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Coaster Quest<br />
THE PHYSICS AND MATHEMATICS OF AMUSEMENT PARK RIDES<br />
Physics<br />
© Copyrighted by The Center for Mathematics, Science,<br />
and Technology Education, Kutztown University of<br />
Pennsylvania. This material is based upon work supported<br />
by the National Science Foundation under Grant<br />
No. 9986753.<br />
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
<strong>Dorney</strong> <strong>Park</strong>/Kutztown University<br />
Coaster Quest<br />
Introduction<br />
The Lehigh Valley is rich in tradition, culture and beauty. We are most<br />
fortunate to have a community of fine people who are dedicated to the enhancement of<br />
our quality of life. To these ends, <strong>Dorney</strong> <strong>Park</strong> and Kutztown University have<br />
collaborated in the development of an educational experience that will benefit the<br />
children of the Lehigh Valley and beyond.<br />
We call it Coaster Quest. Our goal is to provide a stimulating and challenging<br />
exploratory experience for high school students. We utilize some of <strong>Dorney</strong> <strong>Park</strong>’s best<br />
attractions in ways that promote a deeper and more profound understanding of select<br />
scientific and mathematical principles. Students are given the opportunity to examine<br />
and study relationships between the dynamics of the mechanical universe and the<br />
unique, structural features of the rides.<br />
Kutztown University of Pennsylvania is pleased once again to participate in a<br />
collaborative project that engages future teachers in serious work with leading<br />
educators and the community. For science and mathematics teachers, this represents the<br />
best of two worlds, a living classroom replete with experiential activities and a forum<br />
for examining the connections between theory and practice. For <strong>Dorney</strong> <strong>Park</strong>, this is yet<br />
another opportunity to showcase their outstanding amusement park. All who<br />
participate will examine the extraordinary structural design process that went into the<br />
construction of these fabulous rides.<br />
We extend to you the opportunity to examine our laboratory manual, review<br />
procedural aspects, and participate in our tenth annual Coaster Quest day that will be<br />
held on May 6, 2011. Well over 45,000 students from regional schools have participated<br />
in our annual Coaster Quest. With the addition of new and exciting activities, we<br />
believe that you and your students will find the day both thrilling and enlightening.<br />
Dr. Joseph S. Elias<br />
Professor of Science Education<br />
College of Education<br />
Kutztown University of Pennsylvania
Coaster Quest<br />
Table of Contents<br />
Planning Team Page i<br />
Tips for Teachers Page ii<br />
Things to Bring Page iii<br />
The Rides Page 1<br />
Apollo 2000 Page 1<br />
The Antique Carrousel Page 8<br />
The Ferris Wheel Page 13<br />
The Enterprise Page 19<br />
Revolution Page 23<br />
The Dominator Page 27<br />
The Sea Dragon Page 32<br />
White Water Landing Page 37<br />
The Scrambler Page 42<br />
The Wave Swinger Page 47<br />
Steel Force Page 52<br />
Energy Curves for Steel<br />
Force<br />
Page 61<br />
Centripetal Force and Steel<br />
Force<br />
Page 65<br />
The Talon Page 67<br />
Thunderhawk Page 75<br />
The Hydra Page 79<br />
Interpreting Graphs Page 94<br />
Possessed Page 101<br />
PA State Science and Technology<br />
Standards<br />
Page 113
Coaster Quest
Coaster Quest<br />
<strong>Dorney</strong> <strong>Park</strong>/Kutztown University<br />
Planning Team<br />
The making of an event of such monumental scope can only be<br />
accomplished when the “players” are truly dedicated to its goals. Such is the<br />
nature of our planning team. The planning process began in August of 1997. Since<br />
then, a core of science and mathematics teachers has enthusiastically participated<br />
in all phases of development. The professional staff of <strong>Dorney</strong> <strong>Park</strong> has graciously<br />
opened their doors, extending their guidance and technical support to those who<br />
developed the laboratories. One park professional likened it to a magician<br />
“revealing” well-kept secrets. The faculty, students, and administrators of<br />
Kutztown University have made the commitment of their time, energy and<br />
enthusiasm. Our goal has been and always will be academic excellence. We<br />
recognize the value of Coaster Quest as an instrument befitting this goal. The<br />
combined efforts of all represent the true spirit of education and service.<br />
Acknowledgment<br />
Mr. Richard Button<br />
Mr. Patrick Callahan<br />
Dr. Kathleen Dolgos<br />
Dr. David Drummer<br />
Dr. Joseph Elias<br />
Dr. Deborah Frantz<br />
Mr. Glenn Frey<br />
Mr. Joseph Greene<br />
Mr. Robert Guigley<br />
Mr. Keith Koepke<br />
Mr. William Landis<br />
Dr. Neal Shea<br />
Mrs. Brenda Snyder<br />
Mr. Jeffrey Wetherhold<br />
Mr. Brent Ohl<br />
Ms. Maggie Woodward<br />
Mr. Gerry Farnsworth<br />
Kutztown University of Pennsylvania<br />
Delaware Regional School District<br />
Kutztown University of Pennsylvania<br />
Kutztown Area School District<br />
Kutztown University of Pennsylvania<br />
Kutztown University of Pennsylvania<br />
Northwestern Lehigh School District<br />
<strong>Dorney</strong> <strong>Park</strong> of Allentown<br />
Reading Area School District<br />
<strong>Dorney</strong> <strong>Park</strong> of Allentown<br />
Allentown School District<br />
Kutztown University of Pennsylvania<br />
Kutztown University of Pennsylvania<br />
<strong>Park</strong>land School District<br />
East Penn School District<br />
Upper Perkiomen School District<br />
<strong>Park</strong>land School District<br />
And<br />
To the many graduate students of the Kutztown University of Pennsylvania who<br />
contributed to the development of this manual.<br />
i
Coaster Quest<br />
Tips for Teachers<br />
To help make your day at the park more enjoyable, we have created a list of<br />
“tips for teachers.” Hopefully, this list will guide you through the pre-visit<br />
planning stage and answer some of your questions.<br />
<br />
<br />
<br />
<br />
<br />
<br />
Please don't forget your equipment, supplies and laboratory manuals. You may find<br />
that a camcorder might be functional in a variety of ways. Perhaps you wish to discuss<br />
the dynamics of the rides as a review, incorporate them within a laboratory practical,<br />
use as introductory preparation for next year’s trip to the park.<br />
You and your students should decide on which of the many rides you want to explore.<br />
Carefully peruse the complete list of activities and find those rides that will best benefit<br />
your students.<br />
Some rides may take more time than others to complete. You may find it necessary to<br />
ride several times on some of the rides in order to collect good data.<br />
As much as is feasible, introduce to the students the concepts to be studied and rides<br />
that you have chosen during the weeks leading up to the event. Plan time in class for<br />
calculations and analysis during the days following the experience.<br />
Each teacher needs to decide how the students from his/her school will complete the<br />
data collection sheets, and any other information, that her/ his students may need. We<br />
recommend that teachers in charge advise students who may be fearful of some rides,<br />
that riding is optional and not mandatory.<br />
Kutztown University students will serve as general assistants to the teachers. They will<br />
be stationed at each listed ride and the reserved pavilion from 10:00 AM until 3:00<br />
PM. Follow the park map to the pavilion site and look for the Coaster Quest banner.<br />
Inform your students that they may ask the university students any questions related to<br />
the event with the exception of specific questions that may be contrary to your<br />
objectives.<br />
Further information may be obtained by contacting:<br />
Mr. Bernie Bonuccelli <strong>Dorney</strong> <strong>Park</strong> (610)395-3724<br />
bbonuccelli@dorneypark.com<br />
Dr. Joseph Elias Kutztown University (610) 683-4762<br />
of Pennsylvania<br />
elias@kutztown.edu<br />
ii
Coaster Quest<br />
Things to Bring<br />
To make your day at the park as functional and enjoyable as possible we<br />
suggest that you arrange to bring some or all of the items listed below:<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
tickets for you, your students and your chaperones<br />
copies of the activities that you and your students plan on doing<br />
stopwatches<br />
calculators<br />
clipboards<br />
paper and pencils<br />
masking tape<br />
protractors<br />
accelerometers<br />
inclinometers<br />
CBL (calculator based laboratory) if you have them and low range sensors for<br />
acceleration<br />
appropriate clothing with a change of clothing<br />
sunscreen, hats, raincoats<br />
money for food, drinks or phone<br />
measuring tape or string<br />
backpacks or plastic bags to keep laboratory manuals and equipment dry and<br />
together<br />
a good reserve of energy and enthusiasm for exploration<br />
<strong>Dorney</strong> <strong>Park</strong> Information<br />
For general information call (800) 551-5656<br />
(610) 395-3724<br />
Group Sales Information (610) 395-2000<br />
or<br />
Bernie Bonuccelli at 1(800) 551-5656 with any specific questions<br />
about ticket sales for Coaster Quest.<br />
or<br />
visit our website: www.dorneypark.com<br />
Thank you.<br />
iii
Apollo 2000<br />
Introduction:<br />
Rotational motion is a topic in physics that looks at<br />
objects that rotate or revolve around a point. This point is<br />
called the point of rotation. These objects have many<br />
properties associated with them. Two of these properties are angular velocity and<br />
centripetal acceleration. You will be using two different techniques to calculate<br />
centripetal acceleration. You will then be asked to compare the two methods. You will<br />
also graph the relationship between linear velocity, centripetal acceleration and the<br />
radius. Conceptual questions pertaining to your perceptions of speed and acceleration as<br />
you are riding the Apollo 2000 are at the end of the laboratory.<br />
Apparatus:<br />
stopwatch, calculator, inclinometer<br />
Procedure:<br />
Look for the Coaster Quest sign or any position to the right of the entry area of the<br />
ride for a good place to stand when taking the following measurements. This will<br />
provide a clear point of observation when doing the off ride data taking.<br />
1. Use a stopwatch to measure the time that it takes for the ride to rotate five (5) times<br />
when at full speed.<br />
t = ____________________ sec<br />
2. Calculate the time that it takes for one rotation.<br />
T =<br />
t<br />
5<br />
_________________sec<br />
3. The angular velocity, , is the angle that is swept out over a period of time of a<br />
rotating object. Calculate the angular velocity. Remember one rotation is 2<br />
radians angular distance.<br />
= __________________ rad/sec<br />
1
Apollo 2000<br />
4. When the ride is in full operation, the arms are oscillating inward and outward. Use<br />
the inclinometer to find the minimum angle and maximum angle of the arms with<br />
respect to the vertical (dashed line) as shown below. Hold the inclinometer as<br />
shown.<br />
max<br />
min<br />
4.73 meters<br />
8.4 meters<br />
across center<br />
Inclinometer<br />
Inclinometer<br />
min = ___________________degrees<br />
max = ___________________degrees<br />
NOTE: If you are using a PASCO or CENCO inclinometer, then you need to subtract<br />
from 90 to get the desired angle because they are designed to take angle measurements<br />
with respect to the horizontal.<br />
5. Examine the diagram above. On it or the rear of this sheet, sketch and apply your<br />
trigonometric rules to calculate the radius of motion of the car when it is at its<br />
maximum and minimum positions. You will be using your trigonometric skills to<br />
do this. Treat the 4.73 meters as the hypotenuse and add the opposite side of the<br />
triangle to the radius of the ride center.<br />
radius at minimum angle = rmin = ___________________ meters<br />
radius at maximum angle = rmax = __________________ meters<br />
6. By finding the radius of curvature at these two locations we can find the linear<br />
speed that you are traveling by using the appropriate equation. Calculate the linear<br />
velocity at the minimum position and maximum position. This can be found by<br />
actual distance (circumference) calculations but you may find your linear/rotational<br />
conversion easier by using V= r.<br />
linear velocity at minimum radius = vmin = _________________ m/sec<br />
linear velocity at maximum radius = vmax = _______________ m/sec<br />
2
Apollo 2000<br />
7. Whenever an object is moving in a curved path, there is acceleration applied to that<br />
object toward the center of the curve. That acceleration, which causes an object to<br />
follow that curved path, is called centripetal acceleration. You are going to find the<br />
centripetal acceleration of yourself caused by the rotational motion of the ride.<br />
Calculate the centripetal acceleration using the values of velocity that you just<br />
calculated.<br />
centripetal acceleration at vmin = ac(min) = __________________ m/sec 2<br />
centripetal acceleration at vmax = ac(max) = _________________ m/sec 2<br />
8. Complete the table by using the same equations and methods that you used in sections<br />
5 – 7. By completing the table, you will be graphing the relation of velocity to the<br />
radius and the centripetal acceleration to the radius.<br />
Complete the table:<br />
ANGLE<br />
(degrees)<br />
RADIUS<br />
(meters)<br />
VELOCITY<br />
(m/sec)<br />
CENTRIPETAL<br />
ACCELERATION<br />
(m/sec 2 )<br />
min<br />
1 <br />
2<br />
max<br />
3 <br />
4<br />
max<br />
max<br />
3
Apollo 2000<br />
9. Make a graph of centripetal acceleration ac, versus radius, r, by using the coordinate<br />
axis below. You will have to scale the axis yourself, so do so appropriately.<br />
centripetal<br />
acceleration<br />
(m/sec 2 )<br />
Graph of ac versus r.<br />
radius (meters)<br />
10. Make a graph of linear velocity, v, versus radius, r by using the coordinate axis<br />
below. You will have to scale the axis yourself, so do so appropriately<br />
velocity<br />
(m/sec)<br />
Graph of v versus r<br />
radius (meters)<br />
4
Apollo 2000<br />
Do the graphs in questions 9 and 10 represent a linear, quadratic, or inverse<br />
relationship?<br />
<br />
How can you be sure it is linear? Include any equations that created the data<br />
you graphed.<br />
Finding maximum and minimum centripetal acceleration<br />
by using force vectors<br />
11. Another method of finding centripetal accelerations is by using vectors. Vectors<br />
are the arrows shown below which show size and direction of particular values.<br />
Calculate the maximum and minimum centripetal accelerations using the<br />
following diagram and the values you found for the maximum and minimum<br />
angle. As before, the dashed line is vertical!<br />
<br />
FN<br />
<br />
Fc<br />
FW = mg<br />
Equation to use<br />
F<br />
F<br />
N<br />
N<br />
cos<br />
mg<br />
mg<br />
FN<br />
, and<br />
cos<br />
sin<br />
ma<br />
mgsin<br />
ma<br />
cos<br />
g tan<br />
a<br />
c<br />
c<br />
c<br />
centripetal acceleration at min = ac(min) = ___________________ m/sec 2<br />
centripetal acceleration at max = ac(max) = ___________________ m/sec 2<br />
5
Apollo 2000<br />
12. Collect data from three other lab groups and put the values into the table provided<br />
for you. When working on real world data, it is always best to get multiple values<br />
for each measurement. This helps find and eliminate random error in lab work.<br />
Comparison table:<br />
Answers from Procedure #5-7 Answers from Procedure #11<br />
GROUPS<br />
CENTRIPETAL<br />
ACCELERATION<br />
CENTRIPETAL<br />
ACCELERATION<br />
CENTRIPETAL<br />
ACCELERATION<br />
CENTRIPETAL<br />
ACCELERATION<br />
a c(min)<br />
(m/sec 2 )<br />
a c(max)<br />
(m/sec 2 )<br />
a c(min)<br />
(m/sec 2 )<br />
a c(max)<br />
(m/sec 2 )<br />
YOUR<br />
GROUP<br />
1<br />
2<br />
3<br />
Analyze the accuracy and precision of the data of the four laboratory groups by<br />
comparing the groups' data in the column to each other.<br />
Next, analyze the accuracy and precision of the data by comparing the four sets of<br />
answers collectively in problem #12.<br />
6
Apollo 2000<br />
Concept Questions<br />
1. How do you perceive the speed of the ride when you are swinging outward?<br />
2. How do you perceive the speed of the ride when you are swinging inward?<br />
3. When the car is at its maximum angle, why don't you feel as if you are going to<br />
fall out?<br />
4. Does the change in radius have anything to do with the angular velocity? Linear<br />
velocity? Centripetal acceleration?<br />
7
The Antique Carrousel<br />
The Physics of Just Going in Circles<br />
Introduction:<br />
Sometime between 1918 and 1925 W. H. Dentzel built<br />
a classic carrousel that <strong>Dorney</strong> <strong>Park</strong> obtained in 1995. While<br />
simple, the carrousel can demonstrate many basic and advanced<br />
concepts of circular motion.<br />
In this lab, you will progress from simple to more<br />
advanced computations on curvilinear measurement.<br />
<br />
<br />
<br />
Part One will address basic tangential speed measurements.<br />
Part Two will take you through a series of centripetal accelerations and lastly<br />
Part Three will have you analyze the system through angular measurements.<br />
Apparatus:<br />
Stopwatch, calculator, inclinometer<br />
Data Table and Measurements:<br />
In order to do all parts of this lab, several measurements will be needed. In the<br />
blanks below, measure and record the values indicated:<br />
1. Time for one revolution: ____________________<br />
(Pick a point on the carrousel and time 3 complete revolutions. Divide this by 3<br />
for a more accurate single revolution time.)<br />
2. Angle reading for the inclinometer.<br />
(Be careful of the zero degree point. Hold your inclinometer vertically against<br />
the upright bar on the horse and read values before and after rotation starts. The<br />
angle is the change in these values from the rest angle to the angle it reaches<br />
when in motion. You must do this as the bar on the horse is not vertical!)<br />
Angle 1 change (inner row)________<br />
Angle 3 change (third row)________<br />
Angle 2 change (second row)_________<br />
Angle 4 change (outer row) _________<br />
8
The Antique Carrousel<br />
Part One<br />
Basic Rotational Motion<br />
The analysis of rotational motion in the basic sense uses the general equation:<br />
V=D/T where D is the distance covered by the horse and T is the time to complete one<br />
revolution (a period). D is the circumference of the ring where the horse is located and is<br />
found by 2 R, where R is the radius of the horse’s ring (row). Find the velocities of the<br />
horses from the inner to outer rows:<br />
1. V1= 2* meters / T=_______________________<br />
(5.8 meters is the radius of the inner row of horses)<br />
2. V2= 2*meters / T=_______________________<br />
(this row radius is 6.6 meters)<br />
3. V3= 2* meters / T=_______________________<br />
4. V4= 2* meters / T=_______________________<br />
5. As you observe the motion of the horses, which appear to be going the fastest?<br />
6. How does this compare to the calculated values above?<br />
7. As you ride the horses, what factors make you feel like you are moving?<br />
8. Compare these factors with the speeds you found above.<br />
9
The Antique Carrousel<br />
Part Two<br />
Accelerations<br />
As you ride the carrousel, you may notice a different “feel” between the inner and<br />
outer horse row. This is due to the different speeds and accelerations you experience.<br />
The human body is a good accelerometer.<br />
<br />
In which direction do you feel you are accelerating and on which horses is this the<br />
most noticeable?<br />
______________________<br />
The general equation for centripetal acceleration is a=V 2 /R. (Note that V and R vary<br />
as we go from the inner to outer ring of horses. Find the values for the four horse rows<br />
below:<br />
a1=_______________<br />
a2=___________________<br />
a2=_______________<br />
a4=___________________<br />
<br />
Do these values match what you felt on the ride?<br />
_______________________<br />
We can double-check these values by using the inclinometer data. Since the<br />
inclinometer you used shows the net angle between the gravitational and centripetal<br />
acceleration components, we can show ac =g * tan In the space below, compute the<br />
values for the accelerations of the 4 rows of horses using the angles you measured and<br />
tangent equation.<br />
a1=_______________<br />
a3=_______________<br />
a2=___________________<br />
a4=___________________<br />
On the axes below, graph the values for your accelerations (found above) verses the<br />
radius. What relationship is this? Start your graph with zero and scale (R) and (a)<br />
carefully.<br />
a<br />
R<br />
10
The Antique Carrousel<br />
Part 3<br />
Angular computations<br />
Many people have trouble understanding the rotational components of motion. They<br />
are actually simple to do. Consider the following:<br />
<br />
Which row of horses takes the longest to go around one revolution?<br />
OK, a simple question, they all take the same time. While the velocities differ (as seen<br />
in Part One), the time and angle they cover are all the same. We call this measure the<br />
angular velocity. If we have the period T from the data we took in the beginning:<br />
radians)/T (seconds).<br />
<br />
What is the angular velocity for the carrousel?<br />
<br />
<br />
This value is the same for all horses, but the tangential velocity differs with radius,<br />
R. In general, the rotational measure times radius gives the tangential component. We<br />
find V=*R.<br />
For example V1=5.8 meters.<br />
<br />
How does the angular acceleration compare to angular velocity?<br />
If we start with ac=V 2 /R, and substitute V=R, we prove ac = *R.<br />
11
The Antique Carrousel<br />
As you see, there is a linear relationship between acceleration, a, and radius, R.<br />
Graph this relationship below using the value for you found on the previous page.<br />
a<br />
0 2 4 6 8 meters<br />
<br />
How does this graph compare with the data you found in Part Two?<br />
<br />
Are angular methods easier for some calculations than others?<br />
12
The Ferris Wheel<br />
Observations:<br />
The Ferris Wheel is a wonderful experience of vertical circular motion.<br />
1. Describe the feelings you would experience as you move around in<br />
the circle. Compare what you feel at the top and bottom of the ride;<br />
also compare your feelings on the way up and on the way down.<br />
Activity 1<br />
Calculating the magnitude of the linear velocity and centripetal acceleration<br />
Part (a)<br />
Observe the ride and measure the time for a gondola to repeat one full trip around the<br />
wheel. The time for one complete rotation is called the Period and indicated by the letter T.<br />
Make sure that the ride is in the midst of a full rotation (i.e. it is loaded and will not stop to pick<br />
up or discharge passengers), gather data for at least 3 different trials and find the average period.<br />
The distance traveled in one rotation is the circumference of the circle (2R). Using the radius<br />
indicated, calculate the velocity from:<br />
v = 2 R/t<br />
Data Chart for Calculating Magnitude of Velocity and Centripetal Acceleration Radius<br />
of Wheel = 12.3 m (40 ft)<br />
One Rotation Trial 1 Period(s) Trial 2 Period(s) Trial 3 Period(s ) Average Period(s)<br />
Velocity (m/s)<br />
Acceleration (m/s/s)<br />
Circular motion results from an acceleration directed towards the center of the circle (centripetal<br />
acceleration). Find the acceleration using:<br />
Centripetal acceleration = velocity squared divided by radius<br />
or<br />
aC = v 2 /r<br />
See Data Chart for Activity 1<br />
13
The Ferris Wheel<br />
Activity 2<br />
Determining the forces acting on a rider at key points<br />
To find the force required to keep you moving in this circle, according to Newton’s Second Law<br />
of Motion, you need to multiply your mass by this acceleration.<br />
Centripetal Force = mass times centripetal acceleration<br />
or<br />
FC = m aC<br />
If mass is in kg and acceleration is in m/s/s, then the unit for force is a Newton (symbol N)<br />
Data Chart for Finding Centripetal Force<br />
Your mass (kg) = _______<br />
Your Weight (N) = m * 9.8 m/s/s = _______<br />
Hint:<br />
To find your mass in kg, you may find it useful to know that the weight of a 1 kg mass on earth is<br />
approximately 2.2 pounds.<br />
velocity (m/s)<br />
Radius of Wheel<br />
(m)<br />
12.3<br />
Acceleration<br />
(m/s/s)<br />
Centripetal<br />
Force (N)<br />
14
The Ferris Wheel<br />
Part (b)<br />
The centripetal force will be the same value throughout the ride. However, the forces<br />
that combine to create the centripetal force change as the position on the circle changes. At all<br />
positions on the ride the forces add to give a total force towards the center of the wheel.<br />
Seat Force<br />
Fs<br />
A<br />
Weight Fg<br />
Seat<br />
Force Fs<br />
SeatBack<br />
Force FB<br />
Seat Back<br />
Force FB<br />
Seat Force Fs<br />
Weight<br />
Fg<br />
D<br />
B<br />
Weight<br />
Seat<br />
Force Fs<br />
Fg<br />
C<br />
Weight<br />
Fg<br />
Position A - The seat force and the weight are in opposite directions. The weight must be larger<br />
than the seat force to give a total downward force.<br />
FS = FW - FC<br />
Position B - The vertical seat force and the weight are in opposite directions and are of the same<br />
magnitude since the total must add to a force in the direction toward the center of the circle. This<br />
force acts on the rider through friction with the seat or through the back of the seat.<br />
FS = FW<br />
15
The Ferris Wheel<br />
Position C - The seat force and weight are in opposite directions. The seat force must be larger<br />
than the weight to give a total force that is upward.<br />
FS = FW + FC<br />
Position D - The vertical seat force and the weight are in opposite directions and are of the same<br />
magnitude since the total must add to a force in the direction toward the center of the circle. This<br />
force acts on the rider through friction with the seat or through the back of the seat.<br />
FS = FW<br />
Using the data calculated in previous activities, find the magnitude of the vertical seat force at<br />
each of the 4 locations.<br />
If mass is in kg and acceleration is in m/s/s, then the unit for force is a Newton (symbol N).<br />
Data Chart for Finding Seat Force<br />
Position<br />
A<br />
C<br />
Fw (N)<br />
Your Weight<br />
Vertical F C (N)<br />
From Activity 2a<br />
Fs (N)<br />
Seat Force<br />
Position<br />
Fw (N)<br />
Your Weight<br />
Vertical F C (N)<br />
B 0<br />
D 0<br />
Fs (N)<br />
Seat Force<br />
Part (c)<br />
Force factors give an indication of what the rider experiences on the ride. In a vertical circle, the<br />
force factor (FF) is defined as the ratio of the forces you feel to the force of your weight:<br />
Force Factor = Seat Force/Weight<br />
or<br />
FF = Fs/Fw<br />
The resulting number is often referred to as a “g” force, indicating how the force you feel<br />
compares to your weight. One “g” means that the forces you feel match your weight. This is<br />
what you normally experience. Two g’s mean that the force you feel is twice your weight and<br />
many people would indicate that they feel “heavier.”<br />
Use the data from Activity 2b and predict the “g” forces acting on you through the four<br />
curves:<br />
16
The Ferris Wheel<br />
Activity 2c<br />
Data Chart for Predicting Force Factors<br />
Location<br />
A<br />
B<br />
C<br />
D<br />
Fs (N)<br />
Seat Force from 2b<br />
Fw (N)<br />
Your Weight<br />
Force Factor<br />
Activity 3<br />
Measuring “g’s”<br />
Someone in your group needs to ride the Ferris Wheel. Using your vertical<br />
accelerometer (long tube), measure the g's at the four locations being studied. If possible, take<br />
three runs so that you can average your data. Remember that 1 g means that you feel forces<br />
equal to your weight, 2 g’s mean that you feel forces that are double your weight, etc. To<br />
measure “g” forces, hold the accelerometer parallel to your body (perpendicular to the floor).<br />
Carefully observe the accelerometer through one complete rotation and record your best<br />
approximation of the reading at the four points of interest.<br />
Data Chart for Measurement of “g” Forces<br />
Location A Trial 1 g force Trial 2 g force Trial 3 g force<br />
Average “g”<br />
force<br />
Location B Trial 1 g force Trial 2 g force Trial 3 g force<br />
Average “g”<br />
force<br />
Location C Trial 1 g force Trial 2 g force Trial 3 g force<br />
Average “g”<br />
force<br />
Location D Trial 1 g force Trial 2 g force Trial 3 g force<br />
Average “g”<br />
force<br />
17
The Ferris Wheel<br />
Questions for Analysis:<br />
1. Compare your calculated (predicted) force factors with the “g” forces measured on the ride.<br />
2. Where is the “g” force largest? Explain.<br />
3. Where is the “g” force smallest? Explain.<br />
4. Describe what happens to the “g” forces as you complete one full rotation on the Ferris<br />
Wheel.<br />
5. Would it be possible to design a Ferris Wheel ride where the passengers feel “weightless” at<br />
some point of the ride? Explain your reasoning.<br />
6. Explain the effects of changing the radius of the Ferris Wheel while keeping the speed of the<br />
ride the same. Describe the effects for both a larger and smaller radius.<br />
7. Explain the effects of changing the speed of the Ferris Wheel while keeping the radius of the<br />
wheel the same.<br />
18
The Enterprise<br />
GOING IN CIRCLES<br />
Introduction:<br />
The Enterprise is a good ride to experience and measure what<br />
people call “g's of force.” What they are actually measuring are the<br />
forces a body experiences as compared to the standard contact force<br />
of mg, which we experience in equilibrium. When contact forces accelerate a body, it is<br />
natural to compare the sensation and value to mg, thus the ratio of the force on a body to<br />
mg gives rise to “g's of force.” When standing or sitting with no acceleration, the contact<br />
force on our body = mg, and we experience a “g” value of mg/mg = 1.<br />
Objective:<br />
In this lab you will compare calculated "g" values of force of your experience with<br />
force meter values as measured on the Enterprise ride.<br />
Procedure<br />
Part I: Theoretical values<br />
During this ride you will be able to experience and measure “g” values for three<br />
different situations: moving in a horizontal circle, at the top of a vertical circle, and at the<br />
bottom of a vertical circle.<br />
Place all responses on the data/calculation tables that can be found within the<br />
laboratory.<br />
Using the diagrams below, write the equation for the net force on the rider. In the<br />
first two cases, it is the net vertical force, in the third case it is the horizontal force.<br />
Based on the diagrams, fill in the blanks on the data table, and then solve for the contact<br />
force Fs.<br />
19
The Enterprise<br />
Part I: Theoretical Results<br />
Fill in the blanks based on the diagrams.<br />
Diagram A Diagram B Diagram C<br />
F net = ______ - mg F net = F s + ______ F net = ______<br />
Newton's Second Law says F net = _______<br />
Finally, solving for the contact force F s<br />
Bottom Top Horizontal<br />
F s = ma + ___ F s = ____ - mg F s = ____<br />
Part II: The Experience<br />
To do this part you must go on the ride.<br />
When you are on the ride, sit on your hands, if possible, so you can better feel the<br />
force of the seat on your body. It may also be beneficial to shut your eyes at the key<br />
points of the ride so your sensations are not biased.<br />
As the ride commences take note of the push of the seat on your body, and try to<br />
compare it to the 1g feeling of the seat when you are first strapped in.<br />
After the ride is over, record on your data table whether the g's are greater, less<br />
than, or equal to 1 at each of the key positions.<br />
g values >,
The Enterprise<br />
Part III: Numerical<br />
1. Before going on the ride, you will need the centripetal acceleration of the<br />
ride at top speed by using the period and radius. The radius is taken from<br />
the blueprints and is 8.5 m. This is on your data sheet.<br />
For you to measure the period, you must climb the hill a bit to get a good<br />
view of the ride. Choose a rider or car that is easily identified. Wait until the<br />
ride is at full speed (you can tell by the sound) and time. (two revolutions).<br />
Calculate the period, which is the time for one revolution. Car # 5 is marked<br />
with a red spot.<br />
1. r = 8.5 meters<br />
Number of revolutions Total time Time for one revolution<br />
_________ ________ ____________<br />
2. Calculate the centripetal acceleration using a c = 4 2 r / T 2<br />
a c = 4 2 r / T 2<br />
a c = _____ / _____ = ____________<br />
number substitutes<br />
answer<br />
3. Now you are ready to record the “g” values by taking a force meter on<br />
the ride. Record the readings in a horizontal circle, at the top of the<br />
loop and at the bottom of the loop.<br />
Force meter readings:<br />
a. Full speed in a horizontal circle: __________________<br />
b. At the top of the vertical loop: __________________<br />
c. At the bottom of the vertical loop: __________________<br />
21
The Enterprise<br />
4. Since the force factor F f is a ratio of F s to mg, the equations in Part I<br />
become:<br />
a. Horizontal circle: F f = F s /mg = ma/mg = a/g<br />
b. Top of loop: F f = F s /mg = (ma -mg)/mg = a/g - 1<br />
c. Bottom of loop: F f = F s /mg = (ma + mg)/mg = a/g +1<br />
Calculate the predicted force factor value for each situation. The value of (a) is the<br />
centripetal acceleration and (g) is 9.8 m/s 2 on earth.<br />
Horizontal circle : F f = F s /mg = ma/mg = a/g = ______/_______ = _______<br />
Top of loop: F f = F s /mg = (ma -mg )/mg = a/g – 1 = ______/______ -1 = _______<br />
<br />
Bottom of loop: F f = F s /mg = (ma + mg)/mg = a/g +1 = _____/______ + 1 = _______<br />
Conclusion:<br />
Do the “g” values recorded compare reasonably well with those calculated from the<br />
centripetal acceleration? Support your answer.<br />
Conclusion: ______________________________________________________________<br />
_________________________________________________________________________<br />
_________________________________________________________________________<br />
_________________________________________________________________________<br />
22
Revolution<br />
The Revolution is a unique and exciting ride that combines two of the most<br />
frequently discussed motions in physics, pendulum and rotational. As the ride picks<br />
up speed the passengers are set into these two motions simultaneously, producing<br />
an unusual sensation of motion not experience in daily life. As you watch this ride<br />
you will take time measurements involving both the pendulum and rotational motions<br />
then do some calculations to determine the amount of force acting on the riders<br />
and compare the pendulum motion with that of a simple pendulum.<br />
Revolution<br />
The ride consists of a large, vertical beam that is swung back and forth like<br />
a simple pendulum. At the bottom of the beam, a large circular ring type of<br />
arrangement is attached. The riders sit along the outer rim of the ring. As the<br />
pendulum swings, the ring rotates. You will measure the period of oscillation of the<br />
vertical beam and the period of the circular motion of the ring.<br />
23
Revolution<br />
DATA: Length of the vertical beam: L= 7.25 m. (added dimension is 10.24 meters)<br />
Radius of the ring: r= 4.26 meters<br />
The Theory<br />
A. The Pendulum<br />
As you may recall from your physics class, a simple pendulum consist of a mass<br />
hanging at the end of along string or rod. The period of the motion is the time<br />
required to swing through one complete cycle from point A to point B and back to<br />
A. See the diagram below.<br />
A<br />
B<br />
The period T is given by<br />
T = 2<br />
Where L is the length of the pendulum and ‘g’ is the acceleration due to gravity.<br />
G = 9.90 m/s 2<br />
B. Centripetal Force<br />
24
Revolution<br />
Whenever an object of mass ‘m’ is moving on a circular path of radius ‘r’ with a<br />
speed ‘v’ there is a centripetal force ‘F’ acting on the object and it is given by the<br />
formula:<br />
F =mv 2 / r<br />
This force is always directed toward the center of the circle. The passengers on<br />
the ride are seated around the circumference of a circle. As the ring rotates, the<br />
passengers feel a centripetal force given by equation number 2.<br />
V =<br />
Where T is the period (time to complete one cycle).<br />
The Procedure<br />
A. Pendulum Motion<br />
1. When the ride begins, use a stopwatch to measure the time it takes for the<br />
system to complete 4 cycles of the pendulum type motion. From this time,<br />
calculate the time for one cycle (the period T).<br />
Time for 4 cycles = ________________________________seconds<br />
T = ____________________________________________seconds<br />
2. Solve equation number 1 for the length L of a simple pendulum that has the<br />
same period as the revolution pendulum. Compare this length to the length of<br />
the actual vertical beam.<br />
B. Rotational Motion<br />
25
Revolution<br />
3. When the ride begins to move, measure the time it takes for the passengers<br />
to complete 4 rotations. From this time, calculate the time required for one<br />
rotation. From this time and equation number 3, calculate the speed ‘v’ of<br />
the riders. Using equation number 2 to calculate the force on a rider (use<br />
your own mass ‘m’)<br />
Time for 4 cycles = __________________________seconds<br />
T = _______________________________________seconds<br />
V = ______________________________________m/s<br />
F = ______________________________________N<br />
4. From the force ‘N’, calculate the ratio of the force ‘F’ to the weigh ‘mg’.<br />
This would be the so-called ‘g’ force acting on the rider.<br />
F /mg = ________________________________<br />
26
If there was one scientist who would love modern amusement parks, it<br />
would probably be Galileo Galilei. The freefall condition he studied so<br />
carefully richly experience in this modern day environment. Advanced<br />
technology had made experiencing freefall not only safe, but exciting as<br />
well. We will analyze freefall in this laboratory activity.<br />
Dominator at <strong>Dorney</strong> <strong>Park</strong> is two different rides built on one common<br />
tower. One side launches you upward at 22 m/s and allows you almost<br />
four seconds of freefall condition while you decelerate and return to the<br />
launch point. The other side lifts you to 52 meters and launches you<br />
downward at nearly 18 m/s where YOU bounce on an air cushion to<br />
almost half of the initial height. The two different versions of the ride will be used to analyze<br />
two different aspects of motion. Launch side will<br />
look at basic kinematics and accelerated motion while the Drop side will<br />
examine momentum/impulse and work/energy conditions.<br />
Launch Side and Kinematics: To study the basic kinematics of Dominator,<br />
you will need to observe the following details:<br />
Sketch Dominator and mark in<br />
relative positions and time data.<br />
Time of launch acceleration_______ seconds (observe the bodies of riders<br />
to see when acceleration begins and ends)<br />
Time of freefall condition _______________ seconds (observe between<br />
acceleration and deceleration periods)<br />
Time of deceleration ____________________ seconds<br />
(watch when arms and legs drop)<br />
When you ride, you may also take acceleration data with your force meter<br />
and log them below:<br />
launch acceleration force reading ____________<br />
freefall acceleration force reading ____________<br />
deceleration force reading __________________<br />
With the motion data collected, you will be able to find the following values:<br />
Since in a frictionless environment (which we will assume since air drag is minimal)<br />
V up =-V down V = V down - V up = 2 V up = g T freefall<br />
27
Since we are on Earth, g = 9.8 m/s/s downward and the delta V value is negative (your<br />
instructor may ask you to show that!), we can find the Velocity by using the previous equation.<br />
Vup = g * _______________=______________ m/sec<br />
With this value, we can find the acceleration and deceleration you experience at the start and<br />
end of the ride. Note you may get a 4g reading, but the calculations below will be much less.<br />
Don’t worry; trust the numbers, differences will be discussed in question #3.<br />
Aup= Vup / Tup= _____________m/s/s / _______________sec.= ________________m/s/s<br />
Adown=Vdown/Tdown=Vup/Tup=______________m/s / ____________sec.=__________m/s/s<br />
Convert these two accelerations to g’s or Force Factor readings by dividing by 9.8 m/s/s.<br />
FFup=Aup/9.8m/s/s=_____________ “g’s”, FFdown=Adown/9.8m/s/s=___________”g’s”<br />
Questions<br />
1. How do the force factors or “g” readings compare? What are sources of error?<br />
2. What is wrong with the advertising statement?<br />
Riders reach speeds of nearly 50 mph almost instantly after takeoff then experience<br />
negative gravity before they plummet back towards earth.<br />
3. The specifications for Dominator are a 4.g launch and landing. You probably noticed the 4g<br />
reading but did not find 4g’s in your calculations, why? (Hint: average vs. constant<br />
accelerations)<br />
4. How do the average and maximum values compare? Did you observe linear or nonlinear<br />
accelerations? If they are linear with zero as one end point you can use the numeric<br />
average. Did that work here?<br />
28
Dominator Part II, The Drop Side: or Work/Energy on the bounce……<br />
By using the inclinometer and standing at some convenient distance from the base of<br />
Dominator, find the angle of incline for the maximum height and height after the first bounce.<br />
Angle at maximum height ____________________________(note this is 52 meters of altitude)<br />
Angle where riders begin deceleration=____________________________<br />
Angle at max height after first bounce ___________________________<br />
By using trigonometry, calculate the height where deceleration begins and after first bounce.<br />
The Law of Sine’s works well or use a scaled drawing and find the distance from the ride to<br />
your measuring location.<br />
Height where deceleration begins=__________________<br />
Height after first bounce ______________________<br />
First measure a total time for the drop, then measure the time the riders are decelerating by<br />
watching their bodies. Arms and legs are a good cue to see when deceleration is occurring.<br />
T(drop)=_____________ seconds<br />
T(decel)= ____________seconds<br />
Calculate your energy at these two positions. The maximum Mechanical Energy is the sum of<br />
the potential energy at the top and kinetic energy gained during the launch. The ride applies<br />
g/2 acceleration for approximately 10 meters. The remainder is covered in the PE calculation.<br />
ME(max) = PE + F * d = mgh + mg/2*10m =<br />
___________________(units also)<br />
PE (first bounce) = m g hbounce=____________________________________(units also)<br />
29
1. How much energy was lost from maximum height to first bounce height?<br />
2. What is the efficiency of the pneumatic spring used to bounce you? (remember it<br />
should not be very elastic, they want you to stop eventually)<br />
3. Did you notice your fall was not “freefall” soon after launch? The pneumatic system<br />
begins your deceleration soon after launch. If it were not for that, what would your final<br />
speed be before the 10-meter main deceleration? Use KE=PE + Work to find your<br />
velocity.<br />
30
4. Compare this velocity with an approximation based on landing time and average<br />
deceleration of 2g’s. How do they compare?<br />
5. Since we know the distance the riders came to rest in, using the fact that change in<br />
energy is due to work done we can find the average force on you. Find F given<br />
F=Energy / distance (work/energy theorem).<br />
6. Compare this to the force found by change in momentum divided by time. (application<br />
of impulse/momentum calculations)<br />
7. In all cases above, we have used average values. Calculus students should use the linear<br />
change in acceleration and reanalyze questions 5 and 6 using the appropriate F/t and<br />
F/d graphs in the area below. This question is meant to be open ended. It is safe to<br />
assume the force varies linearly with distance increasing from 0 to the 4g force. Be<br />
careful when looking at the time values due to the distance/velocity relationship.<br />
31
The Sea Dragon<br />
(Part 1)<br />
The following two activities involve the use of the<br />
conservation of mechanical energy and Newton's Second Law to<br />
determine the maximum speed of the Sea Dragon. It is<br />
recommended that the student first observe the motion of the ride to<br />
determine when and where the ride undergoes the motion of a<br />
physical pendulum. The portion of the ride studied should be while<br />
the boat is traveling freely.<br />
Activity I - Maximum Speed Using Energy<br />
Objective: To determine the maximum speed of the Sea Dragon using the principle of<br />
conservation of mechanical energy.<br />
Procedure:<br />
1. Use the inclinometer to measure the maximum angle, , that the ride makes with<br />
the vertical.<br />
Maximum angle, _________________<br />
32
The Sea Dragon<br />
(Part 1)<br />
2. The length of the swing arm, L is 10.7 m. (See diagram above.) Knowing this and<br />
that the maximum angle determines the maximum height, h, use the following<br />
guide to find h.<br />
h = 10.7(l - cos) meters<br />
Maximum height, h_________________<br />
3. Assuming that mechanical energy is conserved, the potential energy at the<br />
maximum height is equal to the kinetic energy, KE, at the lowest point. The<br />
lowest point is where the boat is traveling freely with maximum speed, v.<br />
PE = KE<br />
mgh = 1/2(m)v 2<br />
Solve mgh = ½ (m)v 2 for v and then calculate the maximum speed, v.<br />
33
The Sea Dragon<br />
Maximum speed, v_________________<br />
(Part 1)<br />
Activity 2 – Maximum Speed Using Newton’s Second Law<br />
Objective: To determine the maximum speed of the Sea Dragon using Newton's Second<br />
Law and to compare this value to the speed found in Activity 1.<br />
1. Ride the Sea Dragon. Using a hand held vertical accelerometer measure the<br />
"g's" at the lowest point of the ride's swing. Remember that 1 g means you feel<br />
the seat exerting a force, FN, on you that is equal to your normal weight, making<br />
you feel you normal. Two "g's" mean that you feel like you weigh is twice your<br />
normal weight in that the seat exerts a force, FN, on you equal to twice your<br />
weight.<br />
Number of g’s at the lowest point: _________________<br />
2. Since the motion of the ride near the bottom of the swing is approximately<br />
uniform circular motion, Newton’s Second Law predicts that<br />
FN -Fg = (mv 2 )/r<br />
where,<br />
FN is your support force (the force that the seat exerts on you)<br />
Fg is your weight<br />
m is your mass<br />
v is your speed and is a maximum value<br />
r is the radius of curvature (10.7 m)<br />
Solve this equation for maximum speed, v.<br />
What is the maximum speed equation, solved for v =_________________<br />
3. Determine your support force by multiplying the number of “g’s” by your<br />
weight.<br />
34
The Sea Dragon<br />
What is the support force, FN_________________<br />
(Part 1)<br />
4. Determine your mass using Newton’s Second Law.<br />
m= Fg/g<br />
Where g is the acceleration due to gravity<br />
What is your mass, m_________________<br />
5. Calculate the maximum speed, v, using the equation in #2 of this Activity.<br />
What is your maximum speed, v_________________<br />
6. Compare the two speeds using a percentage difference. If the speeds do not<br />
agree, discuss possible sources of error.<br />
What is the comparison of two speeds_________________<br />
35
The Sea Dragon<br />
(Part 2)<br />
The following activity involves the use of oscillatory motion concepts. It is<br />
recommended that the student first observe the motion of the ride to determine when and<br />
where the ride undergoes the motion of a physical pendulum. The portion of the ride<br />
studied should be while the boat is traveling freely.<br />
Objective: To determine the period of oscillation of the Sea Dragon in two different<br />
ways.<br />
Procedure:<br />
1. Using a stopwatch, measure the period of oscillation of the Sea Dragon.<br />
1. period of oscillation, T (first way)_________________<br />
2. Assume that the ride behaves like a simple pendulum and calculate the period using<br />
the following equation:<br />
T =2(L/g) 1/2<br />
where,<br />
T is the period of oscillation<br />
L is the length of the pendulum (10.7 m)<br />
g is the acceleration due to gravity<br />
2. period of oscillation, T (second way)_________________<br />
3. Compare the two periods using percentage difference. Is the Sea Dragon a simple<br />
pendulum?<br />
36
White Water Landing<br />
Observations:<br />
White Water Landing will give you an opportunity to use<br />
the concepts of momentum and impulse to determine the forces<br />
acting on you during the “splashdown.”<br />
1a. After observing a number of boats “splashing down,” does<br />
the size of the splash vary or is it fairly constant?<br />
_____________________________<br />
1b. If it varies, what observable factors seem to influence the size of the splash?<br />
2a. Is there any time during the ride that riders appear to lunge forward?<br />
2b. If yes, where and why does this occur?<br />
Activity 1<br />
Determining the magnitude of the velocity of the boat before<br />
and after “splashdown"<br />
Potential Energy PE = mgh mass (x) gravitational field (x) height<br />
(Top of the incline)<br />
Kinetic Energy KE = 1/2 mv 2 1/2 mass (x) velocity squared<br />
(Bottom of the incline)<br />
gravitational field g = 9.8 m/s/s at <strong>Dorney</strong> <strong>Park</strong><br />
height of incline 25 meters<br />
Potential Energy Joules (J)<br />
Length of Boat 5.2 m<br />
Part (a) Velocity immediately before splashdown<br />
37
White Water Landing<br />
To find the approximate velocity of the boat immediately before splashdown, we<br />
can make the assumption that the Potential Energy of the boat at the top of the incline is<br />
completely converted to Kinetic Energy at the bottom.<br />
Find the Potential Energy of a passenger at the top of the incline:<br />
PE=___________<br />
Lets assume that all of the Potential Energy becomes Kinetic Energy at the bottom of<br />
the incline. Use the information already obtained to find the velocity at the bottom of<br />
the incline.<br />
Part (a): Before splashdown<br />
your mass<br />
(kg) = _______________<br />
Hint: To find your mass in kg, you may find it useful to know that the<br />
weight of a 1 kg mass on earth is approximately 2.2 pounds.<br />
height of incline<br />
gravitational field<br />
Potential Energy at top of hill<br />
Kinetic Energy at bottom of hill<br />
25 meters<br />
9.8 m/s/s<br />
(J) =_______________<br />
(J) =_______________<br />
Velocity at bottom of the incline (m/s) = _______________<br />
Part (b): After splashdown<br />
Measure the time for the complete boat to pass under the bridge (after it has completed its<br />
“splashdown”). Observe at least three boats and find the average time for a boat to pass<br />
under the bridge. Use the information concerning the length of a boat to find the average<br />
final velocity of the boat.<br />
Data Chart for Finding Velocity of the Boat Before and After “Splashdown”<br />
Time to pass<br />
under the<br />
bridge<br />
Trial 1 Time (s) Trial 2 Time (s) Trial 3 Time (s ) Average Time (s)<br />
Velocity after<br />
splashdown (m/s)<br />
38
White Water Landing<br />
Activity 2<br />
Determining momentum change and impulse acting during the “splashdown”<br />
Momentum is defined as the mass of an object times its velocity.<br />
Physicists represent the quantity of momentum with the letter p.<br />
momentum = mass x velocity<br />
or<br />
p = mv<br />
Use your own mass to determine the momentum of a passenger riding in a boat<br />
both before and after splashdown. As a result of the boat splashing down, the<br />
momentum of each passenger changes. Find the change in momentum of the abovementioned<br />
passenger.<br />
momentum change = momentum after splashdown - momentum before splashdown<br />
or<br />
p = pafter - pbefore<br />
(the symbol delta means change)<br />
Data Chart for Finding Momentum Changes<br />
pbefore<br />
(kg m/s)<br />
pafter<br />
(kg m/s)<br />
p<br />
(kg m/s)<br />
Momentum of an object is changed by the application of an impulse.<br />
Impulse is defined as the product of an applied force and the time that the force acts:<br />
Impulse = Force x Time for force to act<br />
or<br />
J = F t<br />
The impulse applied to the passenger is equal to the momentum change for the<br />
passenger.<br />
J = p<br />
39
White Water Landing<br />
The time that the force acts to change the momentum is approximately the same<br />
as the time that the “splash” lasts, since the splash is a result of the water applying an<br />
impulse to the boat and the boat applying an impulse on the water.<br />
Observe at least three “splashdowns” and time how long each splash lasts to find<br />
an average splash time. From this information, determine the size of the force required<br />
to change the momentum of a passenger with your mass.<br />
If mass is in kg and acceleration is in m/s/s, then the unit for force is a newton<br />
(symbol N).<br />
Data Chart for Finding Forces Acting<br />
Trial 1<br />
Splash time<br />
(s)<br />
Trial 2<br />
Splash time<br />
(s)<br />
Trial 3<br />
Splash time<br />
(s)<br />
Average<br />
Splash time<br />
(s)<br />
p<br />
(kg m/s)<br />
<br />
Impulse<br />
(kg m/s)<br />
FA = Average Applied<br />
Force - FA(N)<br />
Activity 3<br />
Comparing Forces<br />
You can now determine how the force applied to the rider to slow down compares<br />
with other forces. A common force with which to compare is your weight. Determine<br />
how the force applied compares to your weight by using the following:<br />
Force Factor = Applied Force/Weight<br />
Data Chart<br />
If mass is in kg and acceleration is in m/s/s, then the unit for force is a newton (symbol N).<br />
FA (N)<br />
Applied Force from<br />
Activity 2<br />
Fw (N)<br />
Your Weight = mass *<br />
9.8 m/s/s<br />
Force Factor<br />
40
White Water Landing<br />
Questions for Analysis:<br />
1. Compare your force factor with other students’ of different mass. Explain your<br />
observations.<br />
2. Predict the size of the force acting on the entire loaded boat (the boat has a mass of<br />
approximately 1000 kg when empty). Estimate the total mass of riders and boat.<br />
41
The Scrambler<br />
Introduction:<br />
The Scrambler consists of two sets of arms, the upper<br />
sweep arms and the lower arms, that have different radii<br />
and revolve around different points of rotation to<br />
produce varying forces. You will be studying the paths of<br />
these arms and the cars attached to them, along with<br />
their properties, such as angular velocity, tangential<br />
velocity, and centripetal force.<br />
Apparatus:<br />
Stopwatch, calculator<br />
Part I:<br />
Procedure<br />
Stand at some point around The Scrambler so that you can see the entire ride.<br />
Watch the ride rotate several times.<br />
1. What direction do the sweep arms appear to be rotating? (clockwise or<br />
counter-clockwise)<br />
_____________________<br />
2. What direction do the lower arms appear to be rotating? (clockwise or<br />
counter-clockwise)<br />
_____________________<br />
Do you notice anything about the ride that seems to be cyclical? Try focusing on<br />
one particular car or one spot along the outside of the ride.<br />
You may notice that each sweep arm returns to the same point along the outside<br />
of the rides’ path every revolution, but each lower arm (and attached car) does<br />
not.<br />
Before the ride starts, find a car that is closest to the fence surrounding The<br />
Scrambler. It should be pointing almost directly at you. Remember this car, as<br />
you will be following its motion.<br />
Laboratory courtesy of Andrew Snyder, Materials Engineering, Rensselaer Polytechnic Institute Page 42
The Scrambler<br />
3. As the ride is rotating, what do you notice about the group of 4 cars to which<br />
the car you picked out belongs?<br />
4. How many revolutions does it take for that car to return to the same point<br />
that it started at?<br />
____________________<br />
5. What is the length of the sweep arms and what is the circumference of their<br />
path?<br />
Length: _________________<br />
Circumference: ____________________<br />
6. What is the length of the lower arms and what is the circumference of their<br />
path?<br />
Length: _________________<br />
Circumference: ____________________<br />
Part II:<br />
Now you will need your stopwatch and calculator. When the ride is up to full<br />
speed, record the time it takes for the ride to rotate 3 times. The easiest way to<br />
do this is record the time it takes for one of the sweep arms to pass you 3 times.<br />
Then divide by 3 to calculate the time of one revolution.<br />
Time of 3 revolutions: _______________________<br />
Period (time of 1 revolution): _______________________<br />
Now calculate the angular velocity, keeping in mind that each revolution is<br />
2*pi radians and your period has the units seconds/revolution.<br />
Angular velocity (in radians/second):<br />
________________________________<br />
Laboratory courtesy of Andrew Snyder, Materials Engineering, Rensselaer Polytechnic Institute Page 43
The Scrambler<br />
The tangential velocity is simply the speed that the object is travelling in its<br />
circular path. This can be obtained by multiplying the angular velocity by the<br />
radius of the path, or the length of the sweep arms.<br />
Tangential velocity (in meters/second):<br />
_______________________________<br />
The next part is a little trickier. Your task is to calculate the time it takes for the<br />
group of 4 cars to rotate one revolution. The easiest way is to orient yourself to<br />
the ride the same way you were before, lined up with the closest car to the<br />
outside, and to time 4 rotations of the upper arm, while counting how many<br />
times the group of 4 cars spins in a full circle. (Remember: the car completes<br />
one spin every time it is swung to the outside of the fence, at the point furthest<br />
away from the middle of the ride)<br />
Time of 4 revolutions: ______________________<br />
Number of spins in 4 revolutions: _______________________<br />
Period (time of 1 spin): _____________________<br />
You can now calculate the angular and tangential velocities for the lower<br />
arms attached to the cars using the same method you used for the sweep arms.<br />
Angular velocity (radians/second): _________________________<br />
Tangential velocity (meters/second): _________________________<br />
Part III:<br />
Now that you have calculated the velocities of both sets of arms it’s time to use<br />
them to reveal some interesting things about The Scrambler. Do the cars on The<br />
Scrambler have a higher speed when they are closer to the center of the ride or<br />
when they are closer to the outside of the ride? Hopefully, your answer was<br />
they travel faster when they are closer to the inside of the ride. Why is this? The<br />
speed of the cars is a product of the tangential velocity of both sets of arms.<br />
The sweep arms are moving clockwise, while the lower set of arms are moving in<br />
a counter-clockwise motion. This causes the tangential velocities of each set<br />
of arms to work together when the cars are closer to the center of the ride and<br />
offset each other when the cars are at their furthermost point from the center.<br />
Laboratory courtesy of Andrew Snyder, Materials Engineering, Rensselaer Polytechnic Institute Page 44
The Scrambler<br />
Given the information provided above you should now be able to calculate the<br />
maximum and minimum speeds of the cars when the ride is at full speed. An<br />
important thing to remember when doing these calculations is that while the<br />
angular velocity is always constant, the tangential velocity varies as a<br />
function of the radius, or the distance of the object from the point of rotation.<br />
Also, remember that when the tangential velocities are opposing each other<br />
you need to make one positive and one negative.<br />
Radius of the lower arm at the point of maximum speed:<br />
__________________<br />
Radius of the sweep arm at the point of maximum speed<br />
(distance of the car from the point of rotation of the sweep arm):<br />
_____________________<br />
Tangential velocity of the car due to the lower arm at the point of<br />
maximum speed:<br />
_______________________<br />
Tangential velocity of the car due to the sweep arm at the point<br />
of maximum speed:<br />
_______________________<br />
Maximum speed of the car: _______________________<br />
Radius of the lower arm at the point of minimum speed:<br />
__________________<br />
Radius of the sweep arm at the point of minimum speed<br />
(distance of the car from the point of rotation of the sweep arm):<br />
_____________________<br />
Laboratory courtesy of Andrew Snyder, Materials Engineering, Rensselaer Polytechnic Institute Page 45
The Scrambler<br />
Tangential velocity of the car due to the lower arm at the point of<br />
minimum speed: _______________________<br />
Tangential velocity of the car due to the sweep arm at the point<br />
of minimum speed: _______________________<br />
Minimum speed of the car: ___________________ (does this answer<br />
surprise you?)<br />
Part IV:<br />
The final part of this exercise is to calculate the centripetal force on the rider<br />
at the innermost and outermost points on the ride’s path. This must be done<br />
similarly to the way you calculated the tangential velocity of the car at both<br />
points, as centripetal force is also a radius dependant value. The centripetal<br />
force always points toward the center of rotation for each set of arms, so be sure<br />
to make one positive and one negative, if needed.<br />
The equation for centripetal force is Force = mass * radius * (angular<br />
velocity) 2 . You can use your own mass (in kg) in this calculation. (1 kg = 2.2<br />
lbs.)<br />
Centripetal force on the rider at the innermost part:<br />
_______________________<br />
Centripetal force on the rider at the outermost part:<br />
_______________________<br />
Length of Sweep Arm: 4.23 meters<br />
Length of Lower Arm: 3.65 meters<br />
Pivot arm from pivot to car: 1.82 meters<br />
Laboratory courtesy of Andrew Snyder, Materials Engineering, Rensselaer Polytechnic Institute Page 46
The Wave Swinger<br />
A SWINGING TIME<br />
Introduction:<br />
The Wave Swinger is a fairly simple ride, but it does<br />
have some interesting aspects. The rate of the rotation of<br />
the ride is constant and there are only two forces acting on<br />
the swing itself. This allows the easy analysis used in Part<br />
IV. However, because the ride tilts, the plane of swing is<br />
not horizontal. This adds some interesting possibilities to<br />
the motion of the swing and rider.<br />
Part I<br />
Theory<br />
Shown below is a crude picture of a rider on the swing seat. The swing seat and<br />
rider will be treated as one object.<br />
Since the forces F 1 and F 2 (actually there are four) are in the same direction, they can be<br />
considered as a single force F 1 and F 2 = F. This is shown below.<br />
Procedure:<br />
Place all answers where indicated within the procedures.<br />
1. Is the force of the chain F or mg? ________________________<br />
47
The Wave Swinger<br />
2. The force mg is the force due to what phenomena?<br />
____________________________________________________<br />
3. Draw the diagonal across the parallelogram.<br />
4. The diagonal of the parallelogram is the magnitude of what force?<br />
____________________________________________________<br />
____________________________________________________<br />
5. The direction of the force in number 4 is the same as the:<br />
speed or acceleration of the object?<br />
____________________________________________________<br />
6. If the speed is constant, which acceleration is equal to (0), the tangential<br />
acceleration or radial acceleration?<br />
______________________________________________________________<br />
7. Is v 2 /r the tangential or radial acceleration?<br />
Note: radial is another name for centripetal.<br />
______________________________________________________________<br />
8. Noting that the diagram in #3 shows the net force (thus acceleration) to be slightly<br />
up, would you conclude that the swing is at a low or high spot in its rotational path?<br />
48
The Wave Swinger<br />
Part II<br />
Observations relating to the theory<br />
Procedure:<br />
Make the following observations of the ride.<br />
1. Using the outside swings only, does the weight on the swing effect the angle of the<br />
chains?<br />
____________________________________________________<br />
<br />
Note: comparing an empty swing to a loaded one can do this.<br />
2. Do the riders on the inside swings travel at a faster or slower speed than those riding<br />
on the outside swings?<br />
____________________________________________________<br />
3. Use the inclinometer (as shown in the diagram below) to measure the angle that the<br />
chains make with the vertical for when the swings are at their highest point and<br />
lowest point. Within experimental error, are they the same or different?<br />
____________________________________________________<br />
4. Which swings have the greater angle from the vertical? The outside swings or the<br />
inside swings?<br />
____________________________________________________<br />
49
The Wave Swinger<br />
Part III<br />
Observations to be made on the ride<br />
1. Watch the chain as the ride begins. Which way does it move relative to you?<br />
____________________________________________________<br />
2. As you ride, how does the force of the seat on your “bottom” feel at a low point as<br />
opposed to that at the high point in your rotational path?<br />
Note: This force variation is indicative of the force variation in the chain.<br />
____________________________________________________<br />
Objective:<br />
Part IV<br />
Numerical Analysis<br />
To determine whether the radial (centripetal) acceleration is equal to the acceleration<br />
value of g (tan ) where is the angle that the chains make with the vertical.<br />
Procedure:<br />
1. Use the inclinometer to measure the angle that the outer swings make<br />
with the vertical as shown in the figure of Part II, Procedure step 3. If<br />
you feel there is significant difference between the angle when the swings<br />
are at a low point and high point, record both angles.<br />
Angle Value (low point) ________________________________________________<br />
Angle Value (high point)________________________________________________<br />
2. Time the ride for five complete revolutions. ________________________<br />
*The radius used is given as 9.0 meters.<br />
50
The Wave Swinger<br />
Analysis:<br />
1. Calculate the predicted acceleration using g(tan ), where g= 9.8 m/s 2 . If<br />
you used two different angles do this, perform calculation twice.<br />
____________________________________________________<br />
2. Find the period of the swing. (This is the time for one revolution.)<br />
____________________________________________________<br />
3. Calculate the acceleration using a = 4 2 r/T 2 .<br />
____________________________________________________<br />
4. Compare the accelerations in Parts 1 and 3 using percent difference.<br />
____________________________________________________<br />
5. Bonus: Based on the force diagram and a vertical component of the chain<br />
force equal to mg, show how Newton's Second Law produces an<br />
acceleration of g(tan).<br />
51
The Physics of<br />
Since the Gravity Rides of the 1500’s, the<br />
concept of the roller coaster has been a<br />
thrilling challenge for both rider and engineer.<br />
In this lab, you will have the chance to test the design of Steel Force, the “longest,<br />
tallest, fastest coaster in the East.” This laboratory is divided into 3 sections. Each<br />
section is a necessary step to evaluate the next section, so work in order and go as far as<br />
your instructor requires. The sections will help you examine kinematics, work/energy<br />
theorem, and curvilinear motion. The diagram below shows the parts of the ride we<br />
will analyze.<br />
Data Point A:<br />
is anywhere about half way up the first hill. At this point, the<br />
chain drive system is pulling the train uphill at a constant velocity.<br />
Data Point B: is at the bottom of the first hill. At this point, there is a tunnel 34<br />
meters long. You will use the length of the tunnel to find the speed<br />
at this point on the ride.<br />
Data Point C:<br />
Data Point D:<br />
Data Point E:<br />
is at the top of the second hill, 49.1 meters above the ground. You<br />
will use the length of the train to find its speed here.<br />
is the spiral curve at the far end of the coaster. You will measure<br />
the time to go around the curve for one full revolution. The radius<br />
of this turn is 31 m.<br />
is the return camelback’s first “hump.” You will use the train<br />
length to find its speed at this point.<br />
All data can be logged on the Steel Force Data Sheet, which follows this lab. The data<br />
will help you complete the computations for all of the following sections.<br />
52
Steel Force<br />
Section #1<br />
Koaster Kinematics......<br />
One of the primary measurements we must take in physics is the motion value called<br />
speed. In this section, we will compute the speed and acceleration values at the five<br />
points of interest on Steel Force.<br />
In general, we will use:<br />
v =d /t and a = v /t.<br />
Speed at points A, C, and E:<br />
At these points you will compute speed by using train length divided by time<br />
taken to pass a point. The train is 19.6 meters long. Check your Steel Force Data<br />
Sheet for the time to pass a point on the track at each of these locations. Use the<br />
measured times and complete the calculations in the chart on the next page for<br />
each of the points A, C and E.<br />
Speed at point B:<br />
This is the tough one! The tunnel is 34 meters long. If you measure the time<br />
through the tunnel, it will be short and you can compute the speed by the basic<br />
equation in chart line #4.<br />
Can you think of a way of measuring this more accurately? If you can, take the<br />
measurement your way and the way described above, then compare. If not, see if<br />
you can find another group who has done this.<br />
Hint: the train is 19.6 meters long and its length will increase the time of passing a<br />
point.<br />
Speed at curve D:<br />
Your measure of the time around the curve, along with the distance traveled, will<br />
give you this solution in line #5.<br />
Acceleration on first hill:<br />
Now apply your acceleration equation to solve for the average acceleration on the<br />
first hill. This is done in line #6. You will need the velocity at the top and bottom<br />
of the hill (Data points A and B) and also the time down the hill. Measure the<br />
time from when the center of the train passes the top of the hill to when that point<br />
enters the tunnel.<br />
53
Steel Force<br />
Deceleration on second hill:<br />
Using the same type of calculation, find the deceleration rate when going up to<br />
point B in line #7.<br />
Line 1<br />
Line 2<br />
Line 3<br />
Line 4<br />
Line 5<br />
Line 6<br />
Line 7<br />
VA=19.6m/____________ seconds = ______________<br />
don't forget units<br />
VC=19.6m/____________ seconds = ______________<br />
units<br />
VE=19.6m/____________ seconds = ______________<br />
units<br />
VB=34 m/____________ seconds = ______________<br />
units<br />
VD=*62 m/_________ seconds = ______________<br />
units<br />
Ahill=V/t =(________-_________)/____________ = ______________<br />
units<br />
Ahill=V/t =(________-_________)/____________ = ______________<br />
units<br />
Section #2<br />
Using the Work/Energy Theorem......<br />
Once you have been lifted to the top of the first hill, your trip is entirely<br />
controlled by a simple concept in physics, work/energy. The motor drive system simply<br />
is designed to propel you to the top of the first hill. This motor/chain drive acts on you<br />
and the train but, for this example, we will only work with you (all other parts like the<br />
train and passengers are proportionately larger). We will work on the assumption that<br />
friction is negligible to make our calculations easier.<br />
54
Steel Force<br />
Up the first hill: As you are pulled up the hill, the motor system must apply a<br />
force parallel to the hill in order to move you along. This hill is at an angle of 25<br />
degrees.<br />
8. Find the force on you as you go up the hill:<br />
F parallel =__________________<br />
Note: Recall the equation F par = mg sin<br />
<br />
This force will be applied up the entire length of the hill, 144 meters.<br />
9. What work is done on you during this part of the trip?<br />
Work = ___________________<br />
Before going further, how much power is required to pull you up, if you reach the top in<br />
the amount of time that you found?<br />
Find this in both Watts and Horsepower.<br />
P = #9_______/_______ (time) = _____________watts = _____________hp<br />
(10)<br />
Now, back to Work... The work done on you in a frictionless environment would<br />
remain as part of the total mechanical energy.<br />
11. At the top of the hill, what two types of energy do you have?<br />
12. List them and compute their values for you below.<br />
Use your mass for this analysis:<br />
(11) E (total mechanical energy) = _______________+________________<br />
name of one<br />
name of the other<br />
(12) E (total mechanical energy) = _____________+____________ =<br />
compute P<br />
compute K<br />
Since this value will remain nearly constant between the first and second hills, find the<br />
values for the stored part of the energy at points B and C. Note the first hill (at B) is<br />
below the starting level by 1.5 meters.<br />
(13) P at B = _____________<br />
(14) P at C = _____________<br />
55
Steel Force<br />
The work done to get you to the top of the 61 meter hill can be found the same way as finding the<br />
stored energy.<br />
15. Using this type of calculation, what is the stored energy at the top of the hill?<br />
P at Top = _______________<br />
Does this compare favorably to your calculation from calculation #9? Why?<br />
_____________________________________________________________<br />
_____________________________________________________________<br />
_____________________________________________________________<br />
If we assume E initial =E final , we can use the equation:<br />
_______________ (value from 12) = P + K.<br />
With this we can solve for velocity at two points of interest, points B and C.<br />
E (12) = P + K therefore K = E (12) - P<br />
Find the values for the motion energy at B and C; then compute the velocity from the equation K<br />
=1/2 m v 2 .<br />
K B = _______________ therefore V B = _________________<br />
K C = _______________ therefore V C = _________________<br />
We have measured the velocity at points B and C. Using Work/Energy we have<br />
predicted it. Compare the two values. How do they compare? What sources of error exist and<br />
how bad were they? In the blocks below, assuming the actual measures from Section #1 to be<br />
accurate, compute experimental error and explain.<br />
Data Analysis at Point B<br />
Data Analysis at Point C<br />
56
Steel Force<br />
Section #3<br />
Curvilinear Motion and Vectors<br />
reaction forces<br />
The basic motion we experience on roller coasters was<br />
explained in the sixteenth century. We will look at these<br />
principles using the physics and trigonometry studied in class.<br />
When you are traveling in the train, your body is<br />
moving in a straight line until the track or gravity changes<br />
your motion. We will start by looking at changes in the<br />
horizontal motion that your train travels.<br />
Mg<br />
F c<br />
When you travel through the far point spiral, you are traveling at a speed calculated in<br />
equation. You have the radius and speed, so find the centripetal acceleration.<br />
a centripetal = V 2 /R = _______ 2 /31 meters = _________________<br />
The average angle of the track at this spiral is 44 o . Compare this to a vector<br />
diagram of the track’s gravitational force verses its centripetal force. Fill in the values<br />
and draw scaled reaction forces with resultant on the drawing above. What do you<br />
notice? Discuss below: (include not just values, but what you felt, which way the forces<br />
acted on you, etc.)<br />
57
Steel Force<br />
Points B, C and E are other interesting<br />
positions. In these areas, you have a combination of<br />
forces acting on you in the vertical directions. If we<br />
assume a person to be ideally viewed as shown, create<br />
a free body diagram (FBD) including the seat and<br />
gravitational forces on the rider. Use the dot to the<br />
right for your FBD.<br />
gravity<br />
seat force<br />
At point B, we will define the upward force of the seat to be N for normal force. The<br />
centripetal force is also upward and gravity is downward. From this, we can predict the<br />
seat force on you by applying Newton’s Second Law as follows:<br />
F = m a<br />
The values, that we can see from the FBD, expand to the following:<br />
N - m g = m v 2 /r, or N = m(g+v 2 /r)<br />
16. Since these values are all known, we can easily find the force on your body. The<br />
radius of the tunnel curve is 34m. Using your value for speed from (4) and your<br />
mass, find the seat force N.<br />
N = ___________________<br />
17. Divide this (16) by your weight and compare to your accelerometer reading.<br />
N/mg =_____________ g’s compared to ___________________ g’s<br />
58
Data Point A, You are looking for the<br />
velocity of the train going up the hill.<br />
Find the time for the train to pass a<br />
point on the hill.<br />
t =________________<br />
Data Taking Sheet for<br />
Side 1, Kinematics<br />
Data Point C, The velocity at the<br />
top of the second hill is again found<br />
using train length and<br />
Time, t, =_________________<br />
Data Point B, Finding the velocity at the<br />
bottom of the big hill. Use the time it takes<br />
the train to go through the tunnel. Be<br />
careful, it will be a very short interval......<br />
t =____________________<br />
Data Point E, The top of the first<br />
Camelback Hump will be used as<br />
a reference. Measure the time it<br />
takes the train to pass the very<br />
top point.<br />
t =_________________<br />
59<br />
Data Point D, To find the speed<br />
through the curve, use the<br />
circumference and time to pass a<br />
vertical point through one<br />
revolution.<br />
t =_______________
Data Taking Sheet for<br />
Side 2, Curvilinear Motion and Vectors<br />
Data Point A, As you go up the hill,<br />
which way do you feel a force?<br />
Using your accelerometer, find the<br />
acceleration you are experiencing.<br />
a=_______________<br />
Data Point A to B, as you accelerate down<br />
the hill, you should see your accelerometer<br />
reading change. Find the acceleration<br />
going down the hill and at the bottom.<br />
a down =__________ a bottom =__________<br />
Data Point E, What is the<br />
acceleration at the peak of this<br />
hump? Take a reading and listen<br />
to the train on the track. What do<br />
you notice?<br />
a=________________<br />
60<br />
Data Point D, We will need<br />
acceleration through this curve.<br />
Use your accelerometer to<br />
measure this value.<br />
a=________________
Energy Curves for Steel Force<br />
Objective: To investigate a rider’s energy curves for a portion of the Steel Force ride<br />
Equipment: stopwatch, scaled photo of Steel Force’s second hill (see Diagram 1 in data section),<br />
small ruler<br />
Note: In this investigation the x-axis runs along the track.<br />
Procedure:<br />
1. Determine the speed of the coaster at position A (0 meter). To do this, time how long it<br />
takes the 19.6 meter long train to pass position A and record. (See Diagram 1 in data<br />
section).<br />
2. Repeat step # 1 for each of the remaining positions (B through L).<br />
3. Record your weight in pounds.<br />
4. Using Newton’s Second Law and the fact that 1 pound equals 4.448 Newtons, calculate<br />
the rider’s mass in kilograms and record. Show your work in the analysis section.<br />
5. Determine the rider’s kinetic energy at each position and record.<br />
6. Using Diagram 1 with its provided scale (the 20 m width), determine the distance each<br />
position is from position A (0 meters) and record. Note: This distance is equal to the<br />
magnitude of the position, x.<br />
7. Using Diagram 1 with its provided scale (the 20 m width), determine the height each<br />
position is from the ground and record.<br />
8. Determine the potential energy of the rider at each position and record. Show your work<br />
in the analysis section.<br />
Special thanks to Jeff Wetherhold 61
Energy Curves for Steel Force<br />
Data:<br />
A, 0 m<br />
B<br />
C<br />
D<br />
E<br />
F<br />
G<br />
H<br />
height of hill = 46<br />
m<br />
I<br />
J<br />
K<br />
L<br />
20 m<br />
Diagram 1<br />
Length of train = 19.6 meters<br />
Rider’s weight = _____ pounds<br />
Rider’s mass = ______ kilograms<br />
Special thanks to Jeff Wetherhold 62
Energy Curves for Steel Force<br />
Position<br />
mark<br />
Position,x<br />
(m)<br />
A 0<br />
Position,y<br />
(m)<br />
Time to<br />
pass<br />
position<br />
mark<br />
Speed at<br />
position<br />
mark<br />
(m/s)<br />
Kinetic<br />
energy at<br />
position<br />
mark, K<br />
(J)<br />
Potential<br />
energy at<br />
position<br />
mark, U<br />
(J)<br />
Total<br />
energy at<br />
position<br />
mark, E<br />
(J)<br />
B<br />
C<br />
D<br />
E<br />
F<br />
G<br />
H<br />
I<br />
J<br />
K<br />
L<br />
Special thanks to Jeff Wetherhold 63
Energy Curves for Steel Force<br />
Analysis:<br />
1. Show work for finding the rider’s mass.<br />
2. Show work for finding the rider’s kinetic energy.<br />
3. Show work for finding the rider’s potential energy.<br />
4. Using the provided graph paper, graph the kinetic energy, the potential energy, and the<br />
total energy as a function of the position, x. Plot the energies on the same set of axes.<br />
5. Based on analysis # 4 results, construct the corresponding net force vs. position graph<br />
(use the same piece of graph paper that you used for analysis # 4).<br />
6. According to the net force vs. position graph, what is the net force on the rider at the<br />
top of the hill? Does this make sense to you? Explain.<br />
7. Is the mechanical energy of the rider conserved? If not, what happens to the lost<br />
mechanical energy?<br />
Special thanks to Jeff Wetherhold 64
Centripetal Force and Steel Force<br />
Objective: To determine the centripetal force on a person riding Steel Force<br />
Equipment: stopwatch, scaled photo of Steel Force’s second hill (see Diagram 1 in data section),<br />
small ruler<br />
Procedure:<br />
1. Have someone ride the Steel Force and measure, with the vertical accelerometer,<br />
the “g-force” at the top of the second hill (see Diagram 1) and record.<br />
2. Time how long it takes the 19.6 meter long train to pass the top and record.<br />
3. Record the rider’s weight in pounds.<br />
4. Using Diagram 1 and its scale, determine the radius of the curvature of the hill at the top<br />
and record.<br />
Data:<br />
TOP<br />
20 m<br />
Diagram 1<br />
Special thanks to Jeff Wetherhold 65
Centripetal Force and Steel Force<br />
g-force at top of hill = _______ g<br />
length of train = 19.6 meters<br />
time for train to pass top = ______ seconds<br />
rider’s weight, W = ______ pounds<br />
radius of curvature of the second hill at the top, r = ______ meters<br />
Analysis:<br />
1. Draw a force diagram for the rider at the top of the hill. The forces involved include the<br />
normal force, F N and weight, W.<br />
2. Knowing that 1 pound equals 4.448 Newtons, determine the rider’s weight, W in Newtons.<br />
3. Knowing the g-force on the rider, determine the normal force on the rider at the top. For<br />
example, if the rider measured 2 g’s, then the normal force on the rider would be equal to<br />
two times the rider’s weight.<br />
4. Using Newton’s Second Law and the fact that 1 pound equals 4.448 Newtons, calculate<br />
the rider’s mass, m in kilograms.<br />
5. The centripetal force on the rider is equal to the net center directed force, Σ F on the<br />
rider. Use this fact to determine the centripetal force, F c on the rider at the top.<br />
6. Knowing the length of the train and the time for the train to pass the top, determine the<br />
speed, v of the rider at the top of the hill.<br />
7. Knowing that acceleration of the rider at the top is given by the equation ac =<br />
v 2 ,<br />
r<br />
determine the rider’s acceleration.<br />
8. From Newton’s Second Law, the centripetal force on the rider is also equal to the rider’s<br />
mass times the rider’s acceleration or F <br />
= māc . Use this fact to determine the<br />
c<br />
centripetal force on the rider at the top.<br />
9. Using a % difference, compare the centripetal forces you found in analysis # 5 and # 8.<br />
Special thanks to Jeff Wetherhold 66
The Talon will allow the opportunity to study the forces that act as your body goes through a variety of<br />
loops and curves. Before riding, spend some time looking at the ride. If possible watch a number of trains<br />
going through the complete circuit.<br />
1. Describe what your body would expect to feel at the following points on the ride:<br />
(See the accompanying diagram to identify these points)<br />
o Bottom of the first hill:<br />
o Top of the vertical loop (when you are upside down):<br />
o As you pass through the top of the Zero “g” Roll<br />
(the title of this element may be helpful!):<br />
o The middle of the horizontal Spiral:<br />
Mass in kg =<br />
Formulas required for these activities:<br />
Weight in pounds/2.2<br />
Magnitude of velocity = Distance traveled/time interval or v = d/t<br />
Centripetal acceleration = Velocity squared divided by radius or a C =v 2 /r<br />
Centripetal Force = Mass times centripetal acceleration or F = ma c<br />
Force due to gravity<br />
(weight) =<br />
Mass times gravitational acceleration or F g =mg (g = 9.8 m/s/s at<br />
<strong>Dorney</strong> <strong>Park</strong>)<br />
Force Factor = Seat Force/Force of Gravity or FF = F s /F g<br />
67
Most of the required measurements can be taken while observing the Talon from the area around the<br />
Antique Carousel near the Main Gate.<br />
Part 1 - Determining the magnitude of the velocity at key points on the ride.<br />
Observe some cars traveling through the ride. Find the magnitude of the velocity of the cars as they pass<br />
each of the following locations. To find the velocity, use the length of the train (12.2 meters) and measure the<br />
time it takes the complete train to pass a certain point. Be sure to collect data for at least three trials and average<br />
your results. Measure time in seconds (s) and calculate the velocity in meters per second (m/s)<br />
Bottom of the first hill:<br />
Length of Train = 12.2 m<br />
Time for train to pass the point = _______________<br />
Magnitude of the velocity of train = ____________________________<br />
Top of the vertical loop (when you are upside down)<br />
Length of Train =12.2 m<br />
Time for train to pass the point = _______________<br />
Magnitude of the velocity of train = ____________________________<br />
At the peak of the Zero “g” Roll<br />
Length of Train = 12.2 m<br />
Time for train to pass the point = _______________<br />
Magnitude of the velocity of train = ____________________________<br />
In the middle of the horizontal Spiral<br />
Length of Train = 12.2 m<br />
Time for train to pass the point = _______________<br />
Magnitude of the velocity of train = ____________________________<br />
68
Part 2 - Determining the accelerations and forces acting on a rider at key points:<br />
You will need to have your mass in kg determined: Your mass = ___________kg<br />
The accelerations and forces experienced moving through a curve or loop can be considered by using<br />
the principles of circular motion.<br />
Bottom of the first hill:<br />
Radius of curve= 25.0 m<br />
Centripetal Acceleration = ____________<br />
velocity (from part 1) = ______________<br />
Centripetal Force = _________________<br />
Top of the vertical loop (when you are upside down):<br />
Radius of curve= 6.0 m<br />
velocity (from part 1) = _____________<br />
Centripetal Acceleration = ____________<br />
At the peak of the Zero “g” Roll<br />
Radius of curve= 18. 0 m<br />
Centripetal Acceleration = ____________<br />
In the middle of the horizontal Spiral<br />
Radius of curve= 9.1 m<br />
Centripetal Acceleration = ____________<br />
Centripetal Force = ________________<br />
velocity (from part 1) = _____________<br />
Centripetal Force = ________________<br />
velocity (from part 1) = _____________<br />
Centripetal Force = ________________<br />
69
Part 3: Determining the force that a rider feels at key points and calculating expected “g” forces.<br />
In addition to moving along the curve, a force is also required to “hold you up”. This additional force<br />
would be an upward force equal in amount to your weight. The centripetal forces that you calculated in Part 2<br />
are simply a combination of the force that the seat exerts (Fs) and the force due to gravity (Fg). The force due<br />
to gravity is often referred to as your weight. Calculate your weight in Newtons.<br />
Force due to gravity (weight) = ____________________N<br />
Bottom of loop.<br />
Fc is up, so<br />
F c =F s -F g<br />
Seat Force F s = F c +F g<br />
Fs<br />
Top of loop.<br />
This situation works for top<br />
of vertical loop and top of<br />
Zero “g” roll<br />
Fc is down, so<br />
F c =F g +F s<br />
Seat Force F s = F C -F g<br />
Fs<br />
Fg<br />
Fg<br />
Your weight in newtons = __________________N<br />
Bottom of the first hill:<br />
Centripetal Force (from part 2)= ____________N<br />
Seat Force = ____________________N<br />
Top of the vertical loop (when you are upside down):<br />
Centripetal Force (from part 2)= ____________N<br />
Seat Force = ____________________N<br />
70
At the peak of the Zero “g” Roll<br />
Centripetal Force (from part 2)= ____________N<br />
Seat Force = ____________________N<br />
Analysis of the forces in the horizontal spiral requires knowledge of vector mathematics. This analysis may<br />
be optional.<br />
The forces in the horizontal spiral are a bit more complicated, the centripetal force is a combination of the force<br />
required to hold you up (opposite of force of gravity) and the seat force, both of which are vectors.<br />
Since these are vectors that are not parallel to one another you need to use vector addition techniques.<br />
Seat Force<br />
(Fs)<br />
Force holding you<br />
up = your weight<br />
(Fg)<br />
From the Pythagorean Theorem:<br />
Centripetal Force<br />
(Fc)<br />
Fs 2 = Fg 2 + Fc 2<br />
In the middle of the horizontal Spiral<br />
Centripetal Force (from part 2)= ____________N<br />
Seat Force = ____________________N<br />
Part 4: Calculated “g” Forces:<br />
Of interest to many roller coaster enthusiasts are the “g” forces experienced at various places on the ride.<br />
Use the calculations you have just completed to find the Force Factor (or “g” forces) that you can expect at<br />
the key points on the ride.<br />
Bottom of the first hill:<br />
Seat Force (from part 3)= ____________N Predicted Force Factor (“g” force) = ______________<br />
Top of the vertical loop (when you are upside down):<br />
Seat Force (from part 3)= ____________N Predicted Force Factor (“g” force) = ______________<br />
At the peak of the Zero “g” Roll<br />
Seat Force (from part 3)= ____________N Predicted Force Factor (“g” force) = ______________<br />
In the middle of the horizontal Spiral<br />
Seat Force (from part 3)= ____________N Predicted Force Factor (“g” force) = ______________<br />
71
Part 5: - Measuring “g’s”<br />
Someone in your group needs to ride the roller coaster. Using your vertical accelerometer (long tube)<br />
measure the g's at the points being studied. Remember 1 g means that you feel forces equal to your weight,<br />
2 g’s mean that you feel forces that are double your weight, etc. To measure g forces, hold the accelerometer<br />
parallel to your body (perpendicular to the lap bar). As you ride, try to remember the readings as you pass<br />
through each of the key points, do not attempt to write down the readings in the midst of the ride!!!<br />
Bottom of the first hill:<br />
Measured “g” Force = ______________<br />
Top of the vertical loop (when you are upside down):<br />
Measured “g” Force = ______________<br />
At the peak of the Zero “g” Roll<br />
Measured “g” Force = ______________<br />
In the middle of the horizontal Spiral<br />
Measured “g” Force = ______________<br />
72
Questions for Analysis:<br />
1. Which of the four points has the rider traveling at the greatest speed? Explain why this is the fastest of<br />
the four points. <strong>Dorney</strong> <strong>Park</strong> ads say that Talon reaches speeds of 58 mph, how do your results compare<br />
to this claim? (either convert your results to mph or convert 58 mph to m/s to do the comparison)<br />
2. Compare the calculated force factors at each point to the measured force factors. Why may there be<br />
some differences?<br />
3. Why do they refer to the third element studied as the Zero “g” Roll? Do your results seem to agree with<br />
this claim?<br />
4. Why is the radius of the vertical loop so much smaller at the top than at the bottom? How do you think<br />
the experience of Talon would be affected if the vertical loop had a large radius at the top (like it does at<br />
the bottom)?<br />
5. Describe what factors make Talon exciting and different from other coasters like Steel Force or<br />
Hercules? If you studied another coaster, compare the results and explain what makes the other coaster<br />
exciting and different from Talon.<br />
73
Inclined Spiral<br />
Immelman<br />
Zero “g” Roll<br />
Horizontal Spiral<br />
Vertical Loop<br />
Bottom of First Hill
Thunderhawk<br />
An Enlightening Lab<br />
Introduction:<br />
Thunderhawk is the original roller coaster for <strong>Dorney</strong> <strong>Park</strong>. Although it looks small compared to<br />
Steel Force it is an excellent ride in design and function. As with all wooden type coasters the vibrations<br />
are part of the experience. It is for this reason this lab has no measurements taken on the ride though it is<br />
highly recommended you ride it to experience the usual thrills and also the decrease in energy as you<br />
move from beginning to end.<br />
Purpose:<br />
To measure the lost mechanical energy from the top of the first hill to the small hump near the<br />
end of the ride.<br />
Theory:<br />
There are no blueprints of this 1923 ride so all measurements must be determined by you.<br />
Position yourself in the vicinity of the ride called, Possessed so that you have an unobstructed view of the<br />
first hill of the Thunderhawk. In line with the top of the hill and approximately twelve feet off the<br />
ground you will see a red spot. Notice that this spot is the same height as the small hump behind the hill.<br />
See figure one. This small hump is near the end of the ride. This height will be zero potential energy,<br />
thus when the coaster goes over the small hump it will have all kinetic energy and no potential energy.<br />
Note: potential energy is based on position relative to a zero reference level. Any height below<br />
the red spot would be a negative potential energy and the kinetic energy would be more than our value.<br />
Top of hill<br />
6 ft<br />
Top of hump<br />
Red dot<br />
Figure 1<br />
75
Thunderhawk<br />
An Enlightening Lab<br />
You will find the mechanical energy you have left at the top of the small hump as a percentage of<br />
the mechanical energy you have at the top of the first hill. Since energy is conserved this "lost"<br />
mechanical energy is actually converted to small molecular motions associated with thermal energy.<br />
This percentage is in a sense a measure of our coaster's efficiency.<br />
Equations:<br />
1. Top of the first hill:<br />
Total MechanicalEnergy PE KE mgh 1 mv 2<br />
2<br />
2. Top of the hump:<br />
Total MechanicalEnergy KE 1 2 mV 2<br />
3. Fraction of Mechanical Energy Remaining<br />
<br />
<br />
1<br />
2 mV2<br />
mgh 1 2 mv2<br />
1<br />
2 V 2<br />
gh 1 2 v2<br />
(mass cancels)<br />
V 2<br />
<br />
2 gh v 2 (multiplyby two)<br />
4. Percentage of Mechanical Energy Remaining<br />
<br />
<br />
<br />
<br />
<br />
<br />
V 2<br />
<br />
2gh v 2 100<br />
<br />
76
Thunderhawk<br />
An Enlightening Lab<br />
Procedure and Data:<br />
1. Using the red spot as h = 0 determine the height of the first hill given that the vertical boards are 6 feet<br />
long. Notice we will be using English units, so g = 32 ft/s 2 . Also the nearest whole foot will be uncertain<br />
so generally we will be working with two significant digits.<br />
Estimated height of hill as measured from the red spot<br />
h = _____ feet<br />
2. The trains are 40 ft long. Measure the time it takes the entire train to pass a vertical rail at the top of<br />
the hill.<br />
time = _________ seconds<br />
3. Now measure the time it takes an entire train to pass over the small hump behind the first hill. This is<br />
near the end of the ride. You can use the top of the hump as the reference point. You can move your<br />
position to line up a vertical board with this spot.<br />
time = _________ seconds<br />
Calculations:<br />
1. Calculate the speed v in ft/s as the train passes over the first hill.<br />
2, Calculate the speed V in ft/s as the train passes over the hump.<br />
3. Use equation 4 from the theory to calculate the percentage of the energy remaining near the end of the<br />
ride.<br />
77
Thunderhawk<br />
An Enlightening Lab<br />
Want an "A”? Answer the following:<br />
1. If the weight of the train is 4000 pounds find the potential energy at the top of the first hill. Note: the<br />
unit "pounds" is weight, therefore mg = 4000 pounds so just multiply by h.<br />
The unit will be ft-lb.<br />
2. Find the mechanical energy "LOST" during the ride.<br />
3. If this energy were heat what would be the temperature increase of a cup of water (0.52 lbm) if the<br />
specific heat of the water were 1 BTU / ( lbm o F). Assume no heat was used to heat the container. 1 BTU<br />
= 778 ft lb A BTU is a British Thermal Unit<br />
78
The Hydra<br />
Introduction: This experiment is written in three different parts. Lab 1 will be using the speed of the<br />
Hydra train at various places on the ride along with the radius of curvature of the track at those locations<br />
to calculate the force factor that the rider experiences. Lab 2 will also calculate force factor but this time<br />
the track is banked which makes the problem a little more challenging. Lab 3 will be calculating the total<br />
amount of energy at various places looking at the amount of energy lost throughout the ride.<br />
Preliminary Data:<br />
The information found in the Preliminary Data section will be used throughout the Hydra Labs.<br />
Equipment needed:<br />
Stopwatch<br />
Vertical accelerometer<br />
Special thanks to Brent Ohl 79
The Hydra<br />
C<br />
D<br />
A<br />
B<br />
G<br />
E<br />
F<br />
Measure the time it takes the train to pass the reference points shown below. Start the stopwatch when<br />
the front of the train reaches the reference point and stop the stopwatch when the back of the train reaches<br />
that point. The pictures will help you find the reference points. It is recommended that at least two<br />
people measure the time and take the average for more accurate results. Enter the values of time in Table<br />
#1.<br />
Point A:<br />
The bottom of the first hill. Look for the red dot on the middle of the track.<br />
Special thanks to Brent Ohl 80
The Hydra<br />
Point B:<br />
The top of the zero-g roll. Use the track junction as the reference.<br />
Point C:<br />
Point D:<br />
The bottom of the hill just after the zero-g roll. Look for the red dot.<br />
The middle of the cobra roll (a.k.a. Happy Face). Use the support post as the reference<br />
point.<br />
Point E:<br />
The top of the camel back just after the train passes the station. Use the support post as<br />
the reference point.<br />
Point F: The middle of the spiral near the end of the ride. Use the support post as the<br />
reference point.<br />
Point G:<br />
The end of the ride just before entering the breaking segment. Use the first vertical post<br />
on the handrail as the reference point.<br />
Now ride Hydra and measure the force factor at Points A-F using the vertical accelerometer holding it<br />
parallel to your upper body. Once again, it would be best if at least two people measure the force factor<br />
and compare them for more accurate results. Enter the values for the force factor in the table below.<br />
In the table below use the descriptors; lighter, heavier, or same to describe the sensation you experienced<br />
at the designated locations in reference to how you feel motionless, upright.<br />
Special thanks to Brent Ohl 81
The Hydra<br />
Knowing the that the length of the train is 12.298 meters long, ∆x, and<br />
train at the designated locations.<br />
x<br />
v , calculate the speed of the<br />
t<br />
Table #1<br />
Track<br />
Section<br />
A<br />
Time, ∆t<br />
(seconds)<br />
Train Speed, v<br />
(m/sec)<br />
Force<br />
factor<br />
Sensation<br />
(lighter, heavier,<br />
same)<br />
B<br />
C<br />
D<br />
E<br />
F<br />
G XXX XXX<br />
This information will be used throughout the three labs for Hydra.<br />
Your weight in lbs, Fw = ________________ x 4.45 N = __________________N<br />
lbs<br />
Your mass in kg, m =<br />
F w<br />
g<br />
______________________ kg<br />
Special thanks to Brent Ohl 82
The Hydra<br />
Lab 1—Force Factor Analysis<br />
Using the orientation represented in the picture for each location, draw the force diagram of the rider.<br />
Then use Newton’s laws to calculate the force of the seat and force factor experienced by the rider. The<br />
radii of curvatures are given for each part. The speed of the train was calculated in table #1.<br />
Part A<br />
Radius of the track, r = 26.25 m<br />
Calculate the seat force using:<br />
F<br />
seat<br />
F<br />
w<br />
mv<br />
<br />
r<br />
2<br />
F<br />
force factor <br />
F<br />
seat<br />
w<br />
___________<br />
Part B – top of zero-g roll<br />
Radius of the track, r = 16.0 m<br />
Calculate the seat force using:<br />
F<br />
w<br />
F<br />
seat<br />
mv<br />
<br />
r<br />
2<br />
Fseat<br />
force factor ___________<br />
Fw<br />
Part C – After zero-g Roll<br />
Radius of the track, r = 20.8 m<br />
Calculate the seat force using:<br />
F<br />
seat<br />
F<br />
w<br />
mv<br />
<br />
r<br />
2<br />
Special thanks to Brent Ohl 83
The Hydra<br />
F<br />
force factor <br />
F<br />
seat<br />
w<br />
___________<br />
Part D—Cobra Roll (a.k.a. Happy Face)<br />
Radius of the track, r = 15.5 m<br />
Calculate the seat force using:<br />
F<br />
seat<br />
F<br />
w<br />
mv<br />
<br />
r<br />
2<br />
F<br />
force factor <br />
F<br />
Part E—Camel Back<br />
Radius of the track, r = 16.0 m<br />
Calculate the seat force using:<br />
seat<br />
w<br />
F<br />
___________<br />
w<br />
F<br />
seat<br />
mv<br />
<br />
r<br />
2<br />
F<br />
force factor <br />
F<br />
seat<br />
w<br />
___________<br />
Special thanks to Brent Ohl 84
The Hydra<br />
Questions:<br />
1. How do the force factors you experienced while riding compare to the force factors you<br />
calculated using Newton’s laws? Why are the values not exactly the same?<br />
2. The force factors experienced from the Camel Back and the Zero-g Roll are the same, but<br />
the orientation of the rider is very different. Why is this the case?<br />
Lab 2: Force<br />
Factor on the<br />
Spiral—The<br />
Banked Curve of<br />
This activity is designed for the Honors/Advanced Placement Physics student.<br />
The radius of curvature of the spiral is 16.1 m.<br />
Using the diagram below, draw the force diagram of the rider while on the spiral (Point F) described in<br />
the preliminary data section. Assume there are no forces applied to the rider that are parallel to the seat.<br />
Special thanks to Brent Ohl 85
The Hydra<br />
Front view of the rider<br />
Using the force diagram along with force factor and speed of the train you found in the preliminary data<br />
section, generate the equation for the banking angle of the spiral.<br />
Calculate the banking angle of the spiral:<br />
Banking Angle, θ = _______________________<br />
According to your force diagram, generate another equation to calculate the banking angle of the spiral<br />
and solve for it.<br />
Banking Angle, θ = ____________________<br />
Special thanks to Brent Ohl 86
The Hydra<br />
Analysis:<br />
According to the force diagram, we made the assumption that there are no parallel forces applied<br />
to the rider by the seat. This means that the banking angle of the track is perfect. When dealing with<br />
roller coasters, this typically does not happen. This way the train “searches” for equilibrium, and the<br />
train will wobble from side to side while traveling around the curve similar to that of a passenger train.<br />
So, engineers correct this problem by not making the banking angle perfect. Does your data verify this?<br />
Explain.<br />
Special thanks to Brent Ohl 87
The Hydra<br />
Lab 3: Work/Energy<br />
considerations using<br />
Equipment needed:<br />
Stopwatch<br />
Inclinometer<br />
Power of the chain lift:<br />
Hold the inclinometer parallel to the lift hill and record the angle of the lift hill below:<br />
Angle of incline: _________________<br />
Calculate the force of the chain lift, F|| to get the 12,560 kg train to the top of the hill assuming the train<br />
moves up the hill at constant speed.<br />
F||<br />
θ<br />
mg<br />
θ<br />
mg sinθ<br />
F|| = mg sinθ = ___________________<br />
Measure the total time the front car of the train takes to make it up the lift hill.<br />
Time, t = ______________________<br />
Calculate the average speed v of the lift hill chain knowing the hill is 69.5 m long.<br />
d<br />
v = _________________<br />
t<br />
Calculate the amount of work done by the chain to lift the train up the hill.<br />
Special thanks to Brent Ohl 88
The Hydra<br />
W = F|| d = ______________________<br />
Calculate the power output of the chain lift motor in watts and horsepower knowing there is 746W/hp.<br />
P =<br />
W<br />
t<br />
_______________Watts = ___________________hp<br />
Compare the power found above to the power calculated by using the following equivalent equation:<br />
P = F|| v = ______________________<br />
Total Energy of the train at various locations along the track (NOTE: All track height measurements<br />
will be in reference to the bottom of the first hill)<br />
Keeping in mind that gravitational potential energy is represented by the following equation:<br />
and kinetic energy is given by the equation:<br />
PE = mgh<br />
You can now find the total energy at any given point on the track by<br />
1 KE mv<br />
2<br />
2<br />
Where mass m is the mass of the train.<br />
TE = PE + KE<br />
Calculate the energy at the top of the lift hill: The lift hill is 32.1m.<br />
PE = _________________________<br />
KE = __________________________<br />
TEinitial = ______________________________<br />
Calculate the energy at Point A: The height at A is 0 m above the bottom of the lift hill.<br />
PE = _________________________<br />
TEA = _________________________<br />
KE = __________________________<br />
TEinitial - TEA = ______________________<br />
Special thanks to Brent Ohl 89
The Hydra<br />
Calculate the energy at Point B: The height at B is 20.2 m above the bottom of the lift hill.<br />
PE = _________________________<br />
TEB = _________________________<br />
KE = __________________________<br />
TEinitial – TEB = ______________________<br />
Calculate the energy at Point C: The height at C is 5.5 m above the bottom of the lift hill.<br />
PE = _________________________<br />
TEC = _________________________<br />
KE = __________________________<br />
TEinitial – TEC = ______________________<br />
Calculate the energy at Point D: The height at D is 8.5 m above the bottom of the lift hill.<br />
PE = _________________________<br />
TED = _________________________<br />
KE = __________________________<br />
TEinitial – TED = ______________________<br />
Calculate the energy at Point E: The height at E is 10.1 m above the bottom of the lift hill.<br />
PE = _________________________<br />
TEE = _________________________<br />
KE = __________________________<br />
TEinitial – TEE = ______________________<br />
Calculate the energy at Point F: The height at F is 6.1 m above the bottom of the lift hill.<br />
PE = _________________________<br />
TEF = _________________________<br />
KE = __________________________<br />
TEinitial – TEF = ______________________<br />
Calculate the energy at Point G: The height at G is 7.3 m above the bottom of the lift hill.<br />
PE = _________________________<br />
TEG = _________________________<br />
KE = __________________________<br />
TEinitial – TEG = ____________________<br />
Special thanks to Brent Ohl 90
The Hydra<br />
The work energy theorem Wbrakes = KE can be used to calculate the average force needed to stop the<br />
train when it reaches the braking section of the ride.<br />
The kinetic energy of the train just before the brakes are applied is the KE at Point G.<br />
The kinetic energy of the train when the train stops is<br />
KEG = ________________________<br />
KEstop = _______________________<br />
Calculate the amount of work needed to stop the train:<br />
Wbrakes = _____________________<br />
Calculate the average force applied to the train by the brakes knowing W = Fd and the distance the brakes<br />
are applied to the train is 6.2 m.<br />
Fbrakes = _______________________<br />
Questions:<br />
1. Is the total energy the same at every point on the track you measured? Should it be the<br />
same—Explain.<br />
2. How much energy was lost on the ride? What is the cause of this loss of energy?<br />
3. It was mentioned previously that the brakes apply an average force to the train. Explain<br />
why it is an average force and not an instantaneous force.<br />
Special thanks to Brent Ohl 91
The Hydra<br />
4. You calculated the total amount of energy of the train at the top of the lift hill. Where did<br />
that energy come from?<br />
Critical Thinking Problem:<br />
Try to calculate the average frictional force applied to the train starting at the top of the lift<br />
hill to Point G given the length of the track being approximately 810 m.<br />
Lab 4: The JoJo<br />
Roll of. . .<br />
This is a short conceptual activity using the JoJo Roll of the Hydra. The JoJo roll is the first element<br />
when leaving the station. This element is quite unique to roller coasters.<br />
Part 1<br />
Go to the Cobra Roll side of the ride facing the "happy face" to get a front view of the train<br />
Special thanks to Brent Ohl 92
The Hydra<br />
passing through the JoJo Roll.<br />
Question:<br />
1. Estimate your force factor just before entering the roll. Explain your reasoning.<br />
2. Estimate your force factor when you are upside down in the roll. Explain your reasoning.<br />
Special thanks to Brent Ohl 93
The Hydra<br />
Part 2:<br />
While riding through the JoJo Roll, hold one vertical accelerometer upside down, hold one horizontally<br />
left, hold one horizontally right, and hold one right side up.<br />
Questions:<br />
1. What was the difference in force factor during the JoJo Roll? Explain your reasoning.<br />
2. Compare the JoJo roll to other roller coasters that go upside down with regards to the<br />
weightless feeling and the force factor.<br />
3. Since you are going upside down, can you do something to the ride to create a weightless<br />
feeling on the JoJo roll? Why/Why not.<br />
4. The JoJo is considered a heartline roll. By watching the train pass through the roll, explain<br />
the meaning of heartline roll.<br />
Special thanks to Brent Ohl 94
Interpreting Graphs<br />
Part I: - Directions: Using Graph 1 and 2 below answer the questions found below the graphs.<br />
Graph 1: Dominator: Shot Downward<br />
Questions:<br />
1. A. If you and a friend were watching and waiting in line to ride the Dominator,<br />
at what point of the drop would you tell him/her on the ride that they will<br />
experience a feeling of weightlessness?<br />
B. At what time interval does this occur at according to the graph?<br />
____________________________________<br />
2. If zero altitude is your starting position on the Dominator, according to the<br />
graph how high does the Dominator climb before dropping you?<br />
__________________________________<br />
3. The same friend you advised in question #1 is afraid that the Dominator is<br />
going to drop straight to the ground. According to graph 1, how much distance<br />
is between the ground and the lowest point on the first drop?<br />
__________________________________<br />
95
Interpreting Graphs<br />
4. From the graph of The Dominator, notice that the ride lasts longer than 120<br />
seconds. From your interpretation of the first 120 seconds of the ride, and after<br />
looking at the ride in the park, draw what you think the altitude and the x-<br />
acceleration due to gravity would look like if the graph actually took into<br />
account the ENTIRE ride.<br />
Hint: Take a stop watch and see how much longer the ride actually goes and<br />
how many more up and down motions the ride will experience after the 120<br />
seconds represented on the graph.<br />
Graph 2: Revolution<br />
5. According to graph #2 (Revolution), how many revolutions actually occurred in<br />
the 120 seconds?<br />
______________________________________________<br />
6. What is the correlation between the altitude and the G forces acting on the x-<br />
axis according to the data obtained from Revolution?<br />
_______________________________________________<br />
7. If you think of Revolution as a pendulum, at what point would you experience<br />
the greatest G forces? The highest peak or at the lowest point in the ride?<br />
___________________________________<br />
96
Interpreting Graphs<br />
Explain how you determined this by using specific references to the graph.<br />
______________________________________________________________________________<br />
______________________________________________________________________________<br />
______________________________________________________________________________<br />
______________________________________________________________________________<br />
________________________________________________<br />
8. After viewing the ride “Revolution” compare the graph to the actions of the<br />
actual ride. Notice again that the entire ride is not present on the graph. If<br />
“Revolution” runs an identical path each time it operates, do you think the g-<br />
force shown on the graph has reached its highest peak? If not, how many more<br />
peaks would there be before it reaches its highest peak?<br />
______________________________________________________________________________<br />
______________________________________________________________________________<br />
____________________________________________________________<br />
Part II<br />
Directions: For the following Graphs A – J, match the graph with the ride in<br />
<strong>Dorney</strong> <strong>Park</strong>. Answer the questions after all the graphs.<br />
Graph A<br />
97
Interpreting Graphs<br />
Graph B<br />
Graph C<br />
98
Interpreting Graphs<br />
Graph D<br />
Graph E<br />
99
Interpreting Graphs<br />
Graph F<br />
Graph G<br />
100
Interpreting Graphs<br />
Graph H<br />
Graph I<br />
Graph J<br />
101
Interpreting Graphs<br />
<strong>Dorney</strong> <strong>Park</strong> Ride<br />
Apollo 2000<br />
Wave Swinger<br />
Thunderhawk<br />
Steel Force<br />
The Hydra: Revenge<br />
Talon<br />
Enterprise<br />
Music Express<br />
Dominator: Being Shot Up<br />
Sea Dragon<br />
Matching Graph Letter<br />
____________________________<br />
____________________________<br />
____________________________<br />
____________________________<br />
____________________________<br />
____________________________<br />
____________________________<br />
____________________________<br />
____________________________<br />
____________________________<br />
Analysis<br />
1. Write a brief statement that describes your reasoning for selecting the graph you<br />
did for Thunderhawk? Were there specific details on the graph that made you 100%<br />
sure that this graph was the graph for Thunderhawk?<br />
____________________________________________________________________________________<br />
____________________________________________________________________________________<br />
________________________________________________<br />
2. Which graphs to rides interpretations were the hardest to make? For what reasons<br />
were they the most difficult?<br />
____________________________________________________________________________________<br />
____________________________________________________________________________________<br />
________________________________________________<br />
3. Which rides had the most similar graphs? Why do you think they have similar<br />
graphs?<br />
____________________________________________________________________________________<br />
____________________________________________________________________________________<br />
____________________________________________________________________________________<br />
____________________________________<br />
4. On graph I, what trend do you notice about the G forces when the altitude is at its<br />
peak versus when the altitude has reached its low point?<br />
____________________________________________________________________________________<br />
____________________________________________________________________________________<br />
____________________________________________________________________________________<br />
_________________________________<br />
102
Possessed<br />
Preliminary Data:<br />
Your weight in pounds = ________________lb X 4.45 N/lb = ___________________N<br />
weight in Newtons<br />
Your mass, m in kilograms =<br />
___________________kg<br />
2<br />
9.8m<br />
sec<br />
Mass of loaded train = 13,065 kg<br />
Length of the train = 15.75 m<br />
Measure the time it takes for the train to do its first launch (L1) from rest. Suggestion: Use the center of<br />
the train as your reference point. This is the time it takes the train to be accelerated by the LIMs (linear<br />
induction motors). You may want to stand back from the ride to get a better overall view of the station to<br />
take your measurements.<br />
tL1 = ____________________sec<br />
Measure the time it takes for the train to pass through the second boost which is the same time it takes to<br />
pass through the station after the first launch.<br />
here (x = 60 m) here<br />
tL2 = ____________________sec<br />
103
Possessed<br />
Measure the time it takes for the train to pass through the first braking pass in the station.<br />
tB1 = ____________________sec<br />
Measure the time it takes for the train to pass through the second braking pass in the station.<br />
tB2 = ____________________sec<br />
Section 1: Linear Acceleration<br />
1. Since the distance that the train is traveling during its first launch is 48 m and the train starts from<br />
rest, use the linear equation given to calculate the average constant acceleration of the first launch.<br />
Remember that you measured the time.<br />
1 2<br />
x v<br />
i t at<br />
2<br />
Acceleration of the launch, a = ____________________m/sec 2 .<br />
2. Assuming no friction, calculate the average net force you experience.<br />
Favg = ma _______________________N<br />
3. Calculate the average amount of work the LIM’s do on you during the launch knowing the<br />
distance traveled during the launch given in #1.<br />
W = Fdcos______________________J<br />
4. Calculate your force factor you experience while launching.<br />
104
Possessed<br />
ff =<br />
F avg<br />
weight<br />
______________________<br />
5. Using a linear equation given, calculate the speed of the train upon reaching the vertical section<br />
of the track.<br />
2 2<br />
v v 2ax<br />
OR v v at<br />
f<br />
i<br />
f<br />
i<br />
vL1 = _________________________m/sec<br />
6. For the students with the CENCO lateral accelerometers, get in line and ride POSSESSED.<br />
While in line, secure and familiarize yourself with the lateral accelerometer. When on the ride,<br />
have your lateral (horizontal) accelerometer ready for launch. Position the accelerometer as<br />
instructed by your teacher. Measure the average lateral force factor of the first launch by<br />
recording the average location of the BB’s in the tube.<br />
ff = ____________________<br />
Alt. 6. For students with the PASCO or handmade lateral accelerometers, get in line and ride<br />
POSSESSED. While in line, secure and familiarize yourself with your version of the inclinometer (used<br />
as a lateral accelerometer). When on the ride, have your inclinometer ready for launch. Position the<br />
accelerometer as instructed by your teacher. Measure the average angle of the first launch.<br />
Calculate the accelerating force, FN on you by using the following:<br />
θ<br />
θ<br />
Fnety = may<br />
FN cosθ – w = may<br />
FN cosθ – w = 0<br />
FN cosθ = w<br />
w<br />
Calculate your force factor while launching.<br />
ff =<br />
F N<br />
weight<br />
_____________________<br />
Compare your results with that calculated in #4 elaborating on reasons for errors.<br />
105
Possessed<br />
Section 2: Work/Energy considerations for the Launch and Boost<br />
7. Using the conservation of energy and the speed of the train after the initial launch found in<br />
procedure 5, calculate the height of the train on the spiral section of the track.<br />
KEL1 = PEvert.<br />
1<br />
mv<br />
2<br />
<br />
2<br />
L1<br />
mgh vert<br />
h = _________________________m<br />
8. Using the work/energy theorem and the values found in #6, calculate the average amount of work<br />
the LIM’s do on you during the first launch using the<br />
W<br />
LIM<br />
WLIM = KE<br />
1 2 1<br />
mvL<br />
1<br />
mvi<br />
2 2<br />
2<br />
W = _______________________J<br />
9. Now calculate the average amount of work the LIM’s do on the train during the first launch.<br />
WLIM = KE<br />
1 2 1 2<br />
WLIM<br />
mvL<br />
1<br />
mvi<br />
2 2<br />
W = _______________________J<br />
106
Possessed<br />
10. Calculate the average power delivered by the LIMs to the train during the first launch.<br />
P =<br />
W<br />
t L1<br />
_______________________W<br />
OPTIONAL: 11. Calculate the average current supplied by the LIMs during the launch. The voltage<br />
provided to each LIM during launch is 240 V and assuming there are 4 LIMs operating at any given time.<br />
(NOTE: This is an over simplified version as to what actually is occurring electrically during the<br />
launch.)<br />
P = current x voltage<br />
Current = _______________________amperes<br />
12. Assuming no friction, the speed of the train at the end of the first launch must the same as the<br />
speed of the train at the beginning of the second boost because of the conservation of energy.<br />
Knowing the speed of the train at the end of the first launch given in procedure 5, the distance<br />
(xL2 = 60.0 m) of the train during the boost (see picture on page 1), and the time it takes for the<br />
second boost from the initial data, calculate the acceleration and speed of the train after the<br />
second boost using the given linear equation.<br />
1 2<br />
xL2<br />
vL<br />
1t<br />
at AND vL2<br />
vL<br />
1<br />
at<br />
2<br />
aL2 = _________________________m/sec 2 and vL2 = _____________________m/sec<br />
12. Using the work energy theorem, calculate the average amount of work on the train to accelerate it<br />
through the second boost.<br />
WLIM = KE<br />
1 2 1 2<br />
WLIM<br />
mvL2<br />
mvL<br />
1<br />
2 2<br />
W = _______________________J<br />
13. Calculate the average net force on the train for the second boost using the equation.<br />
107
Possessed<br />
F<br />
ma<br />
OR<br />
W F( 2)cos<br />
net<br />
x L<br />
F = _______________________N<br />
14. Compare the force of the second boost to that of the first launch. Are they same or different and<br />
why?<br />
15. Using the conservation of energy and the speed of the train after the second boost, calculate the<br />
height of the train on the straight vertical section of the track.<br />
KEL1 = PEvert.<br />
1<br />
mv<br />
2<br />
<br />
2<br />
L2<br />
mgh vert<br />
h = _________________________m<br />
108
Possessed<br />
Section 3: The Vertical Braking<br />
The train gets stopped for 1 second by standard mechanical clamp brakes when it reaches its highest<br />
point of approximately 37 m as measured from the center of the train on the straight vertical section of<br />
the track.<br />
16. How energy does the train have while held<br />
stationary by these brakes at this height?<br />
PE train<br />
mgh<br />
W = ________________________J<br />
17. How much power is delivered by the brakes at this<br />
point?<br />
PEtrain<br />
P <br />
t<br />
P = _________________________W<br />
18. How much force must the brakes be applying to the train to keep it held in this vertical position?<br />
Force = ________________________N<br />
Section 4: Stopping the train at the end of the ride<br />
19. Using the conservation of energy, calculate the speed of the train upon entering the station after<br />
the vertical brake.<br />
PE KE<br />
mgh<br />
vert.<br />
brake<br />
vert.<br />
brake<br />
<br />
1<br />
2<br />
station<br />
mv<br />
2<br />
station<br />
109
Possessed<br />
vstation = ___________________________m/sec<br />
20. You know the distance and the time, tB1, for the train to pass through the braking pass while<br />
passing through the station. You also know how fast the train is moving upon entering the station<br />
along with the initial speed upon entering the station from procedure 19. Calculate the<br />
acceleration and speed of the train at the end of the first braking pass through the station by using<br />
the equations.<br />
1 2<br />
xstation<br />
vstationt<br />
at AND vB<br />
1<br />
vstation<br />
at<br />
2<br />
aB1 = _____________________m/sec 2 and vB1 = _______________________m/sec<br />
21. Calculate the amount of work required to slow the train in the first braking pass.<br />
W<br />
LIM<br />
WLIM = KE<br />
1 2 1<br />
mvB<br />
1<br />
mv<br />
2 2<br />
2<br />
station<br />
WB1 = ________________________J<br />
22. Calculate the average force the LIMs apply to the train to slow it down during the first braking<br />
pass.<br />
ma OR W F( x)cos<br />
F net<br />
Favg = __________________________N<br />
110
Possessed<br />
23. Since the train stops during it second braking pass through the station, calculate the amount of<br />
work required to slow the train in the second braking pass.<br />
WLIM = KE<br />
1<br />
WLIM<br />
mv<br />
2<br />
2<br />
0<br />
B1<br />
WB2 = ________________________J<br />
24. Calculate the average force the LIMs apply to the train to slow it down during the second braking<br />
pass.<br />
W F x<br />
cos<br />
<br />
Favg = __________________________N<br />
25. Compare the work done or force applied by the LIMs to launch the train at the beginning of the<br />
ride to that in braking the train. Be sure to explain your reasoning.<br />
111
Possessed<br />
Section 4: Vertical Sections of the Ride<br />
. In this section of the lab, you will be looking at the vertical sections of the track to see if the spiral<br />
vertical section of the track affects freefall. Secure the vertical accelerometer as shown in the<br />
diagram below. This orientation is for when you are on the spiral vertical section of the track.<br />
Reverse the accelerometer for the straight vertical section of the track. You will need to orient the<br />
accelerometer so that the weight hangs suspended by the spring when the train is on these sections<br />
of the track.<br />
Spiral side<br />
straight side<br />
When the train is at the highest on these sections of the track, record the force factor. Be sure you<br />
are not recording the force factor while the train is being stopped on the straight vertical section of<br />
the track.<br />
If you do not have a vertical accelerometer, you can use a stopwatch to measure the time it takes<br />
for the train to freefall on these sections.<br />
Vertical Spiral section of track<br />
ffspiral or time = ________________<br />
Vertical straight section of track<br />
ffstraight or time =________________<br />
112
Possessed<br />
Explain any differences in the force factor on these two sections of track. Should there be a difference?<br />
Why or why not?<br />
Section 5: The Upward Curved Sections and Centripetal Force<br />
In this section of the lab you will calculate the radius of each vertical curve by using the force factors<br />
and speeds that you measure. This section can be done as a stand-alone activity or can utilize the<br />
data from the previous sections. You can use the speeds from the previous sections. It would be<br />
helpful if you have several students taking measurements at the same time.<br />
Measure the time the train takes to pass the lone vertical support post outside of the station on each side<br />
of the station shown in the picture. If time permits, measure the speed at these points for one,<br />
two, or three passes. The more data you have, the more accurate your calculations. Enter the data<br />
into the table below.<br />
By knowing the length of the train given in the preliminary data at the beginning of the lab, calculate the<br />
speed of the train just as it enters the vertical curves. Enter the data in the table below.<br />
Secure the vertical accelerometer and measure the force factor you experience while passing through the<br />
curves for each pass you predetermined. Be sure you are measuring the force factor that<br />
corresponds to the time you measured. Also, be sure that you are holding the vertical<br />
accelerometer parallel to your body as shown in the picture on the next page.<br />
113
Possessed<br />
Pass<br />
time<br />
(sec)<br />
Spiral side<br />
speed<br />
(m/sec)<br />
force<br />
factor<br />
radius<br />
(m)<br />
time<br />
(sec)<br />
Vertical Side<br />
speed<br />
(m/sec)<br />
force<br />
factor<br />
radius<br />
(m)<br />
1<br />
2<br />
3<br />
According to the free-body diagram and the two expressions given,<br />
Fseat<br />
ac<br />
F<br />
ff <br />
w<br />
F<br />
seat<br />
seat<br />
w <br />
mv<br />
r<br />
2<br />
w<br />
1. Derive an expression for calculating the radius of curvature of the track.<br />
2. Calculate the radius of curvature for each curve and enter the data into the table on the<br />
previous page.<br />
QUESTIONS:<br />
1. Compare the radius on the straight side and the spiral side of the ride.<br />
114
Possessed<br />
2. As the speed increased, explain what happened to the force factor.<br />
3. As the speed increased, explain what happened with the radius?<br />
4. If the radius was smaller, what would happen to the force factor? Speed? Support your answer.<br />
115
Coaster Quest<br />
Pennsylvania Standards in Science and Technology<br />
Unifying Themes<br />
Academic<br />
Standard<br />
Standard<br />
Category<br />
3.1.10 C<br />
Standard<br />
Statement<br />
C. Apply<br />
patterns as<br />
repeated<br />
processes or<br />
recurring<br />
elements in<br />
science and<br />
technology.<br />
Content<br />
Descriptors<br />
Examine and<br />
describe physical<br />
patterns in motion.<br />
Performance<br />
Tasks and<br />
Associated<br />
Learning<br />
Activities<br />
Antique Carrousel<br />
Apollo 2000<br />
Enterprise<br />
Ferris Wheel<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
White Water<br />
Landing<br />
Unifying<br />
Themes<br />
3.1.10 D<br />
3.1.12 C<br />
3.1.12 D<br />
D. Apply scale as a<br />
way of relating<br />
concepts and<br />
ideas to one<br />
another by<br />
some measure.<br />
C. Assess and<br />
apply patterns in<br />
science and<br />
technology.<br />
D. Analyze scale as<br />
a way of relating<br />
concepts and<br />
ideas to one<br />
another by<br />
some measure.<br />
Apply dimensional<br />
analysis and scale as a<br />
ratio.<br />
Assess and apply<br />
recurring patterns<br />
in natural and<br />
technological<br />
systems.<br />
Compare and<br />
contrast structure and<br />
function relationships<br />
as they relate to<br />
patterns.<br />
Assess patterns in<br />
nature using<br />
mathematical<br />
formulas.<br />
Assess the use of<br />
several units of<br />
measurement to the<br />
same problem.<br />
Analyze and apply<br />
appropriate<br />
measurement scales<br />
when collecting data.<br />
Antique Carrousel<br />
Dominator<br />
Enterprise<br />
Sea Dragon<br />
Steel Force<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Ferris Wheel<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
White Water Landing<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Ferris Wheel<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
White Water Landing<br />
116
Coaster Quest<br />
Pennsylvania Standards in Science and Technology<br />
Inquiry and Design<br />
Academic<br />
Standard<br />
Standard<br />
Category<br />
3.2.7 A<br />
3.2.4 B<br />
Standard<br />
Statement<br />
A. Explain and apply<br />
scientific and technological<br />
knowledge.<br />
B. Describe objects in the<br />
world using the<br />
five senses.<br />
Content<br />
Descriptors<br />
Answer “What if” questions based<br />
on observation, inference or prior<br />
knowledge or experience.<br />
Recognize observational<br />
descriptors from each of the five<br />
senses (e.g., see-blue, feel-rough).<br />
Use observations to develop a<br />
descriptive vocabulary.<br />
Performance<br />
Tasks and<br />
Associated<br />
Learning<br />
Activities<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
Inquiry and<br />
Design<br />
3.2.7 B<br />
3.2.10 B<br />
B. Apply process<br />
knowledge to make and<br />
interpret observations.<br />
B. Apply process<br />
knowledge and organize<br />
scientific and<br />
technological phenomena<br />
in varied ways.<br />
Measure materials using a variety<br />
of scales.<br />
Describe relationships by making<br />
inferences and predictions.<br />
Communicate, use space / time<br />
relationships, define operationally,<br />
raise questions, formulate<br />
hypotheses, test and experiment,<br />
Design controlled experiments,<br />
recognize variables, manipulate<br />
variables.<br />
Interpret data, formulate models,<br />
design models, and produce<br />
solutions.<br />
Develop appropriate scientific<br />
experiments: raising questions,<br />
formulating hypotheses, testing,<br />
controlled experiments, recognizing<br />
variables, manipulating variables,<br />
interpreting data, and producing<br />
solutions.<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Ferris Wheel<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
White Water Landing<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Ferris Wheel<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
White Water Landing<br />
117
Coaster Quest<br />
Pennsylvania Standards in Science and Technology<br />
Inquiry and Design<br />
Academic<br />
Standard<br />
Inquiry and<br />
Design<br />
Standard<br />
Category<br />
3.2.12 B<br />
3.2.10 C<br />
3.2.12 C<br />
Standard<br />
Statement<br />
B. Evaluate experimental<br />
information for<br />
appropriateness and<br />
adherence to<br />
relevant science<br />
processes.<br />
C. Apply the elements of<br />
scientific inquiry to solve<br />
problems.<br />
C. Apply the elements of<br />
scientific inquiry to solve<br />
multi-step problems.<br />
Content<br />
Descriptors<br />
Evaluate experimental data<br />
correctly within experimental<br />
limits.<br />
Judge that conclusions are<br />
consistent and logical with<br />
experimental conditions.<br />
Interpret results of experimental<br />
research to predict new information<br />
or improve a solution.<br />
Generate questions about objects,<br />
organisms and/or events that can be<br />
answered through scientific<br />
investigations.<br />
Evaluate the appropriateness of<br />
questions.<br />
Conduct a multiple step<br />
experiment.<br />
Organize experimental information<br />
using a variety of analytic methods.<br />
Judge the significance of<br />
experimental information in<br />
answering the question.<br />
Suggest additional steps that might<br />
be done experimentally.<br />
Generate questions about objects,<br />
organisms and/or events that can be<br />
answered through scientific<br />
investigations.<br />
Evaluate the appropriateness of<br />
questions.<br />
Organize experimental information<br />
using analytic and descriptive<br />
techniques.<br />
Evaluate the significance of<br />
experimental information in<br />
answering the question.<br />
Project additional questions from a<br />
research study that could be studied.<br />
Performance<br />
Tasks and<br />
Associated<br />
Learning<br />
Activities<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Ferris Wheel<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
White Water Landing<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Ferris Wheel<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
White Water Landing<br />
118
Coaster Quest<br />
Pennsylvania Standards in Science and Technology<br />
Inquiry and Design<br />
Academic<br />
Standard<br />
Standard<br />
Category<br />
Standard<br />
Statement<br />
Content<br />
Descriptors<br />
Performance<br />
Tasks and<br />
Associated<br />
Learning<br />
Activities<br />
Inquiry and<br />
Design<br />
3.2.10 D<br />
3.2.12 D<br />
D. Identify and apply the<br />
technological design<br />
process to solve<br />
problems.<br />
D. Analyze and use the<br />
technological design<br />
process to solve<br />
problems.<br />
Examine the problem, rank all<br />
necessary information and all<br />
questions that must be answered.<br />
Assess all aspects of the problem,<br />
prioritize the necessary information<br />
and formulate questions that must<br />
be answered.<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
119
Coaster Quest<br />
Pennsylvania Standards in Science and Technology<br />
Physical Science<br />
Academic<br />
Standard<br />
Standard<br />
Category<br />
Standard<br />
Statement<br />
Content<br />
Descriptors<br />
Performance<br />
Tasks and<br />
Associated<br />
Learning<br />
Activities<br />
Physical<br />
Science<br />
3.4.4 C<br />
C. Observe and<br />
describe different<br />
types of force and<br />
motion.<br />
Describe various<br />
types of motions.<br />
Compare the relative<br />
movement of<br />
objects and describe<br />
types of motion<br />
that are evident.<br />
Describe the<br />
position of an object<br />
by locating it relative<br />
to another object or<br />
the background (e.g.,<br />
geographic direction,<br />
left, up).<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Ferris Wheel<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
White Water Landing<br />
3.4.7 C<br />
C. Identify and<br />
explain the<br />
principles of force<br />
and motion.<br />
Explain various<br />
motions using models.<br />
<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Ferris Wheel<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
White Water Landing<br />
120
Coaster Quest<br />
Pennsylvania Standards in Science and Technology<br />
Physical Science<br />
Academic<br />
Standard<br />
Physical<br />
Science<br />
Standard<br />
Category<br />
3.4.10 C<br />
3.4.12 C<br />
Standard<br />
Statement<br />
C. Distinguish<br />
among the<br />
principles of force<br />
and motion.<br />
C. Apply the<br />
principles of motion<br />
and force.<br />
Content<br />
Descriptors<br />
Know Newton’s laws<br />
of motion<br />
(including inertia,<br />
action and<br />
reaction) and gravity<br />
and apply them to<br />
solve problems<br />
related to forces and<br />
mass.<br />
Determine the<br />
efficiency of<br />
mechanical systems<br />
by applying<br />
mathematical<br />
formulas, concepts<br />
through words,<br />
models and<br />
mathematical<br />
symbols.<br />
Analyze the<br />
principles of<br />
translational motion,<br />
velocity and<br />
acceleration as they<br />
relate to free fall and<br />
projectile motion.<br />
Analyze the<br />
principles of<br />
rotational motion to<br />
solve problems<br />
relating to angular<br />
momentum, and<br />
torque.<br />
Interpret a model<br />
that illustrates<br />
circular motion and<br />
acceleration.<br />
Describe inertia,<br />
motion, equilibrium,<br />
and action/reaction<br />
concepts through<br />
words, models and<br />
mathematical<br />
symbols.<br />
Performance<br />
Tasks and<br />
Associated<br />
Learning<br />
Activities<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Ferris Wheel<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
White Water Landing<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Ferris Wheel<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
White Water Landing<br />
121
Coaster Quest<br />
Pennsylvania Standards in Science and Technology<br />
Technological Devises<br />
Academic<br />
Standard<br />
Technological<br />
Devises<br />
Standard<br />
Category<br />
3.7.7 A<br />
3.7.7 B<br />
3.7.10 A<br />
Standard<br />
Statement<br />
A. Describe the<br />
safe and<br />
appropriate use of<br />
tools, materials<br />
and techniques to<br />
answer questions<br />
and solve<br />
problems.<br />
B. Use appropriate<br />
instruments and<br />
apparatus to study<br />
materials.<br />
A. Identify and<br />
safely use a variety<br />
of tools, basic<br />
machines, materials<br />
and techniques to<br />
solve problems and<br />
answer questions.<br />
Content<br />
Descriptors<br />
Identify uses of<br />
tools, machines,<br />
materials,<br />
information, people,<br />
money, energy and<br />
time that meet specific<br />
design criteria.<br />
Describe safe<br />
procedures for using<br />
tools and materials.<br />
Assess materials for<br />
appropriateness of<br />
use.<br />
Select appropriate<br />
instruments to<br />
measure the size,<br />
weight, shape and<br />
temperature of living<br />
and non-living<br />
objects.<br />
Apply knowledge of<br />
different<br />
measurement systems<br />
to measure<br />
and record objects’<br />
properties.<br />
Select and safely<br />
apply appropriate<br />
tools, materials and<br />
processes necessary<br />
to solve complex<br />
problems.<br />
Apply advanced tool<br />
and equipment<br />
manipulation<br />
techniques to solve<br />
problems.<br />
Performance<br />
Tasks and<br />
Associated<br />
Learning<br />
Activities<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
122
Coaster Quest<br />
Pennsylvania Standards in Science and Technology<br />
Technological Devises<br />
Academic<br />
Standard<br />
Technological<br />
Devises<br />
Standard<br />
Category<br />
3.7.10 B<br />
3.7.12 A<br />
Standard<br />
Statement<br />
B. Apply<br />
appropriate<br />
instruments and<br />
apparatus to<br />
examine a variety<br />
of objects and<br />
processes.<br />
A. Apply advanced<br />
tools, materials<br />
and<br />
techniques to<br />
answer complex<br />
questions.<br />
Content<br />
Descriptors<br />
Describe and use<br />
appropriate<br />
instruments to gather<br />
and analyze data.<br />
Compare and<br />
contrast different<br />
scientific<br />
measurement<br />
systems; select the<br />
best measurement<br />
system for a specific<br />
situation.<br />
Explain the need to<br />
estimate<br />
measurements within<br />
error of various<br />
instruments.<br />
Apply accurate<br />
measurement<br />
knowledge to solve<br />
everyday problems.<br />
Select and safely<br />
apply appropriate<br />
tools, materials and<br />
processes necessary<br />
to solve complex<br />
problems that could<br />
result in more than<br />
one solution.<br />
Evaluate and use<br />
technological<br />
resources to solve<br />
complex multi-step<br />
problems.<br />
Performance<br />
Tasks and<br />
Associated<br />
Learning<br />
Activities<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Ferris Wheel<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
White Water Landing<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
123
Coaster Quest<br />
Pennsylvania Standards in Science and Technology<br />
Technological Devises<br />
Academic<br />
Standard<br />
Technological<br />
Devises<br />
Standard<br />
Category<br />
3.7.12 B<br />
Standard<br />
Statement<br />
B. Evaluate<br />
appropriate<br />
instruments and<br />
apparatus to<br />
accurately<br />
measure<br />
materials and<br />
processes.<br />
Content<br />
Descriptors<br />
Apply and evaluate<br />
the use of<br />
appropriate<br />
instruments to<br />
accurately measure<br />
scientific and<br />
technologic<br />
phenomena within the<br />
error limits of the<br />
equipment.<br />
Evaluate the<br />
appropriate use of<br />
different<br />
measurement scales<br />
(macro and micro).<br />
Evaluate the utility<br />
and advantages<br />
of a variety of absolute<br />
and relative<br />
measurement scales<br />
for their appropriate<br />
application.<br />
Performance<br />
Tasks and<br />
Associated<br />
Learning<br />
Activities<br />
Antique Carrousel<br />
Apollo 2000<br />
Dominator<br />
Enterprise<br />
Ferris Wheel<br />
Revolution<br />
Sea Dragon<br />
Steel Force<br />
Wave Swinger<br />
White Water Landing<br />
124