Download Motion and Energy

Motion and Energy
Rollercoasters
™
Real Investigations in
Science and Engineering
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Overview Chart for Investigations–Rollercoasters
Investigation
Key Question
Summary
Learning Goals
Vocabulary
A1
Speed on the
Rollercoaster
Pages 1–8
50 minutes
How do hills and
valleys affect
motion?
hypothesis
Students measure the speed of a • Calculate speed.
marble at different positions on • Formulate a hypothesis about
speed
a rollercoaster. They formulate a
the motion of a marble on a
hypothesis about where on the
rollercoaster.
track they think the marble will • Conduct an experiment to test a
be going the fastest. Then, they
hypothesis and use data to support
set up an experiment to test the
or refute it.
hypothesis.
A2
Graphing
Motion on the
Rollercoaster
Pages 9–16
50 minutes
How does height
on a rollercoaster
affect speed?
Students conduct an experiment • Explore how height is related to
speed.
to determine the relationship
between speed and height on a • Make a graph of the motion of the
rollercoaster. They make a graph
marble on the Rollercoaster.
of their data and identify the
• Identify variables in an experiment.
relationship, then describe how
height affects speed.
control variable
dependent variable
direct relationship
graph
independent
variable
inverse relationship
scatterplot
variable
A3
Energy
Transformations
Pages 17–22
50 minutes
How is motion
on a rollercoaster
related to energy?
• Identify the relationship between
Students discover how
kinetic energy and speed.
potential and kinetic energy
are transformed back and forth • Identify the relationship between
on the rollercoaster track. This
potential energy and position.
leads to an understanding of the • Describe energy transformations on
law of conservation of energy,
a rollercoaster.
which states that energy can be
transformed from one form to
another, but the total amount of
energy remains the same.
energy
kinetic energy
law of conservation
of energy
potential energy
system
A4
Rollercoasters with How do
rollercoasters work?
Loops
Pages 23–30
100 minutes
• Ask scientific questions.
Students apply their
understanding of energy
• Explain how the concept of
transformations to the Loop Track
gravitational potential energy is
system. They also design and
involved in a rollercoaster system.
conduct an investigation around • Design and conduct an
a research question developed
investigation.
by their group. Finally, they
communicate the results of their
experiment in a lab report.
friction
gravitational
potential energy
gravity
mass
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Overview Chart for Investigations–Rollercoasters
Investigation
Key Question
Summary
Learning Goals
Vocabulary
B1
Energy and the
Rollercoaster
Pages 31–38
50 minutes
How are speed
and height on
a rollercoaster
related to energy?
• Make a hypothesis and test it with
Students develop and test a
an experiment.
hypothesis about where they
think the marble’s speed will be • Discover the relationship between
greatest on the Rollercoaster.
speed and height on a rollercoaster.
Next, they explore the
• Describe how energy is conserved
relationship between speed and
on a rollercoaster.
height on rollercoasters and how
those variables relate to potential
and kinetic energy and the law of
conservation of energy.
kinetic energy
law of conservation
of energy
potential energy
speed
B2
Conservation of
Energy
Pages 39–46
50 minutes
How do you
measure potential
and kinetic energy
on a rollercoaster?
• Develop a model to explain the
Students use the data they
motion and energy of the marble
collected in Investigation B1 to
on the Rollercoaster.
calculate the values for potential,
kinetic, and total energy for the • Develop an understanding of
marble at different positions
energy and the law of conservation
along the track. Through data
of energy.
analysis, they discover that the
• Calculate potential and kinetic
conversion between potential
energy.
and kinetic energy is not 100%
efficient in the system.
acceleration due to
gravity
friction
gravity
gravitational
potential energy
mass
B3
Mass and Motion
Pages 47–54
50 minutes
How does mass
influence motion
on a rollercoaster?
inertia
Students design and conduct an • Explain how Newton’s first law
applies to rollercoasters.
experiment to test the effects of
Newton’s first law
mass on motion. They measure • Apply the law of conservation of
the speed of the steel and plastic
energy to a system.
marbles at seven different
• Develop a theory to explain the
positions on the Rollercoaster
motion of marbles of different mass
track. They apply what they
on a hilly track.
learned about Newton’s laws of
motion (from other modules)
and the law of conservation of
energy, which they explored in
Investigation B2.
B4
Energy and the
Loop Track
Pages 55–64
100 minutes
How is motion on Students design and conduct an • Design and conduct an experiment.
a loop track related experiment to test how energy is • Apply the law of conservation of
transformed on a loop track. They energy to a system.
to energy?
measure the speed of the plastic • Develop a theory to explain the
marble at different positions
motion of a marble on a loop track.
on the track. They apply what
they learned in Investigation B2
about the law of conservation of
energy.
energy
kinetic energy
law of conservation
of energy
potential energy
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Overview Chart for Investigations–Rollercoasters
Investigation
Key Question
Summary
Learning Goals
Vocabulary
B5
Forces and the
Loop Track
Pages 65–70
50 minutes
Why does an
upside-down
rollercoaster stay
on the track?
• Explain the concept of centripetal
Students explore the idea of
force and apply it to a rollercoaster
centripetal forces to explain why
with a loop.
the marble stays on the track
upside down on the loop. They
• Calculate centripetal force or speed
calculate the minimum speed
using the formula for centripetal
required using the formula for
force.
centripetal force and test the
• Conduct a test of a mathematical
mathematical model on the Loop
model and use data to support or
Track using the steel and plastic
refute the model.
marbles.
centripetal force
force
normal force
radius
weight
B6
Designing a
Rollercoaster
Pages 71–78
150 minutes
How do engineers
design thrilling
rollercoasters?
• Understand how engineers work.
Students apply their
understanding of the law of
• Design, build, test, and refine a
conservation of energy to
rollercoaster.
designing a model rollercoaster • Apply the law of conservation of
using foam track. Students use
energy to rollercoaster design.
the engineering cycle to create,
test, and refine their designs and
present their work to the class.
constraints
criteria
engineer
engineering cycle
iteration
prototype
trade-off
C1
Motion on the
Rollercoaster
Pages 79–88
50 minutes
How do you
predict the speed
of a marble on the
Rollercoaster?
• Describe the motion of a marble on
Students will consider how the
the Rollercoaster in terms of speed
shape of the Rollercoaster affects
and energy.
the acceleration of the marble
as it travels along. Students will • Derive an equation for predicting
review how potential and kinetic
speed using the law of conservation
energy are calculated, and then
of energy.
use the law of conservation of
• Compare predicted speeds with
energy to predict the speed of
calculated speeds using a graph.
the marble based on the height
it has dropped from its starting
position.
energy
kinetic energy
law of conservation
of energy
line of best fit
potential energy
slope
C2
Rotational Kinetic
Energy
Pages 89–98
50 minutes
Students learn to include the
How can you
calculate the rolling rotational energy of the marble
energy of a marble? along with its translational
energy and use the conservation
of energy equation to more
accurately predict the speed of
the marble at locations all along
the Rollercoaster.
• Derive an equation for the
rotational kinetic energy of a
marble.
• Calculate the translational and
rotational kinetic energies of a
rolling marble.
• Compare the potential energy of
the marble to the sum of its kinetic
energies.
• Make and interpret a graph of the
energy of the marble.
angular speed
moment of inertia
rotational inertia
rotational motion
translational motion
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Overview Chart for Investigations–Rollercoasters
Investigation
Key Question
Summary
Learning Goals
Vocabulary
C3
Mass, Motion, and
Energy
Pages 99–108
50 minutes
How does mass
influence the
motion of a marble
on a rollercoaster?
• Explore how the mass of a marble
Students compare the motion
influences its motion on the
of a steel marble on the
Rollercoaster.
Rollercoaster to the motion
of a plastic marble. Students
• Develop a theory to explain the
discover that their expectations
motion of marbles of different mass
for how the speeds compare may
on the Rollercoaster.
not match their observations.
• Use the law of conservation of
Using the law of conservation
energy to discover the role of mass
of energy, students develop a
in the marbles’ motion on the
theory to explain how mass
Rollercoaster.
influences the marbles’ motion.
friction
kinetic energy
law of conservation
of energy
mass
potential energy
C4
Centripetal Force
Pages 109–116
50 minutes
Why does a
rollercoaster stay
on the track while
upside down on a
loop?
Students learn to develop
a mathematical model that
predicts the minimum speed
required in order for the marble
to make it successfully around
the Loop Track. They test their
model with an experiment.
• Study a marble’s forces and motion
as it rolls along a looped track.
• Derive a formula that predicts the
minimum speed a marble needs to
have to make it around a loop on
a track.
• Test the minimum speed formula by
conducting an experiment.
centripetal force
free-body diagram
normal force
radius
weight
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Next Generation Science Standards Correlation
CPO Science Link investigations are designed for successful implementation of the Next Generation Science Standards. The
following chart shows the NGSS Performance Expectations and dimensions that align to the investigations in this title.
NGSS Performance Expectations
Rollercoasters Investigations
MS-PS3-1. Construct and interpret graphical displays of data to describe the relationships of kinetic energy to
the mass of an object and to the speed of an object.
A1, A2, A3
MS-PS3-5. Construct, use, and present arguments to support the claim that when the motion energy
of an object changes, energy is transferred to or from the object.
A4
HS-PS3-1 Create a computational model to calculate the change in the energy of one component in a
system when the change in energy of the other component(s) and energy flows in and out of
the system are known.
B1, B2, B4, C2, C3, C4
HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion describes the
mathematical relationship among the net force on a macroscopic object, its mass, and its
acceleration.
B3, C1
HS-PS2-4. Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to
describe and predict the gravitational and electrostatic forces between objects.
B5
HS-PS3-3. Design, build, and refine a device that works within given constraints to convert one form of
energy into another form of energy.
B6
NGSS
Science and
Engineering Practices
Analyzing and
Interpreting Data
Rollercoasters
Investigations
A1, A2, A3, A4,
B3, C1
Using Mathematics and B1, B2, B4, B5, C2,
Computational Thinking C3, C4
Constructing
Explanations and
Designing Solutions
B6
NGSS
Disciplinary Core Ideas
Rollercoasters
Investigations
NGSS Crosscutting
Concepts
PS3.A: Definitions of
Energy
A1, A2, A3, A4,
B1, B2, B4, B6, C2,
C3, C4
Scale, Proportion, and
Quantity
A1, A2, A3, A4
PS3.B: Conservation
of Energy and Energy
Transfer
B1, B2, B4, C2,
C3, C4
Energy and Matter
B1, B2, B4, B6, C2,
C4
PS2.A: Forces and Motion B3, C1
Cause and Effect
B3, C1, C3
PS2.B: Types of
Interactions
Patterns
B5
B5
Rollercoasters
Investigations
B6
ETS1.A: Defining and
Delimiting an Engineering
Problem
*
Next Generation Science Standards is a registered trademark of Achieve. Neither Achieve nor the lead states and partners that
developed the Next Generation Science Standards was involved in the production of, and does not endorse, this product.
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Common Core State Standards Correlation
CCSS-Mathematics
Rollercoasters Investigations
MP.2
Reason abstractly and quantitatively.
A1, A2, A3, A4, B1, B2, B3, C1, C2, C3, C4
MP.4
Model with mathematics.
A1, A2, A3, A4, B1, B2, B3, C1, C2, C3, C4
RP.A.1
Understand the concept of ratio and use ratio language to describe a ratio relationship
between two quantities.
A4
RP.A.2
Recognize and represent proportional relationships between quantities.
A1, A2, A3, A4
8.EE.A.1
Know and apply the properties of integer exponents to generate equivalent numerical
expressions.
A1, A2, A3, A4
8.EE.A.2
Use square root and cube root symbols to represent solutions to equations of the form x2 =
p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect
squares and cube roots of small perfect cubes. Know that √2 is irrational.
A1, A2, A3, A4
HSN.Q.A.1
Use units as a way to understand problems and to guide the solution of multi-step problems; B1, B2, B3, C1, C2, C3, C4
choose and interpret units consistently in formulas; choose and interpret the scale and the
origin in graphs and data displays.
HSN.Q.A.2
Define appropriate quantities for the purpose of descriptive modeling.
B1, B2, B3, C1, C2, C3, C4
HSN.Q.A.3
Choose a level of accuracy appropriate to limitations on measurement when reporting
quantities.
B1, B2, C2, C3, C4
HSA.CED.A.2 Create equations in two or more variables to represent relationships between quantities;
graph equations on coordinate axes with labels and scales
B3, C1, C2, C3, C4
HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in
solving equations.
B3, C1, C2, C3, C4
HSS-IS.A.1
B1, B2, B3, B4, C1, C2, C3, C4
Represent data with plots on the real number line (dot plots, histograms, and box plots)
CCSS-English Language Arts & Literacy
Rollercoasters Investigations
SL.11-12.5
Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive
elements) in presentations to enhance understanding of findings, reasoning, and evidence
and to add interest.
B1, B2, C2, C3, C4
RST.6-8.1
Cite specific textual evidence to support analysis of science and technical texts, attending to
the precise details of explanations or descriptions.
A1, A2, A3, A4
RST.6-8.7
Integrate quantitative or technical information expressed in words in a text with a version of
that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table)
A1, A2, A3, A4
RST.11-12.1
Cite specific textual evidence to support analysis of science and technical texts, attending to
important distinctions the author makes and to any gaps or inconsistencies in the account.
B3, C1
WHST.6-8.1
Write arguments focused on discipline content.
A4
WHST.6-8.9
Draw evidence from informational texts to support analysis, reflection, and research.
B6
B6
WHST.9-12.7 Conduct short as well as more sustained research projects to answer a question (including
a self-generated question) or solve a problem; narrow or broaden the inquiry when
appropriate; synthesize multiple sources on the subject, demonstrating understanding of the
subject under investigation.
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Getting Started with Rollercoasters
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