Lesson 3: Reasoning with Energy Bar Charts
3.1 Represent and Reason
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a) How can we use charts to represent data?
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b) Create a chart that shows that you have $60 in your bank’account, no money in your
pocket, and $20 on a gift card.
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c) Imagine that you withdraw $20 from your bank account and titjLyour pocket.
Create a new chart that represents your new situation.
d) If we place the two charts side-by-side, how does it express a process? Explain.
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We can use a bar chart to represent transformations of a
quantity during some process. We do this by placing
the before bar chart next to the after bar chart.
We can also abbreviate the column headings in order
to make this easier to read. We just have to make sure to
include a key so that we know how to readi the
$430
chart. See below.
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P represents the amount of money in your pocket
CATI represents the amount of money in your ATM card
CGJ represents the amount of money on a rechargeable Best Buy gift card.
Earn/Spend represents the amount of money that you gain or lose through
transaction with other people
For situations with ne-y in a particular column, place a zero (0) to represent a zero bar.
e) What do you notice about the money before and after this process?
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Did You Know?
The total amount of money you have remains the same before and after, unless you earn
some or spend some right? If the total amount of money you have does not change, we
say it is constant. If it changes in a predictable way due to the expenses, we say that it is
conserved, as it does not appear from nowhere and disappear to nowhere.
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PUM f Work & Energy Lesson 3: Reasonirg with Energy Bar Charts
© Copyright 2010, Rutgers. The State University of New Jersey.
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3.2 Represent
Situation Before and After
Bar Chart Representation
a) You have $15 in your pocket, $60 in your ATM
account, and a gift card with $20 on it, You
withdraw $20 cash from the ATM.
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spend
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Represent this transaction on the bar chart. Did you
earn or spend any money?
Represent this transaction with a mathematical
statement
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b) Next, you buy a snow shovel for $10 cash at
Jones Hardware.
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Represent this transaction on the bar chart. Did you
earn or spend any money?
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Represent this transaction with a mathematical
statement
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c) After returning from the hardware store, you
spend three hours shoveling snow for an old lady
who gives you $20 cash.
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Represent this transaction on the bar chart. Did you
earn or spend any money?
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Representtbistransactionwithamathematical
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PUM Work & Eneigy Lesson 3: Reasoning with Energy Bar Charts
© Copyright 2010, Rutgers, The State University of New Jersey.
Situation Before and After
Bar Chart Representation
d) When you are finished shoveling, you spend $20
cash to put gas in your car so you can drive to the
Best Buy.
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Represent this transaction on the bar chart. Did you
earn or spend any money?
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Represent this transaction with a mathematical
statement
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e) At Best Buy, you purchase a “Cher’s Greatest
Hits” DVD Box Set for $40. You empty out your
gift card and use your ATM card to pay for the rest.
After
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Represent this transaction on the bar chart. Did you
earn or spend any money?
Represent this transaction with a mathematical
statement
f) What happens next? Continue the story and make
a graph to match.
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g) Does this graph show something that could
happen? If not, explain why not. If so, describe a
situation it could match.
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PUM j Work & Energy I Lesson 3: Reasoning with Energy Bar Charts
C Copyright 20 10, Rutgers. The State University of New Jersey.
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Situation Before and After
Bar Chart Representation
h) Draw the missing bar,
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Write a mathematical statement to match the chart.
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Describe a story that could match.
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i) Make a chart to match this mathematical
statement:
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$20+$O+$O+$40=$20+$40+$O
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Describe a story that could match.
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For each problem. relate your money at the beginning to the money at the end with an
equation.
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k,) Which of the above follow the principle that money is constant? Conserved?
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1) Compare money triisfers and energy transfer. What similarities do you see?
m) What property of wça1th is illustrated in this activit?
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ii)
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What other physical quantities (besides energy exlhbit this property? What quantities
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3.3 Represent and Reason
While working on the following problem, Alan decided that he could represent work-energy
processes with a bar chart similar to the ones we used for money.
Problem: Jessica stands in an elevator on the first floor. The elevator doors close and the
elevator delivers Jessica to the fourth floor. Identify all the changes that occur.
a) Identify the system of interest.
b) Draw pictures of the initial and final states. (Make sure to include a description.)
c) Review the problem and create your own work-energy bar chart.
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PUM I Work & Energy Lesson 3: Reasoning with Energy Bar Charts
© Copyright 2010. Rutgers. The State University of New Jersey.
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Need Some H4,?
Work-energy bar charts provide a concrete way to represent work-energy processes. In
a
work-energy bar chart, a bar represents each type of energy initially in the system, as well
as the final energies of the system. If external objects do work on the system (positive or
negative), then there is a bar to represent work.
Across the top of the chart, you see several symbols for
different energies..
K,
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t:.
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K—L
K— Kinetic energy
Gravitational potential energy
spring potential energy
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Elastic or
—
W—
C)
Work
—
The
i and the I renresent initial and final
We dont know the exact amount of energy or work usually but we
the
internal energy
(Difference between final and initial)
Change in
can still
make estimates
situation, The column for the
work bar is shaded to indicate that it is not a type
of energy but is instead a process involving an interaction between a system
object and an
object outside the system.
based on
3.4 Represent and Reason
You are investigating the energy of an oscillating pendulum. Use the materials in front of
you to take observations of the bob at different points along its path. Make sure you observe
the bob swinging for a while before you fill out the table.
a)
Complete the tables below to describe all the energy transformations. Be sure to
identif the system in each step.
Initial State
The bob has no
velocity and is at
the highest point
of the swing.
Final State
The bob is at the
Construct the Work-Energy Bar Chart
bottom of the
swing and is going
really fast.
K
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K
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System: t
Equation:
PUM I Work & Energy
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Lesson 3: Reasoning with Energy Bar Charts
© Copyright 2010, Rutgers, The State University of New Jersey.
states
K.
+
B
0
System:
The bob has no
velocity and is at
the highest point
of the swing.
The bob is at the
bottom of the
swing and is going
really fast
backwards.
K
K
System: E€
come to a stop at
the top of the
swing’s motion
and begins to
forward,
swings
the bob eventually
comes to a stop at
the center of the
swing.
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a) Describe how the system’s energy has changed iii each step the bob swung backI
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and-forth,
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b) How has the total energy of the system changed?
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© Copwight 2010, Rutgers, The State Lniversitv of New Jersey.
c) If the rope from the pendulum is not in the system, bow is accounted for in the bar
charts?
3.5 Reason
Adventurous Theo was testing out a stunt cannon. He compressed the spring inside the
cannon and placed himself in the barrel. He then released the spring and was pushed up.
Which of the following graphs accurately represents the situation wh
ere Theo and the
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cannonarethesystem?
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a) Which graph accurately represents the situation where Theo and Earth are the
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b) In which graph(s) is energy constâht?
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c) In which graph(s) is energy conserved?
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Homework
3.6 Bar Chart Jeopardy
In the table that follows, invent a process using words and a sketch (the system, its initial
and final situations, and any work done on the system). Be sure both are consistent with the
qualitative work-energy bar chart shown below.
PUM Work & Energy I Lesson 3: Reasoning with Energy Bar Charts
© Copyright 2010, Rutgers, The State University of New Jersey.
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Bar chart for a process.
before
State what is in your system.
Describe in words one
possible consistent process.
after
Sketch the process just
described.
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W=
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Relate these quantities mathematicafly:
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State what is in your system.
Describe in words one
possible consistent process.
Bar chart for a process.
before
after
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Sketch the process just
described.
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A car screeches to a halt the
tires ofthe carstart smoking.
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Relate these quantities mathematically:
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3.7 Explain
Read through the following problem
and then read Man’s solution below. Use it and your
response to activity 33 to answer the questions
a) How does your answer compare with Alans? Svr
b) Does Alails bar chart help him understand the problem?
Explain your
answer.
What do the lengths of the bars represent in Alan s Work-Energy bar chart?
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d) How do you think Alan decided to make the lengths of the bars in his bar chart?
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Explain.
c)
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Problem: Jessica stands in an elevator on the first floor. The elevator doors close and the
elevator delivers Jessica to the fourth floor. Identify all the changes that occur.
PUM I Work & Energy Lesson 3: Reasoning with Energy Bar Charts
© Copyright 2010. Rutgers, The Stale University of New Jersey.
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Alan’s solution: The system includes Jessica, who might be
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K
moving so we may need to consider kinetic energy. The
system also includes Earth, so we will have to consider
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gravitational potential energy, too. But because Jessica’s initial
and final velocity is zero, the kinetic energy does not change. I
put the initial energies of the system on the left side of the bar
chart and the final energies on the right side. However, I had no energy on the left but some
on the right, which cant be possible. Then I remembered the elevator that pulled Jessica up.
The elevator is not in my system, soit must do positive work on Jessica. I put the work
done in the column labeled Wfor work.
e) Use the rubric below to assess you work-energy bar chart. How did you do?
Describe your difficulties.
Rubric to self-assess your work-energy bar charts
Absent
No work-energy
bar chart is
constructed,
Needs some
improvement
An attempt
.
Work-energy bar chart is
constructed but is missing or
contains extra energy bars; the
initial and final states described
do not match the initial and final
states on the chart The initial
quantities plus the work do not
equal the final quantities.
Work-energy bar chart
lacks a key feature
such as labels, the zero
energy is not indicated,
or quantities are not
drawn to scale.
Acceptable
The chart is labeled
clearly so that one can
understand the initial and
fmal states of the system.
The relative lengths of
the bars are correct And
the zero energy is
indicated,
3.8 Reason
a) Look back at the bar charts from the previous activit. Ifthe elevator only went ¼ as
high, which of the bars would change and by how much?
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b) How would the work-energy bar chart look if we chose a final state when Jessica
was still moving? i,v
c) How can we convert Alan’s bar charts into a mathematical statement?
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d) Describe a situation with Jessica that could be representçd by this energy bar chart.
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PUM I Work & Eneigy I Lesson 3: Reasoning with Eneigy Bar Charts
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3.9 Represent and Reason
Use a bar chart to represent transformations of a quantity. This time.. the exercise concerns
the food in your house, and we are going to make bar charts with estimated quantities
instead of exact numbers. Fill in the bar charts provided, Write a mathematical equation
represented in each chart that relates the quantities of food and shopping and discarding.
F = food in your pantiy
FR = food in the refrigerator
F = food on the stove
AUate = food “U” ate
.
Situation Before and After
Bar Chart Representation
You have some food in your panty and refrigerator
re
before
,
.
,
You go shopping and come home with bags of
groceries.
You put some away in the pantry and some away in
the refrigerator.
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Represent this on the bar chart.
PUM J Work & Energy I Lesson 3: Reasonirg with Energy Bar Charts
© Copyright 2010, Rutgers, The State University of New Jersey.
after
buyer
+ F3+dycard Fs+FRf+FJ±ALJ
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Situation Before and After
Bar Chart Representation
The situation starts from where we left off in the
previous question.
before
after
buy or
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You take some ingredients from the pantry and
some from the refrigerator and make a meal on the
stove.
+F 4F
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F
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+
0
Represent this on the bar chart.
You eat half of the food you cooked and store the
rest in the refrigerator.
before
after
before
after
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Represent this on the bar chart.
.
The next day you come home with a takeout from
White Castle. You eat the stack of White Castles
and throw out your leftovers from the day before.
+
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Represent this on the bar chart.
e) Why do we show AUate on the “after” side but not on the “before” side?
3.10 Observe and Reason
Use the PhET simulation Energy Skate Park to answer the questions below, Go to the
website:
J:L Dhetco
and search for “Energy Skate Parkf’ Click on the first
Simulation and then click Run Now!
a) Identify your system.
b) Draw an energy bar chart for the system as the skater goes from the top of the ramp
down to the bottom. Then draw a bar chart for the process as he continues from the
bottom of the track up the other side. Make sure your charts arc consistent with
your chosen system.
c) Based on your observations, when does the system have the highest kinetic energy?
PUM Work & Energy Lesson 3: Reasoning with Energy Bar Charts
C Copyright 2010, Rutgers, The State University of New Jersey.
d) When does the system have the highest gravitational potential energy?
e) Is the skater your system? If so, is he able to have gravitational potential energy and
kinetic energy by himself?
f) Click on the Bar Graph tab on the right side of the simulation. Compare your bar
charts with the ones provided, How are they similar? How do they differ?
g) What do you notice about the “Total” column on their Bar Graph? What does this
represent?
h) On the Bar Graph provided, what could “Thermal” stand for? What kind of
energy
would that look like on our bar charts?
i) Click “Track Friction>>” and change the coefficient of friction between the skater
and the track. How does that change the bar chart? Use your knowledge of energy
transfer to explain what you observe,
3.11 Reason
In this lesson you have investigated the ideas of constant and conserved quantities.
a) Based on your observations, when is energy constant?
b) Based on your observations, when is energy conserved?
c) What role does work play in the bar charts? Does it affect whether the energy is
constant or conserved?
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Reflect: What is the purpose of work-energy bar charts? flow are they
similar to impulse-momentum bar charts? flow are they different? Find a
family member or a friend and teach her/him about the bar charts, What
difficulties did they have? Prepare to share your experience in class.