints for multiple-choice exams
Often one choice looks good…but a later one is gbetter. Look at them all before choosing.
Which of the following would cause the largest error in a lab determining force by measuring mass & acceleration?A. Misreading the balanceB. Misreading the stopwatch
Example:
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B. Misreading the stopwatchC. Only performing one trial
While A & B would cause errors, C would cause the largest error.
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Avoid the word trap2There’s often more than one way to say something…the test may use another word than the one you’re used to, but they may mean the same thing
Multiple-Choice Tip #2
may mean the same thing.Thermal energy flows from an object with ____ kinetic energy to an object with ____ kinetic energy?A. More, less B. Less, moreC. High, the same
Example:
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D. Thermal energy does not flow from one object to another
“Thermal energy” = heat“Kinetic energy” = energy of motion
Rephrase using more familiar terms:
Essay Tip #1
Understand the question1
Here are some helpful hints for essay exams
Be familiar with questions that include:q
Describe: Give a detailed & sequential account of facts
Discuss: Give a detailed analysis of all facts from your point of view
Calculate: Use givens & constants to find a numerical answer
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Evaluate: Give a judgment given a set of facts
Explain: Give a rationale for a set of facts—don’t just rephrase the facts!
Compare/contrast: Give similarities (compare) and differences (contrast)
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Just answer the question2Be sure that you’ve covered everything asked
Essay Tip #2
Be sure that you ve covered everything asked for…but that’s it. Don’t spend time including extra information (that may not be correct and count against you!)
Describe how mass relates to acceleration with a net force.Example:
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Don’t discuss everything you know about mass, acceleration and net force…just answer the question asked.
Watch your time3Don’t get stuck on one
Essay Tip #3
Don t get stuck on one question—divide your time according to length of exam and difficulty of questions.
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Free-Response Tips
Show partial work!1
Here are some helpful hints for free-response exams
Show as much work as possible so the instructor
Don’t forget the unit!2This is an easy point to miss…make sure every answer has a unit!
Show as much work as possible so the instructor can see your thought process. Many give partial credit if they can see what you understood and where your mistake was
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Don’t judge length of answer on blank space3
answer has a unit!
Tests often have too much or too little blank space after a question…don’t think a question with a lot of blank space requires a long answer and vice versa.
Be sure to thoroughlyBe sure to thoroughly
A problem: anytime you
don’t know how
A problem: anytime you
don’t know how Do your best on exams by
f ll i
Do your best on exams by
f ll i
Learning Summary
thoroughly prepare for the exam.
thoroughly prepare for the exam.
to get from where you are to where you need to be.
to get from where you are to where you need to be.
following exam-taking
tips!
following exam-taking
tips!
U blU bl
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Use the KUDOS problem solving
technique for word problems.
Use the KUDOS problem solving
technique for word problems.
Use problem-solving
techniques for every type of
problem.
Use problem-solving
techniques for every type of
problem.
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Congratulations
You have successfully completed the tutorial
Problem Solving in PhysicsPhysics
Rapid Learning Center
Rapid Learning Center
Wh t’ N t
Chemistry :: Biology :: Physics :: Math
What’s Next …
Step 1: Concepts – Core Tutorial (Just Completed)
Step 2: Practice – Interactive Problem Drill
Step 3: Recap – Super Review Cheat Sheet
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Go for it!
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