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Table of Contents
Overview………………………………………………………………………………………………….….……...........................1
Lab Topics and Suggested Grade Level ………………………………………………………………………….…1
Acknowledgements………………………………………………………………………………..….………………….….1
Roller Coaster Topic 1 – Energy Conservation..............................................................2
Teacher Guide…………………………………………………………………….…….……….………………………….....2
Student Lab Guide…………………………………………………………………………..….………………………….…7
Roller Coaster Topic 2 - Centripetal Acceleration......................................................11
Teacher Guide……………………………………………………………………………………….……………………....11
Student Lab Guide…………………………………………………..………………………………………………...…..20
Roller Coaster Topic 3 – Roller Coaster Design…………………...........………………………24
Teacher Guide………………………………………………………….…………………………………….…..24
Student Lab Guide……………………………………………………………………………………..…….…30
Roller Coaster Assembly Instructions…………………………………………………………..….…….35
Overview
Arbor Scientific has worked with classroom teachers to develop a specialized Roller Coaster
Curriculum Guide. Never before has learning and teaching physics been so fun!
The 3 topics covered are Energy Conservation, Centripetal Acceleration and Roller Coaster Design.
Each topic has been divided into 2 parts. The first part is the teacher’s guide and the second is the
student’s lab guide.
The labs require photogate timers to determine the speed at various points.
The assembly instructions for building the standard loop layout is also available starting at pg 35.
Lab Topics and Suggested Grade Level:
Topic 1
Energy
Conservation
Physical Science (Grade 9)
X
Physics or Honor Physics
(Grade 10-12)
X
Topic 2
Centripetal Acceleration
Topic 3
Roller Coaster
Design
X
X
Acknowledgements:
This teacher’s guide was developed in a partnership between Arbor Scientific and Dale
Freeland from Portage Central H.S. and Stephen Rea from University of Michigan-Dearborn.
1
Roller Coaster Topic 1 – Teacher Guide
ENERGY CONSERVATION
Most students have experienced roller coaster riding. They have been in the car as it crests
the first hill and then picks up speed on the way down the first hill. They have felt
themselves pressed against the car seat or the floor as they reach the bottom of the first hill.
They have sensed many things while at the top of an inverted loop or at the top of one of the
smaller hills on the coaster. The roller coaster track may be used as a table top coaster
model in the science classroom to analyze energy and accelerations. Features of the
coaster include a track which mimics many roller coasters, cars that have rollers above and
below the track so that the car will never leave the track and low friction bearings. The track
may be adjusted to multiple shapes.
Students have read that energy and been told that energy is conserved in a closed system.
Energy may change form but, it is always conserved. The roller coaster track may be used to
examine this principle of the conservation of energy. The sketch below (see fig. 1) shows an
interesting side view of a track with roller coaster features. The roller coaster track may be
adjusted to approximate this profile from points A through E.
Zero line to reference height
Figure 1
This roller coaster track kit can be used in discussion of energy conservation. The roller
coaster train consists of three cars. The lead car and last car each have two seats on them.
The middle car contains a special holder that accommodates a plastic sphere. This sphere is
useful in examining forces at the top of hills. The roller coaster track may be set up to
approximate the track profile above. Some simplifications are made. The hill approaching
point A is not included. Circle sections are used to approximate hill tops, hill bottoms, and
the loop.
An initial run may be made by placing the three car coaster near the top of the first incline
which is labeled A below. Adjust the track so that the coaster starts on the incline at point A
and travels over the hill at E when it is released.
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Students are asked to observe and sketch the track. The students are asked to describe the
energy conversions as the car moves along the track. Students will probably use the phrases
potential energy and kinetic energy. In discussion, students soon realize that they need to
have the speed of the car if they are to numerically compare total energy at various points
along the track.
Figure 2
A
C
B
E
D
Finding the speed of the car is a challenge. It moves much too fast to use a stopwatch for
elapsed time to get reliable speed calculations. A dot tape timer will not work because of the
friction as the tape is pulled through the timing mechanism and the motion is not in a
straight line. The ideal timer should be easy to use, should be easy to position and should
not impact the motion of the coaster. The timers which fit these criteria include Arbor
Scientific photogate timers. To measure the speed of the car, a “flag” will be needed to
temporarily block the light in the photogates as the car passes through. A thin Lego bar (8x2)
connected to the seat of the car by a 2x2 Lego block works well as a flag (see fig 3).
Figure 3
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The photogate timer records the time that light is blocked when an opaque object passes
between the receiver and light sending device. The average velocity at that point may be
computed by dividing the length of the flag by the time the light is blocked. The timer can be
mounted in various positions along the coaster track utilizing a ring stand and clamp.
The 5 speeds at points B, C, D, E, and F are found and converted in minutes. Measurements
are taken to get the heights at the five points. Starting the coaster at the same point on the
slope near point A is crucial if the timer is being moved between the 5 points to make
measurements. Three measurements should be made at each point. Student teams are
asked to measure heights and masses needed and to find velocities at the five points.
Gather Raw Data and record below. It is suggested that the students use the front car for
making measurements in this experiment. For calculating gravitational potential energy
(PE), measure the height of the car at the 5 positions from a base level line as shown in the
diagram on page 1.
1. Mass of Train (kg) ______________
Quantity \ Point
Height (m)
Velocity (m/sec)
A
B
C
D
E
Table 1 Raw Data
Regardless of the method used in determining the speed, students are asked for sample
calculation for the energies listed below.
2. Sample Calculation for Potential Energy
3. Sample Calculation of Kinetic Energy
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4. The information from the table above and the mass of the coaster is summarized and
shared. A table similar to the one below is completed as students perform the energy
calculations.
Position
Height (m)
Mass (kg)
Speed of
the car
(m/sec)
Potential
Energy
(Joules)
Kinetic
Energy
(Joules)
Total
Energy
(Joules)
A
B
C
D
E
Table 2 showing processed data
5. It is good for students to represent the three energy columns on a bar graph. This
graphic representation of the numeric data will help many students understand that there
are patterns and a trend which is shown by the data.
Kinetic Energy
Potential Energy
Total Mechanical Energy
A B C D E F
A B C D E F
A B C D E F
Energy Bar Graphs – Please label
After the table is filled in and graphs are made, three questions now arise:
6. “Why does the Potential Energy change?”
7. “Why does the Kinetic Energy change?”
8. “Is the total Energy conserved for the table top coaster?” If the mechanical energy is
conserved, the Total Energy at points A, B, C, D and E should be nearly the same value in the
column above.
9. Can you explain why the Total Energy column is not a constant?
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The results will still show that there is loss of mechanical energy.
10. Where did this mechanical energy go?
that Energy is conserved.)
(Remember your teacher and your text insists
The answers should include some energy went into sound and some energy went into
heating the track and wheels.
11. A computational question is “If all the ‘missing’ energy went into heating the coaster,
what would be the temperature change of the coaster?” (The specific heat of plastic is listed
in this range 1.2-1.9 kJkg-1 K-1. The actual value depends on the plastic used. Please use
1.5 kJkg-1K-1 for this calculation. Let’s simplify the problem further and assume that 0.050
kg of plastic is involved in this calculation.)
NOTES:
The coaster provides opportunities to apply previous class topics and introduce new ones.
One big area of discussion is that the equations that we have used in class generally involve
point sources. In beginning physics classes, we assume that all mass is concentrated at one
point. In roller coasters, this is not the case. The speed of car 1 at point B is probably not
the same as the speed of car 2 at point B. The speed of car 1, and the speed of car 2 and
the speed of the center of mass of the coater train at point B are all different.
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Name: ___________________________________ Date: ____________ Period: ___________
Roller Coaster Topics - Energy Conservation
Student Lab Guide
Objectives:
a. Measure and calculate the potential and kinetic energy at five different points along the
coaster track.
b. Record the total mechanical energy at each point and show the values to be “nearly” the
same and thereby demonstrating the approximation of the law of conservation of energy.
c. Observe and measure the small loss of mechanical energy due to friction.
Most of us have experienced roller coaster riding. We have been in the car as it crests the first hill
and then picks up speed on the way down the first hill. We have felt ourselves pressed against the
car seat or the floor as we reach the bottom of the first hill. We have sensed many things while at
the top of an inverted loop or at the top of one of the smaller hills on the coaster. We can use the
roller coaster track as a table top coaster model in the science classroom to analyze energy and
accelerations. Features of the coaster include a track which mimics many roller coasters, cars that
have rollers above and below the track so that the car will never leave the track and low friction
bearings. The track may be adjusted to multiple shapes.
Energy is conserved in a closed system. Energy may change form, but it is always conserved. The
roller coaster track may be used to examine this principle of the conservation of energy. The sketch
below shows an interesting side view of a track with roller coaster features. The roller coaster track
may be adjusted to approximate this profile from points A through E.
Zero line to reference height
7
Observe the car as it travels from points A to E on the track. Make a sketch of the track below. Fill in
the table below with your predictions for the amount of each type of energy at each point on the
track. Try to use words and phrases to describe the amount of each energy type at each point. If
you know an equation for that energy, include it as well.
Point
Potential Energy
Prediction
Kinetic Energy Prediction
Total Energy Prediction
A
B
C
D
E
Using a photogate timer, calculate the speed of the car as it passes each point on the track. The
average velocity at that point may be computed by dividing the length of a light-blocking flag by the
amount of time that the light sensor is blocked in the photogate timer. Measure the width of your
flag (the length that will pass through the light sensor). Be sure to convert your measurement into
meters.
Flag Width=___________________m
Now measure the mass of the roller coaster train. Be sure to convert your measurement into
kilograms.
Mass of Train=__________________kg
Measure the height of each point on the track. Using photogates, record in the table below the
amount of time (in seconds) that the photogate sensor was blocked by the flag. Be sure to begin
each test run with the train in the same position on the track (at point A with a constant height).
8
Using the calculation for velocity, determine the train’s velocity at each point on the track using the
flag width and photogate blocking time.
Record these values in the table below.
Quantity/Point Point A
Height (m)
Point B
Point C
Point D
Point E
Time
photogate
blocked (sec)
Velocity (m/s)
Record the calculation (formula) for finding Potential Energy:
Record the calculation (formula) for finding Kinetic Energy:
Using these formulas, calculate the potential energy, kinetic energy, and total mechanical energy at
each point. Use this information to complete the table below.
Position
Height (m)
Mass (kg)
Car Speed
(m/s)
Potential
Energy (Joules)
Kinetic Energy
(Joules)
Total Mechanical
Energy (Joules)
A
B
C
D
E
9
Analyzing and Representing Data
Complete the blank bar graphs below, with a graph each for potential, kinetic, and total mechanical
energy at each point on the track. Each bar represents the energy (in Joules) at a point on the track.
Be sure to label your axes to the left of the graphs. For calculating gravitational potential energy (PE),
measure the height of the car at the 5 positions from a base level line as shown in the diagram on
page 1.
Kinetic Energy
Potential Energy
Total Mechanical Energy
A B C D E F
A B C D E F
A B C D E F
1. Why does the potential energy change?
2. Why does the Kinetic Energy change?
3. Is the total mechanical energy conserved for the table top coaster? If the mechanical energy is
conserved, the total mechanical energy at points A, B, C, D, and E should be nearly the same value at
all of the points in the bar graph above. Are they nearly the same?
4. If the total mechanical energy is less at the end of the track (point E) than at the beginning (point
A), where did this mechanical energy go?
5. Record the loss of mechanical energy below.
10
Roller Coaster Topic 2 – Teacher Guide
CENTRIPETAL ACCELERATION
Most students have experienced roller coaster riding. They have been in the car as it crests
the first hill and then picks up speed on the way down the first hill. They have felt
themselves pressed against the car seat or the floor as they reach the bottom of the first hill.
They have sensed many things while at the top of an inverted loop or at the top of one of the
smaller hills on the coaster. The roller coaster track kit may be used as a table top coaster
model in the science classroom to analyze energy and accelerations. Features of the
coaster include a track which mimics many roller coasters, cars that have rollers above and
below the track so that the car will never leave the track and low friction bearings. The track
may be adjusted to multiple shapes.
For this activity, students are going to compute the centripetal acceleration of the car at
various positions on the model coaster layout. The sketch below shows an interesting track
profile with roller coaster features. The track may be adjusted to approximate this profile.
Zero line to reference height
Figure 1
This track can be used to examine centripetal accelerations. The three car coaster is located
at the top of the first hill which is labeled A above. Students are asked to observe and sketch
the track. The students are asked to describe the centripetal accelerations as the car moves
along the track. In discussion, students soon realize that they need to have the speed of the
car if they are to numerically compare accelerations at various points along the track. They
also realize that they need to find the approximate radius of curvature of the track for this
calculation.
The teacher must decide how much information is to be given to the students. Some groups
may respond to this instruction: “Find the speed of the coaster at points B, C, D and E. Find
the radius of the curves at points B, C, D and E,” by discussing the problem and then trying
different methods until a good solution is reached.
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Most groups probably will require more guided direction. The teacher may find it helpful to
use a string and marker on a white board to sketch a coaster track side view and show how a
radius may be used to plan a track. Consider the first hill and an air hill sketched below (see
fig. 2). This track profile will be approximated by using portions of circles at tops of hills and
bottoms of hills. Three half circles are drawn in black. It is important to label the radius of
each curve. Those radii are shown in blue below. The circles are drawn using a string
attached to a marker. The marker is used to make the three half circles.
Figure 2
Straight line sections of track are added below (see fig. 3) in red to complete the profile of a
track showing first large hill and the first air hill.
Figure 3
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To simplify the diagram, the first half circle is eliminated. This sketch shown in Figure 4
approximates the configuration of the roller coaster track.
Figure 4
Now, let’s move to the track profile sketch and see if we can approximate the radii involved.
We are going to modify the coaster train shown in Figure 5 by attaching a drinking straw to
the front car and by attaching a drinking straw to the rear car. You may find that tape can be
used. We have found that some modeling clay attached to the seats works well for holding
the straws. Use of the clay allows our straw to be held outside the track. The straw may be
moved up or down. This facilitates finding radii at the tops of hills.
Figure 5
Coaster train
Coaster car with straw Car Connector
Coaster train with straws
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With this coaster modification, let’s position the cars at the bottom of the first hill to
determine an approximate radius. The sketch below (see fig. 6) shows the coaster train on
the track. The intersection of the two straws is the approximate location of the center of
curvature for that portion of the track. The radius is measured from that intersection to the
desired point. Some class members may measure to the rider’s eyes while another group
may measure to the position of the rider’s stomach. These will allow class members to
compute and compare centripetal accelerations of the rider’s stomach at various points. The
two ended green arrow below approximates the radius of curvature to the rider’s stomach.
Figure 6
Picture for Figure 6
Radius 0.145 m
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Now, the modified coaster is positioned at the top of the loop to find another a radius. The
coaster can be positioned at the top of the loop and not fall off because of the unique
rollercoaster wheel design which mimics modern roller coasters. The coaster cannot leave
the track. The diagram below (see fig. 7) represents the coaster at the top of the loop.
Figure7
Picture for Figure 7
Radius 0.102 m
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Now, let’s turn our attention to finding the radius of curvature at the hill shown in Figure 8.
Consider the sketch below. The coaster train has been moved to the top of the hill. The
straws must be lowered so that they intersect at the radius of curvature. In this sketch we
have added dashed lines to represent the repositioned straws. The intersection of the
straws is the approximate center of curvature. The green arrow shows the radius of
curvature to the rider’s stomach level (see fig. 8).
Figure 8
Picture for Figure 8
Radius 0.168 m
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Finding the speed of the car is a challenge. It moves much too fast to use a stopwatch for
elapsed time to get reliable speed calculations. A dot tape timer will not work because of the
friction as the tape is pulled through the timing mechanism and the motion is not in a
straight line. The ideal timer should be easy to use, should be easy to position and should
not impact the motion of the coaster. The timers which fit these criteria include Arbor
Scientific photogate timers. To measure the speed of the car, a “flag” will be needed to
temporarily block the light in the photogates as the car passes through. A thin Lego bar
(8x2), connected to the seat of the car by a 2x2 Lego block works well as a flag (see fig. 9).
Figure 9
The photogate timer records the time that light is blocked when an opaque object passes
between the receiver and light sending device. The average velocity at that point may be
computed by dividing the length of the flag by the time the light is blocked. The timer can be
mounted in various positions along the coaster track utilizing a ring stand and clamp.
EXPERIMENT
The 5 speeds at points B, C, D, E, and F are found quickly. Starting the coaster at the same
point on the slope near point A is crucial if the timer is being moved between the 5 points to
make measurements. Three measurements should be made at each point. Student teams
are asked to measure masses needed and to find velocities at the five points.
An alternate method of determining the speed of the car is to use a photo gate timer. The
timer records the time that light is blocked when the flag passes between the receiver and
light sending device. The average velocity at that point may be computed by dividing the
length of a flag by the time that the light signal was blocked. For example, when using a 2cm
flag, with the light blocked for 0.5 seconds, the speed of the car is 0.02m/0.5s=0.04m/s.
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It is suggested that the students use the front car for making measurements in this
experiment.
1. Table 1 Raw Data
Quantity \ Point
Velocity (m/sec)
A
B
C
D
E
F
Students are then asked for sample calculations.
2. Sample Calculation for centripetal acceleration
Centripetal acceleration = v2/r
The information is summarized and shared. A table similar to the one below is completed.
Often, we compare accelerations to the acceleration due to gravity.
The last optional column is a column for comparing the acceleration felt by coaster rider to
the acceleration due to gravity. For instance, if a rider experienced an acceleration of 19.6
m/sec/sec at some point on the ride, the rider experienced 2 “g”s at that point. This
number is found by dividing the acceleration (19.6 m/sec/sec) by the acceleration due to
gravity (9.8 m/sec/sec per “g”) to find the number of “g”s. The acceleration felt by the rider
involves combining centripetal acceleration with acceleration due to gravity. Do not
complete this column without instructor providing instruction.
3. RIDER Stomach Level computations
Position
velocity
(m/sec)
Radius of
curve (m)
Centripetal
acceleration
(m/sec/sec)
Acceleration
due to gravity
(m/sec/sec)
“g”s
A
B
C
D
E
F
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Now, let’s turn our attention to interpreting the information in the table above
4. Centripetal Acceleration Bar Graph –
Please label
A B C D E F
5. How does the centripetal acceleration change as the coaster moves
from point A to Point F?
6. Ignoring the force of friction on the cars, there are two forces acting on the cars that
combine to produce the centripetal force. At the five positions (positions A-F) on the diagram
on page 1, draw each of these pairs of forces. Be careful to draw the length of the force
arrows to represent the relative strength of each force.
NOTES:
The coaster provides opportunities to apply previous class topics and introduce new ones.
One big area of discussion is that the equations that we have used in class generally involve
point sources. In beginning physics classes, we assume that all mass is concentrated at one
point. In roller coasters, this is not the case. The speed of car 1 at point B is not the same
as the speed of car 2 at point B. It is important to measure the appropriate speeds when
computing forces on coaster riders.
To complete the tables above, it is ideal if the speed of the rider’s eyes and the rider’s
stomach may be taken on the same run. Using one speed measurement device on one side
of the track at rider stomach level and a second speed measurement device on the other
side of the track at rider eye level allows this to be accomplished.
Questions about the special seat which reads the force exerted on the rider help students
interpret the table of data and calculations.
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Name: ________________________________ Date: _____________ Period: _________
Roller Coaster Topics – Centripetal Acceleration
Student Lab Guide
Objectives:
a. Measure the radius of curved sections of the track
b. Measure the speed of the coaster at 5 points along the track using photogate timer.
c. Knowing the radius and speeds of the coaster at specific points, calculate the
coaster’s centripetal acceleration.
Most of us have experienced roller coaster riding. We have been in the car as it crests the
first hill and then picks up speed on the way down the first hill. We have felt ourselves
pressed against the car seat or the floor as we reach the bottom of the first hill. We have
sensed many things while at the top of an inverted loop or at the top of one of the smaller
hills on the coaster. We can use the roller coaster track as a table top coaster model in the
science classroom to analyze energy and accelerations. Features of the coaster include a
track which mimics many roller coasters; cars that have rollers above and below the track so
that the car will never leave the track and low friction bearings. The track may be adjusted to
multiple shapes.
For this activity, we will be computing the centripetal acceleration of the car at various
positions on the model coaster layout. The sketch below shows an interesting track profile
with roller coaster features. The track may be adjusted to approximate this profile.
Zero line to reference height
This track can be used to examine centripetal accelerations. Do a test-run of the roller
coaster by placing the three car coaster near the top of the first incline which is labeled A
below. Adjust the track so that the coaster starts on the incline at point A and travels over
the hill at E when it is released (the ball need not be used in this lab).
20
In the table below, describe the centripetal acceleration at each point on the track. You may
use formulas or words to describe the centripetal accelerations.
Point
A
Centripetal Acceleration
B
C
D
E
Now, let’s move to the track profile sketch and see if we can approximate the radii involved.
We are going to modify the coaster train by attaching a drinking straw to the front car and
another to the rear car.
With this coaster modification, position the cars at the bottom of the first hill to determine an
approximate radius. The sketch below shows the coaster train on the track. The
intersection of the two straws is the approximate location of the center of curvature for that
portion of the track. The radius is measured from that intersection to the desired point. With
your group, decide what point on the “rider” your radius will measure (position of the head,
stomach, etc.) and be sure to measure from this point on all radii measurements.
Calculating the Radius at Point B
21
In the table below, record the radii of the curves at each point on the track.
Point
Radiius
(meters)
A
B
C
D
E
You may use a photogate timer to measure the speed. To find the average velocity at a point
on the track, you divide the width of the flag by the amount of time that the light sensor on
the photogate was blocked. Measure the width of your flag (the length that will pass through
the light sensor). Be sure to convert your measurement into meters.
Flag Width=___________________m
Using photogates, record in the table below the amount of time (in seconds) that the
photogate sensor was blocked by the flag. Be sure to begin each test run with the train in
the same position on the track (at point A with a constant height).
Using the calculation for velocity, determine the train’s velocity at each point on the track
using the flag width and photogate blocking time. Record these values in the table below.
Quantity/Point Point A
Time
photogate
blocked (sec)
Velocity (m/s)
Point B
Point C
Point D
Point E
What is the formula (or calculation) for finding centripetal acceleration?
22
Using your data, calculate the centripetal acceleration at each point on the track. Once you
know the centripetal acceleration, you may now compare the acceleration felt by the coaster
rider to the acceleration due to gravity. For instance, if a rider experienced an acceleration
of 19.6 m/sec/sec at some point on the ride, the rider experienced 2 “g”s at that point. This
number is found by dividing the acceleration (19.6 m/sec/sec) by the acceleration due to
gravity (9.8 m/sec/sec per “g”) to find the number of “g”s. The acceleration felt by the rider
involves combining centripetal acceleration with acceleration due to gravity.
Complete the table below:
Position
Velocity
(m/s)
Radius of
Curve (m)
Centripetal
Acceleration
(m/s/s)
Acceleration
due to gravity
(m/s/s)
“g”ss
Point A
Point B
Point C
Point D
Point E
How does the centripetal acceleration change as the coaster moves from Point A to Point E?
Ignoring the force of friction on the cars, there are two forces acting on the cars that combine
to produce the centripetal force. At the five positions (positions A-F) on the diagram on page
1, draw each of these pair of forces. Be careful to draw the length of the force arrows to
represent relative strengths of each force.
23
Roller Coaster Topic 3 – Teacher Guide
ROLLER COASTER DESIGN
Note: Please use data from Energy Conservation and Centripetal Acceleration Labs that you
have previously completed.
Imagine that you are on the design team for a new roller coaster. Your task is to work with
customer recommendations/constraints at points B, C, and E on the track profile shown
below.
Zero line to reference height
Figure 1
The client amusement park has specified that the riders are to experience no more than 5
g’s of acceleration at any time on their rides. For this coaster, the client has asked that the
finished product produce a “weightless” feeling for the coaster rider at points C and E. That
is, when the rider is inverted in the loop at C, the rider should sense that they would fall out
of the coaster if they were not restrained by lap belt and shoulder belt. For Point E, the client
has asked to design the coaster so that the rider would feel weightless at the top of the hill at
E. This would cause the rider to feel like she/he is floating at point E and would travel
horizontally unless restrained by lap belt and shoulder harness.
The amusement park representative is concerned about customers complaining about one
ride at their sister theme park. Customers have complained that when they went over a hill
like that at point E, they were “thrown upwards” and the result was uncomfortable. Several
customers have said that they have bruises on their legs where the lap restraint bar pressed
against them.
Your specific task is to determine the accelerations at points B, C and E on the roller coaster
model and determine if these accelerations meet the design criteria set out by the client
amusement park. If the accelerations do not meet customer’s criteria, you are asked to
submit modifications for any failing point.
Consider the picture showing the connecting car of the coaster. The Car connecting Coaster
passenger cars contains a bowl-shaped carrier for a small sphere.
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Bowl-shaped carrier
Picture 1
Think about the coaster design engineer as the track is planned. We will consider only points
B, C and E from the diagram on page 1.
1. If the design criteria are met, what will happen to the sphere in the bowl-shaped
container when the sphere travels at point B?
What will happen to the sphere at Point C?
What will happen to the sphere at Point E?
2. If the design criteria are not met, what will happen to the sphere in the bowl-shaped
container when the sphere travels at point B?
What will happen to the sphere at Point C?
What will happen to the sphere at Point E?
3. Now try a test run of the car on the coaster track with the sphere in the bowl-shaped
container within the connecting car. What did you observe about the sphere’s
movement as the coaster moved on the track? Did the coaster model meet your
expectations from Question #1?
4. Circle any points where the design criteria were not met. B C
E
5. How would you suggest that the track be altered so that the failing point(s) can meet
the design criteria after the track modifications are completed.
6. Using the table below, create labeled sketches of the ball at each point on the
coaster track in the case that the car travels too slowly, at the correct speed, or too
fast.
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25
Point
Coaster travels too slowly
Design Criteria met – coaster
travels at just right speed
Coaster travels too fast
B
C
D
E
Table 1
Now, let’s turn our attention to the forces exerted on the sphere by the bowl-shaped carrier
at selected points. To compute these forces, the mass of the sphere is needed.
7. Find the mass of the sphere and record here:
mass of sphere = __________ kg
8. What is the weight of the sphere? Please show the calculation here.
If you are having trouble finding the weight of the sphere, here is an example calculation.
The weight of your sphere will not be the same as this example. For discussion purposes,
let’s use 100 grams (0.100 kg) for the mass of the sphere. Please compute the weight of
the sphere by multiplying the mass x gravitational acceleration. The result is:
Weight = mass x gravitational acceleration
= 0.100 kg x 9.8 m/sec/sec = 0.98 Newtons
When the car is on a horizontal surface, the weight of the 0.100 kg sphere is 0.98 Newtons.
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26
Consider the sphere riding in the bowl-shaped carrier on the connector car at point B which is
the bottom of the first hill.
Analysis Point B
Figure 2 bottom of first hill
9. What force must be exerted by the bowl-shaped carrier on the sphere so that the sphere
travels in a circular path at point B? (The force reading will be greater than the weight of the
rider.) How is it computed? What is the force value reading?
10. The centripetal force at point B is calculated using the equation
Fcentripetal = m v2/r. Calculate the centripetal force at point B and record here:
Fcentripetal at B = _________________ N
11. The bowl-shaped carrier must exert a force upward to support the weight of the sphere
and to keep the sphere moving in a circular path. The force exerted by the connecting car
on the sphere is:
Fbowl on sphere at B = Fcentripetal + w, where w represents the weight of the sphere.
Calculate the force by the bowl-shaped carrier on the sphere at point B and record below.
Fbowl on sphere at B = ____________________ N
If the Force exerted by the bowl-shaped carrier is greater than 5 times the weight of the
object, this is a failing point in the design because the maximum acceleration has been
exceeded.
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27
Now, let’s take a look at the top of the loop.
Analysis Point C
Figure 3 Top of Loop
12. Consider the case when the car is at point C. What force must be exerted by the bowlshaped carrier on the sphere so that the sphere travels in a circular path at point C (The
force will be less than the weight of the rider)? How is this force computed?
13. Calculate the centripetal force at point C using the equation Fcentripetal = m v2/r.
Fcentripetal at C = _________________ N
If the rider is to sense weightlessness, the centripetal force will equal the weight of the
sphere. The bowl-shaped carrier will not exert a force to keep the sphere moving in a circular
path. If the weight of the ball is greater than the centripetal force, the sphere will fall out of
the bowl-shaped carrier.
14. To calculate the force of the bowl-shaped carrier on the sphere at point C, we use
Fbowl on sphere at C= Fcentripetal – w, where w represents the weight of the sphere.
Calculate the force from the bowl-shaped carrier on the sphere at point C and record below.
Fbowl on sphere at C = ___________________ N
Moving further on the track, let’s look at the top of the first hill after the loop.
Analysis Point E
Figure 4 Top of Hill
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15. Consider point E at the top of the hill. The gravitational weight of the rider will be acting
downward and provide a centripetal force to keep the person traveling in the circular path.
What force is exerted by the bowl-shaped carrier at point E? (The force will be less than the
weight of the rider.) How is it computed?
16. Using the equation Fcentripetal = m v2/r, calculate and record the centripetal force on the
sphere at point E.
Fcentripetal at E= __________________N
If the rider is to sense weightlessness, the centripetal force will equal the weight of the
sphere. The bowl-shaped carrier will not exert a force to keep the sphere moving in a circular
path. When this condition is met, the sphere will leave the bowl-shaped carrier and begin
traveling horizontally as it leaves the bowl-shaped carrier. If the weight of the ball is greater
than the centripetal force, the sphere will remain in the bowl-shaped carrier as it travels over
the hill. If the weight of the sphere is less than the centripetal force, the sphere will leave the
bowl-shaped carrier and travel initially at an angle above the horizontal.
17. Calculate the force by the bowl-shaped carrier on sphere at point E and record below.
Fbowl on sphere at E= Fcentripetal - w , where w represents the weight of the sphere.
Fbowl on sphere at E = ___________________N
18. Based on your force calculations and the explanations provided, how would you change
your adjustments (question 5) in order to fit the design specifications?
NOTES:
This activity allows students an opportunity to apply ideas about energy and centripetal
acceleration to a design problem.
More than one answer exists for the solution to any failing points found in Question #3. If a
point on the table top model fails, changing radius or starting point A or height of hill will
affect the other points. They are related. Changing one item often causes changes in other
areas.
Questions 1-6 deal with the expected behavior of a sphere that is traveling in a bowl-shaped
connector. For an introduction to roller coaster design, this may be a good place to stop.
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29
Name: ___________________________________ Date: __________ Period: _________
Roller Coaster Topics – Roller Coaster Design
Student Lab Guide
Name ____________________________________________
Objectives:
a. Predict and calculate the centripetal and total forces at various points on a roller
coaster track.
b. Suggest design changes on the track in order to comply with rider specifications.
Imagine that you are on the design team for a new roller coaster. Your task is to work with
customer recommendations/constraints at points B, C, and E on the track profile shown
below.
Zero line to reference height
The client amusement park has specified that the riders are to experience no more than 5
g’s of acceleration at any time on their rides. For this coaster, the client has asked that the
finished product produce a “weightless” feeling for the coaster rider at points C and E. That
is, when the rider is inverted in the loop at C, the rider should sense that they would fall out
of the coaster if they were not restrained by lap belt and shoulder belt. For Point E, the client
has asked to design the coaster so that the rider would feel weightless at the top of the hill at
E. This would cause the rider to feel like she/he is floating at point E and would travel
horizontally unless restrained by lap belt and shoulder harness.
The amusement park representative is concerned about customers complaining about one
ride at their sister theme park. Customers have complained that when they went over a hill
like that at point E, they were “thrown upwards” and the result was uncomfortable. Several
customers have said that they have bruises on their legs where the lap restraint bar pressed
against them.
Your specific task is to determine the accelerations at points B, C and E on the roller coaster
model and determine if these accelerations meet the design criteria set out by the client
30
amusement park. If the accelerations do not meet customer’s criteria, you are asked to
submit modifications for any failing point.
Consider the picture showing the connecting car of the coaster. The Car connecting Coaster
passenger cars contains a bowl-shaped carrier for a small sphere.
Bowl-shaped carrier
Picture 1
Think about the coaster design engineer as the track is planned. We will consider only points
B, C and E from the diagram on page 1.
1. If the design criteria are met, what will happen to the sphere in the bowl-shaped
container when the sphere travels at point B?
What will happen to the sphere at Point C?
What will happen to the sphere at Point E?
2. If the design criteria are not met, what will happen to the sphere in the bowl-shaped
container when the sphere travels at point B?
What will happen to the sphere at Point C?
What will happen to the sphere at Point E?
3. Now try a test run of the car on the coaster track with the sphere in the bowl-shaped
container within the connecting car. What did you observe about the sphere’s
movement as the coaster moved on the track? Did the coaster model meet your
expectations from Question #1?
31
4. Circle any points where the design criteria were not met. B C
E
5. How would you suggest that the track be altered so that the failing point(s) can meet
the design criteria after the track modifications are completed?
6. Using the table below, create labeled sketches of the ball at each point on the
coaster track in the case that the car travels too slowly, at the correct speed, or too
fast.
Point
Design Criteria met – coaster
travels at just right speed
Coaster travels too slowly
Coaster travels too fast
B
C
D
E
Table 1
Now, let’s turn our attention to the forces exerted on the sphere by the bowl-shaped carrier
at selected points. To compute these forces, the mass of the sphere is needed.
7. Find the mass of the sphere and record here:
mass of sphere = __________ kg
32
8. What is the weight of the sphere? Please show the calculation here.
Consider the sphere riding in the bowl-shaped carrier on the connector car at point B which is
the bottom of the first hill.
9. What force must be exerted by the bowl-shaped carrier on the sphere so that the sphere
travels in a circular path at point B? (The force reading will be greater than the weight of the
rider.) How is it computed? What is the force value reading?
10. The centripetal force at point B is calculated using the equation
Fcentripetal = m v2/r. Calculate the centripetal force at point B and record here:
Fcentripetal at B = _________________ N
11. The bowl-shaped carrier must exert a force upward to support the weight of the sphere
and to keep the sphere moving in a circular path. The force exerted by the connecting car
on the sphere is:
Fbowl on sphere at B = Fcentripetal + w, where w represents the weight of the sphere.
Calculate the force by the bowl-shaped carrier on the sphere at point B and record below.
Fbowl on sphere at B = ____________________ N
If the Force exerted by the bowl-shaped carrier is greater than 5 times the weight of the
object, this is a failing point in the design because the maximum acceleration has been
exceeded.
Now consider point C, located at the top of the loop.
12. . What force must be exerted by the bowl-shaped carrier on the sphere so that the
sphere travels in a circular path at point C (the force will be less than the weight of the rider)?
How is this force computed?
13. Calculate the centripetal force at point C using the equation Fcentripetal = m v2/r.
Fcentripetal at C = _________________ N
If the rider is to sense weightlessness, the centripetal force will equal the weight of the
sphere. The bowl-shaped carrier will not exert a force to keep the sphere moving in a circular
path. If the weight of the ball is greater than the centripetal force, the sphere will fall out of
the bowl-shaped carrier.
33
14. To calculate the force of the bowl-shaped carrier on the sphere at point C, we use
Fbowl on sphere at C= Fcentripetal – w, where w represents the weight of the sphere.
Calculate the force from the bowl-shaped carrier on the sphere at point C and record below.
Fbowl on sphere at C = ___________________ N
Moving further on the track, let’s look at the top of the first hill after the loop.
15. Consider point E at the top of the hill. The gravitational weight of the rider will be acting
downward and provide a centripetal force to keep the person traveling in the circular path.
What force is exerted by the bowl-shaped carrier at point E (the force will be less than the
weight of the rider)? How is it computed?
16. Using the equation Fcentripetal = m v2/r, calculate and record the centripetal force on the
sphere at point E.
Fcentripetal at E= __________________N
If the rider is to sense weightlessness, the centripetal force will equal the weight of the
sphere. The bowl-shaped carrier will not exert a force to keep the sphere moving in a circular
path. When this condition is met, the sphere will leave the bowl-shaped carrier and begin
traveling horizontally as it leaves the bowl-shaped carrier. If the weight of the ball is greater
than the centripetal force, the sphere will remain in the bowl-shaped carrier as it travels over
the hill. If the weight of the sphere is less than the centripetal force, the sphere will leave the
bowl-shaped carrier and travel initially at an angle above the horizontal.
17. Calculate the force by the bowl-shaped carrier on sphere at point E and record below.
Fbowl on sphere at E= w - Fcentripetal, where w represents the weight of the sphere.
Fbowl on sphere at E = ___________________N
18. Based on your force calculations and the explanations provided, how would you change
your adjustments (question 5) in order to fit the design specifications?
34
ROLLER COASTER ASSEMBLY INSTRUCTIONS
KIT INCLUDES:
Quantity
Part Name
2
Long Straight
7
Short Straight
9
Short Upbend
5
Short Downbend
2
Long Downbend
18
Long Upbend
4
Rigid2Flex
1
End Bumper
Picture
35
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Quantity
Part Name
2
Rail 14’
3
Flex Track
150
Cross Ties
100
Silver
Bolt/Nut
6
4cm Tube
6
10cm Tube
6
15.5cm Tube
4
22cm Loop
Support
2
30cm Support
Picture
36
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Quantity
Part Name
6
End Flange
4
Base-Spine
12
End Moon
12
Moon-Spine
Sitdown
15
Black
Bolt/Nut
6
Gray Bases
1
Rubber Ball
1
Lego Flag
1
Cart
Picture
37
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