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AP Physics Rapid Learning Series - 03

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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.



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



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



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



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.



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



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



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



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



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 =+

−

=



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



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.



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!



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.



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)



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.



Congratulations

You have successfully completed the tutorial

Problem Solving in PhysicsPhysics

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