Download - Dorney Park

Coaster Quest 

THE PHYSICS AND MATHEMATICS OF AMUSEMENT PARK RIDES 

Physics 

© Copyrighted by The Center for Mathematics, Science, 

and Technology Education, Kutztown University of 

Pennsylvania. This material is based upon work supported 

by the National Science Foundation under Grant 

No. 9986753. 

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.

Dorney Park/Kutztown University 

Coaster Quest 

Introduction 

The Lehigh Valley is rich in tradition, culture and beauty. We are most 

fortunate to have a community of fine people who are dedicated to the enhancement of 

our quality of life. To these ends, Dorney Park and Kutztown University have 

collaborated in the development of an educational experience that will benefit the 

children of the Lehigh Valley and beyond. 

We call it Coaster Quest. Our goal is to provide a stimulating and challenging 

exploratory experience for high school students. We utilize some of Dorney Park’s best 

attractions in ways that promote a deeper and more profound understanding of select 

scientific and mathematical principles. Students are given the opportunity to examine 

and study relationships between the dynamics of the mechanical universe and the 

unique, structural features of the rides. 

Kutztown University of Pennsylvania is pleased once again to participate in a 

collaborative project that engages future teachers in serious work with leading 

educators and the community. For science and mathematics teachers, this represents the 

best of two worlds, a living classroom replete with experiential activities and a forum 

for examining the connections between theory and practice. For Dorney Park, this is yet 

another opportunity to showcase their outstanding amusement park. All who 

participate will examine the extraordinary structural design process that went into the 

construction of these fabulous rides. 

We extend to you the opportunity to examine our laboratory manual, review 

procedural aspects, and participate in our tenth annual Coaster Quest day that will be 

held on May 6, 2011. Well over 45,000 students from regional schools have participated 

in our annual Coaster Quest. With the addition of new and exciting activities, we 

believe that you and your students will find the day both thrilling and enlightening. 

Dr. Joseph S. Elias 

Professor of Science Education 

College of Education 

Kutztown University of Pennsylvania

Coaster Quest 

Table of Contents 

Planning Team Page i 

Tips for Teachers Page ii 

Things to Bring Page iii 

The Rides Page 1 

Apollo 2000 Page 1 

The Antique Carrousel Page 8 

The Ferris Wheel Page 13 

The Enterprise Page 19 

Revolution Page 23 

The Dominator Page 27 

The Sea Dragon Page 32 

White Water Landing Page 37 

The Scrambler Page 42 

The Wave Swinger Page 47 

Steel Force Page 52 

Energy Curves for Steel 

Force 

Page 61 

Centripetal Force and Steel 

Force 

Page 65 

The Talon Page 67 

Thunderhawk Page 75 

The Hydra Page 79 

Interpreting Graphs Page 94 

Possessed Page 101 

PA State Science and Technology 

Standards 

Page 113

Coaster Quest

Coaster Quest 

Dorney Park/Kutztown University 

Planning Team 

The making of an event of such monumental scope can only be 

accomplished when the “players” are truly dedicated to its goals. Such is the 

nature of our planning team. The planning process began in August of 1997. Since 

then, a core of science and mathematics teachers has enthusiastically participated 

in all phases of development. The professional staff of Dorney Park has graciously 

opened their doors, extending their guidance and technical support to those who 

developed the laboratories. One park professional likened it to a magician 

“revealing” well-kept secrets. The faculty, students, and administrators of 

Kutztown University have made the commitment of their time, energy and 

enthusiasm. Our goal has been and always will be academic excellence. We 

recognize the value of Coaster Quest as an instrument befitting this goal. The 

combined efforts of all represent the true spirit of education and service. 

Acknowledgment 

Mr. Richard Button 

Mr. Patrick Callahan 

Dr. Kathleen Dolgos 

Dr. David Drummer 

Dr. Joseph Elias 

Dr. Deborah Frantz 

Mr. Glenn Frey 

Mr. Joseph Greene 

Mr. Robert Guigley 

Mr. Keith Koepke 

Mr. William Landis 

Dr. Neal Shea 

Mrs. Brenda Snyder 

Mr. Jeffrey Wetherhold 

Mr. Brent Ohl 

Ms. Maggie Woodward 

Mr. Gerry Farnsworth 

Kutztown University of Pennsylvania 

Delaware Regional School District 


Kutztown Area School District 



Northwestern Lehigh School District 

Dorney Park of Allentown 

Reading Area School District 

Dorney Park of Allentown 

Allentown School District 



Parkland School District 

East Penn School District 

Upper Perkiomen School District 

Parkland School District 

And 

To the many graduate students of the Kutztown University of Pennsylvania who 

contributed to the development of this manual. 

i

Coaster Quest 

Tips for Teachers 

To help make your day at the park more enjoyable, we have created a list of 

“tips for teachers.” Hopefully, this list will guide you through the pre-visit 

planning stage and answer some of your questions. 

 

 

 

 

 

 

Please don't forget your equipment, supplies and laboratory manuals. You may find 

that a camcorder might be functional in a variety of ways. Perhaps you wish to discuss 

the dynamics of the rides as a review, incorporate them within a laboratory practical, 

use as introductory preparation for next year’s trip to the park. 

You and your students should decide on which of the many rides you want to explore. 

Carefully peruse the complete list of activities and find those rides that will best benefit 

your students. 

Some rides may take more time than others to complete. You may find it necessary to 

ride several times on some of the rides in order to collect good data. 

As much as is feasible, introduce to the students the concepts to be studied and rides 

that you have chosen during the weeks leading up to the event. Plan time in class for 

calculations and analysis during the days following the experience. 

Each teacher needs to decide how the students from his/her school will complete the 

data collection sheets, and any other information, that her/ his students may need. We 

recommend that teachers in charge advise students who may be fearful of some rides, 

that riding is optional and not mandatory. 

Kutztown University students will serve as general assistants to the teachers. They will 

be stationed at each listed ride and the reserved pavilion from 10:00 AM until 3:00 

PM. Follow the park map to the pavilion site and look for the Coaster Quest banner. 

Inform your students that they may ask the university students any questions related to 

the event with the exception of specific questions that may be contrary to your 

objectives. 

Further information may be obtained by contacting: 

Mr. Bernie Bonuccelli Dorney Park (610)395-3724 

bbonuccelli@dorneypark.com 

Dr. Joseph Elias Kutztown University (610) 683-4762 

of Pennsylvania 

elias@kutztown.edu 

ii

Coaster Quest 

Things to Bring 

To make your day at the park as functional and enjoyable as possible we 

suggest that you arrange to bring some or all of the items listed below: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tickets for you, your students and your chaperones 

copies of the activities that you and your students plan on doing 

stopwatches 

calculators 

clipboards 

paper and pencils 

masking tape 

protractors 

accelerometers 

inclinometers 

CBL (calculator based laboratory) if you have them and low range sensors for 

acceleration 

appropriate clothing with a change of clothing 

sunscreen, hats, raincoats 

money for food, drinks or phone 

measuring tape or string 

backpacks or plastic bags to keep laboratory manuals and equipment dry and 

together 

a good reserve of energy and enthusiasm for exploration 

Dorney Park Information 

For general information call (800) 551-5656 

(610) 395-3724 

Group Sales Information (610) 395-2000 

or 

Bernie Bonuccelli at 1(800) 551-5656 with any specific questions 

about ticket sales for Coaster Quest. 

or 

visit our website: www.dorneypark.com 

Thank you. 

iii

Apollo 2000 

Introduction: 

Rotational motion is a topic in physics that looks at 

objects that rotate or revolve around a point. This point is 

called the point of rotation. These objects have many 

properties associated with them. Two of these properties are angular velocity and 

centripetal acceleration. You will be using two different techniques to calculate 

centripetal acceleration. You will then be asked to compare the two methods. You will 

also graph the relationship between linear velocity, centripetal acceleration and the 

radius. Conceptual questions pertaining to your perceptions of speed and acceleration as 

you are riding the Apollo 2000 are at the end of the laboratory. 

Apparatus: 

stopwatch, calculator, inclinometer 

Procedure: 

Look for the Coaster Quest sign or any position to the right of the entry area of the 

ride for a good place to stand when taking the following measurements. This will 

provide a clear point of observation when doing the off ride data taking. 

1. Use a stopwatch to measure the time that it takes for the ride to rotate five (5) times 

when at full speed. 

t = ____________________ sec 

2. Calculate the time that it takes for one rotation. 

T = 

t 

5 

_________________sec 

3. The angular velocity, , is the angle that is swept out over a period of time of a 

rotating object. Calculate the angular velocity. Remember one rotation is 2 

radians angular distance. 

= __________________ rad/sec 

1

Apollo 2000 

4. When the ride is in full operation, the arms are oscillating inward and outward. Use 

the inclinometer to find the minimum angle and maximum angle of the arms with 

respect to the vertical (dashed line) as shown below. Hold the inclinometer as 

shown. 

max 

min 

4.73 meters 

8.4 meters 

across center 

Inclinometer 

Inclinometer 

min = ___________________degrees 

max = ___________________degrees 

NOTE: If you are using a PASCO or CENCO inclinometer, then you need to subtract 

from 90 to get the desired angle because they are designed to take angle measurements 

with respect to the horizontal. 

5. Examine the diagram above. On it or the rear of this sheet, sketch and apply your 

trigonometric rules to calculate the radius of motion of the car when it is at its 

maximum and minimum positions. You will be using your trigonometric skills to 

do this. Treat the 4.73 meters as the hypotenuse and add the opposite side of the 

triangle to the radius of the ride center. 

radius at minimum angle = rmin = ___________________ meters 

radius at maximum angle = rmax = __________________ meters 

6. By finding the radius of curvature at these two locations we can find the linear 

speed that you are traveling by using the appropriate equation. Calculate the linear 

velocity at the minimum position and maximum position. This can be found by 

actual distance (circumference) calculations but you may find your linear/rotational 

conversion easier by using V= r. 

linear velocity at minimum radius = vmin = _________________ m/sec 

linear velocity at maximum radius = vmax = _______________ m/sec 

2

Apollo 2000 

7. Whenever an object is moving in a curved path, there is acceleration applied to that 

object toward the center of the curve. That acceleration, which causes an object to 

follow that curved path, is called centripetal acceleration. You are going to find the 

centripetal acceleration of yourself caused by the rotational motion of the ride. 

Calculate the centripetal acceleration using the values of velocity that you just 

calculated. 

centripetal acceleration at vmin = ac(min) = __________________ m/sec 2 

centripetal acceleration at vmax = ac(max) = _________________ m/sec 2 

8. Complete the table by using the same equations and methods that you used in sections 

5 – 7. By completing the table, you will be graphing the relation of velocity to the 

radius and the centripetal acceleration to the radius. 

Complete the table: 

ANGLE 

(degrees) 

RADIUS 

(meters) 

VELOCITY 

(m/sec) 

CENTRIPETAL 

ACCELERATION 

(m/sec 2 ) 

min 

1 

2 

max 

3 

4 

max 

max 

3

Apollo 2000 

9. Make a graph of centripetal acceleration ac, versus radius, r, by using the coordinate 

axis below. You will have to scale the axis yourself, so do so appropriately. 

centripetal 

acceleration 

(m/sec 2 ) 

Graph of ac versus r. 

radius (meters) 

10. Make a graph of linear velocity, v, versus radius, r by using the coordinate axis 

below. You will have to scale the axis yourself, so do so appropriately 

velocity 

(m/sec) 

Graph of v versus r 

radius (meters) 

4

Apollo 2000 

Do the graphs in questions 9 and 10 represent a linear, quadratic, or inverse 

relationship? 

 

How can you be sure it is linear? Include any equations that created the data 

you graphed. 

Finding maximum and minimum centripetal acceleration 

by using force vectors 

11. Another method of finding centripetal accelerations is by using vectors. Vectors 

are the arrows shown below which show size and direction of particular values. 

Calculate the maximum and minimum centripetal accelerations using the 

following diagram and the values you found for the maximum and minimum 

angle. As before, the dashed line is vertical! 

 

FN 

 

Fc 

FW = mg 

Equation to use 

F 

F 

N 

N 

cos 

mg 

mg 

FN 

, and 

cos 

sin 

ma 

mgsin 

ma 

cos 

g tan 

a 

c 

c 

c 

centripetal acceleration at min = ac(min) = ___________________ m/sec 2 

centripetal acceleration at max = ac(max) = ___________________ m/sec 2 

5

Apollo 2000 

12. Collect data from three other lab groups and put the values into the table provided 

for you. When working on real world data, it is always best to get multiple values 

for each measurement. This helps find and eliminate random error in lab work. 

Comparison table: 

Answers from Procedure #5-7 Answers from Procedure #11 

GROUPS 

CENTRIPETAL 

ACCELERATION 

CENTRIPETAL 

ACCELERATION 

CENTRIPETAL 

ACCELERATION 

CENTRIPETAL 

ACCELERATION 

a c(min) 

(m/sec 2 ) 

a c(max) 

(m/sec 2 ) 

a c(min) 

(m/sec 2 ) 

a c(max) 

(m/sec 2 ) 

YOUR 

GROUP 

1 

2 

3 

Analyze the accuracy and precision of the data of the four laboratory groups by 

comparing the groups' data in the column to each other. 

Next, analyze the accuracy and precision of the data by comparing the four sets of 

answers collectively in problem #12. 

6

Apollo 2000 

Concept Questions 

1. How do you perceive the speed of the ride when you are swinging outward? 

2. How do you perceive the speed of the ride when you are swinging inward? 

3. When the car is at its maximum angle, why don't you feel as if you are going to 

fall out? 

4. Does the change in radius have anything to do with the angular velocity? Linear 

velocity? Centripetal acceleration? 

7

The Antique Carrousel 

The Physics of Just Going in Circles 

Introduction: 

Sometime between 1918 and 1925 W. H. Dentzel built 

a classic carrousel that Dorney Park obtained in 1995. While 

simple, the carrousel can demonstrate many basic and advanced 

concepts of circular motion. 

In this lab, you will progress from simple to more 

advanced computations on curvilinear measurement. 

 

 

 

Part One will address basic tangential speed measurements. 

Part Two will take you through a series of centripetal accelerations and lastly 

Part Three will have you analyze the system through angular measurements. 

Apparatus: 

Stopwatch, calculator, inclinometer 

Data Table and Measurements: 

In order to do all parts of this lab, several measurements will be needed. In the 

blanks below, measure and record the values indicated: 

1. Time for one revolution: ____________________ 

(Pick a point on the carrousel and time 3 complete revolutions. Divide this by 3 

for a more accurate single revolution time.) 

2. Angle reading for the inclinometer. 

(Be careful of the zero degree point. Hold your inclinometer vertically against 

the upright bar on the horse and read values before and after rotation starts. The 

angle is the change in these values from the rest angle to the angle it reaches 

when in motion. You must do this as the bar on the horse is not vertical!) 

Angle 1 change (inner row)________ 

Angle 3 change (third row)________ 

Angle 2 change (second row)_________ 

Angle 4 change (outer row) _________ 

8


Part One 

Basic Rotational Motion 

The analysis of rotational motion in the basic sense uses the general equation: 

V=D/T where D is the distance covered by the horse and T is the time to complete one 

revolution (a period). D is the circumference of the ring where the horse is located and is 

found by 2 R, where R is the radius of the horse’s ring (row). Find the velocities of the 

horses from the inner to outer rows: 

1. V1= 2* meters / T=_______________________ 

(5.8 meters is the radius of the inner row of horses) 

2. V2= 2*meters / T=_______________________ 

(this row radius is 6.6 meters) 

3. V3= 2* meters / T=_______________________ 

4. V4= 2* meters / T=_______________________ 

5. As you observe the motion of the horses, which appear to be going the fastest? 

6. How does this compare to the calculated values above? 

7. As you ride the horses, what factors make you feel like you are moving? 

8. Compare these factors with the speeds you found above. 

9


Part Two 

Accelerations 

As you ride the carrousel, you may notice a different “feel” between the inner and 

outer horse row. This is due to the different speeds and accelerations you experience. 

The human body is a good accelerometer. 

 

In which direction do you feel you are accelerating and on which horses is this the 

most noticeable? 

______________________ 

The general equation for centripetal acceleration is a=V 2 /R. (Note that V and R vary 

as we go from the inner to outer ring of horses. Find the values for the four horse rows 

below: 

a1=_______________ 

a2=___________________ 

a2=_______________ 

a4=___________________ 

 

Do these values match what you felt on the ride? 

_______________________ 

We can double-check these values by using the inclinometer data. Since the 

inclinometer you used shows the net angle between the gravitational and centripetal 

acceleration components, we can show ac =g * tan In the space below, compute the 

values for the accelerations of the 4 rows of horses using the angles you measured and 

tangent equation. 

a1=_______________ 

a3=_______________ 

a2=___________________ 

a4=___________________ 

On the axes below, graph the values for your accelerations (found above) verses the 

radius. What relationship is this? Start your graph with zero and scale (R) and (a) 

carefully. 

a 

R 

10


Part 3 

Angular computations 

Many people have trouble understanding the rotational components of motion. They 

are actually simple to do. Consider the following: 

 

Which row of horses takes the longest to go around one revolution? 

OK, a simple question, they all take the same time. While the velocities differ (as seen 

in Part One), the time and angle they cover are all the same. We call this measure the 

angular velocity. If we have the period T from the data we took in the beginning: 

radians)/T (seconds). 

 

What is the angular velocity for the carrousel? 

 

 

This value is the same for all horses, but the tangential velocity differs with radius, 

R. In general, the rotational measure times radius gives the tangential component. We 

find V=*R. 

For example V1=5.8 meters. 

 

How does the angular acceleration compare to angular velocity? 

If we start with ac=V 2 /R, and substitute V=R, we prove ac = *R. 

11


As you see, there is a linear relationship between acceleration, a, and radius, R. 

Graph this relationship below using the value for you found on the previous page. 

a 

0 2 4 6 8 meters 

 

How does this graph compare with the data you found in Part Two? 

 

Are angular methods easier for some calculations than others? 

12

The Ferris Wheel 

Observations: 

The Ferris Wheel is a wonderful experience of vertical circular motion. 

1. Describe the feelings you would experience as you move around in 

the circle. Compare what you feel at the top and bottom of the ride; 

also compare your feelings on the way up and on the way down. 

Activity 1 

Calculating the magnitude of the linear velocity and centripetal acceleration 

Part (a) 

Observe the ride and measure the time for a gondola to repeat one full trip around the 

wheel. The time for one complete rotation is called the Period and indicated by the letter T. 

Make sure that the ride is in the midst of a full rotation (i.e. it is loaded and will not stop to pick 

up or discharge passengers), gather data for at least 3 different trials and find the average period. 

The distance traveled in one rotation is the circumference of the circle (2R). Using the radius 

indicated, calculate the velocity from: 

v = 2 R/t 

Data Chart for Calculating Magnitude of Velocity and Centripetal Acceleration Radius 

of Wheel = 12.3 m (40 ft) 

One Rotation Trial 1 Period(s) Trial 2 Period(s) Trial 3 Period(s ) Average Period(s) 

Velocity (m/s) 

Acceleration (m/s/s) 

Circular motion results from an acceleration directed towards the center of the circle (centripetal 

acceleration). Find the acceleration using: 

Centripetal acceleration = velocity squared divided by radius 

or 

aC = v 2 /r 

See Data Chart for Activity 1 

13


Activity 2 

Determining the forces acting on a rider at key points 

To find the force required to keep you moving in this circle, according to Newton’s Second Law 

of Motion, you need to multiply your mass by this acceleration. 

Centripetal Force = mass times centripetal acceleration 

or 

FC = m aC 

If mass is in kg and acceleration is in m/s/s, then the unit for force is a Newton (symbol N) 

Data Chart for Finding Centripetal Force 

Your mass (kg) = _______ 

Your Weight (N) = m * 9.8 m/s/s = _______ 

Hint: 

To find your mass in kg, you may find it useful to know that the weight of a 1 kg mass on earth is 

approximately 2.2 pounds. 

velocity (m/s) 

Radius of Wheel 

(m) 

12.3 

Acceleration 

(m/s/s) 

Centripetal 

Force (N) 

14


Part (b) 

The centripetal force will be the same value throughout the ride. However, the forces 

that combine to create the centripetal force change as the position on the circle changes. At all 

positions on the ride the forces add to give a total force towards the center of the wheel. 

Seat Force 

Fs 

A 

Weight Fg 

Seat 

Force Fs 

SeatBack 

Force FB 

Seat Back 

Force FB 

Seat Force Fs 

Weight 

Fg 

D 

B 

Weight 

Seat 

Force Fs 

Fg 

C 

Weight 

Fg 

Position A - The seat force and the weight are in opposite directions. The weight must be larger 

than the seat force to give a total downward force. 

FS = FW - FC 

Position B - The vertical seat force and the weight are in opposite directions and are of the same 

magnitude since the total must add to a force in the direction toward the center of the circle. This 

force acts on the rider through friction with the seat or through the back of the seat. 

FS = FW 

15


Position C - The seat force and weight are in opposite directions. The seat force must be larger 

than the weight to give a total force that is upward. 

FS = FW + FC 

Position D - The vertical seat force and the weight are in opposite directions and are of the same 

magnitude since the total must add to a force in the direction toward the center of the circle. This 

force acts on the rider through friction with the seat or through the back of the seat. 

FS = FW 

Using the data calculated in previous activities, find the magnitude of the vertical seat force at 

each of the 4 locations. 

If mass is in kg and acceleration is in m/s/s, then the unit for force is a Newton (symbol N). 

Data Chart for Finding Seat Force 

Position 

A 

C 

Fw (N) 

Your Weight 

Vertical F C (N) 

From Activity 2a 

Fs (N) 

Seat Force 

Position 

Fw (N) 

Your Weight 

Vertical F C (N) 

B 0 

D 0 

Fs (N) 

Seat Force 

Part (c) 

Force factors give an indication of what the rider experiences on the ride. In a vertical circle, the 

force factor (FF) is defined as the ratio of the forces you feel to the force of your weight: 

Force Factor = Seat Force/Weight 

or 

FF = Fs/Fw 

The resulting number is often referred to as a “g” force, indicating how the force you feel 

compares to your weight. One “g” means that the forces you feel match your weight. This is 

what you normally experience. Two g’s mean that the force you feel is twice your weight and 

many people would indicate that they feel “heavier.” 

Use the data from Activity 2b and predict the “g” forces acting on you through the four 

curves: 

16


Activity 2c 

Data Chart for Predicting Force Factors 

Location 

A 

B 

C 

D 

Fs (N) 

Seat Force from 2b 

Fw (N) 

Your Weight 

Force Factor 

Activity 3 

Measuring “g’s” 

Someone in your group needs to ride the Ferris Wheel. Using your vertical 

accelerometer (long tube), measure the g's at the four locations being studied. If possible, take 

three runs so that you can average your data. Remember that 1 g means that you feel forces 

equal to your weight, 2 g’s mean that you feel forces that are double your weight, etc. To 

measure “g” forces, hold the accelerometer parallel to your body (perpendicular to the floor). 

Carefully observe the accelerometer through one complete rotation and record your best 

approximation of the reading at the four points of interest. 

Data Chart for Measurement of “g” Forces 

Location A Trial 1 g force Trial 2 g force Trial 3 g force 

Average “g” 

force 

Location B Trial 1 g force Trial 2 g force Trial 3 g force 


force 

Location C Trial 1 g force Trial 2 g force Trial 3 g force 


force 

Location D Trial 1 g force Trial 2 g force Trial 3 g force 


force 

17


Questions for Analysis: 

1. Compare your calculated (predicted) force factors with the “g” forces measured on the ride. 

2. Where is the “g” force largest? Explain. 

3. Where is the “g” force smallest? Explain. 

4. Describe what happens to the “g” forces as you complete one full rotation on the Ferris 

Wheel. 

5. Would it be possible to design a Ferris Wheel ride where the passengers feel “weightless” at 

some point of the ride? Explain your reasoning. 

6. Explain the effects of changing the radius of the Ferris Wheel while keeping the speed of the 

ride the same. Describe the effects for both a larger and smaller radius. 

7. Explain the effects of changing the speed of the Ferris Wheel while keeping the radius of the 

wheel the same. 

18

The Enterprise 

GOING IN CIRCLES 

Introduction: 

The Enterprise is a good ride to experience and measure what 

people call “g's of force.” What they are actually measuring are the 

forces a body experiences as compared to the standard contact force 

of mg, which we experience in equilibrium. When contact forces accelerate a body, it is 

natural to compare the sensation and value to mg, thus the ratio of the force on a body to 

mg gives rise to “g's of force.” When standing or sitting with no acceleration, the contact 

force on our body = mg, and we experience a “g” value of mg/mg = 1. 

Objective: 

In this lab you will compare calculated "g" values of force of your experience with 

force meter values as measured on the Enterprise ride. 

Procedure 

Part I: Theoretical values 

During this ride you will be able to experience and measure “g” values for three 

different situations: moving in a horizontal circle, at the top of a vertical circle, and at the 

bottom of a vertical circle. 

Place all responses on the data/calculation tables that can be found within the 

laboratory. 

Using the diagrams below, write the equation for the net force on the rider. In the 

first two cases, it is the net vertical force, in the third case it is the horizontal force. 

Based on the diagrams, fill in the blanks on the data table, and then solve for the contact 

force Fs. 

19


Part I: Theoretical Results 

Fill in the blanks based on the diagrams. 

Diagram A Diagram B Diagram C 

F net = ______ - mg F net = F s + ______ F net = ______ 

Newton's Second Law says F net = _______ 

Finally, solving for the contact force F s 

Bottom Top Horizontal 

F s = ma + ___ F s = ____ - mg F s = ____ 

Part II: The Experience 

To do this part you must go on the ride. 

When you are on the ride, sit on your hands, if possible, so you can better feel the 

force of the seat on your body. It may also be beneficial to shut your eyes at the key 

points of the ride so your sensations are not biased. 

As the ride commences take note of the push of the seat on your body, and try to 

compare it to the 1g feeling of the seat when you are first strapped in. 

After the ride is over, record on your data table whether the g's are greater, less 

than, or equal to 1 at each of the key positions. 

g values >,


Part III: Numerical 

1. Before going on the ride, you will need the centripetal acceleration of the 

ride at top speed by using the period and radius. The radius is taken from 

the blueprints and is 8.5 m. This is on your data sheet. 

For you to measure the period, you must climb the hill a bit to get a good 

view of the ride. Choose a rider or car that is easily identified. Wait until the 

ride is at full speed (you can tell by the sound) and time. (two revolutions). 

Calculate the period, which is the time for one revolution. Car # 5 is marked 

with a red spot. 

1. r = 8.5 meters 

Number of revolutions Total time Time for one revolution 

_________ ________ ____________ 

2. Calculate the centripetal acceleration using a c = 4 2 r / T 2 

a c = 4 2 r / T 2 

a c = _____ / _____ = ____________ 

number substitutes 

answer 

3. Now you are ready to record the “g” values by taking a force meter on 

the ride. Record the readings in a horizontal circle, at the top of the 

loop and at the bottom of the loop. 

Force meter readings: 

a. Full speed in a horizontal circle: __________________ 

b. At the top of the vertical loop: __________________ 

c. At the bottom of the vertical loop: __________________ 

21


4. Since the force factor F f is a ratio of F s to mg, the equations in Part I 

become: 

a. Horizontal circle: F f = F s /mg = ma/mg = a/g 

b. Top of loop: F f = F s /mg = (ma -mg)/mg = a/g - 1 

c. Bottom of loop: F f = F s /mg = (ma + mg)/mg = a/g +1 

Calculate the predicted force factor value for each situation. The value of (a) is the 

centripetal acceleration and (g) is 9.8 m/s 2 on earth. 

Horizontal circle : F f = F s /mg = ma/mg = a/g = ______/_______ = _______ 

Top of loop: F f = F s /mg = (ma -mg )/mg = a/g – 1 = ______/______ -1 = _______ 

 

Bottom of loop: F f = F s /mg = (ma + mg)/mg = a/g +1 = _____/______ + 1 = _______ 

Conclusion: 

Do the “g” values recorded compare reasonably well with those calculated from the 

centripetal acceleration? Support your answer. 

Conclusion: ______________________________________________________________ 

_________________________________________________________________________ 

_________________________________________________________________________ 

_________________________________________________________________________ 

22

Revolution 

The Revolution is a unique and exciting ride that combines two of the most 

frequently discussed motions in physics, pendulum and rotational. As the ride picks 

up speed the passengers are set into these two motions simultaneously, producing 

an unusual sensation of motion not experience in daily life. As you watch this ride 

you will take time measurements involving both the pendulum and rotational motions 

then do some calculations to determine the amount of force acting on the riders 

and compare the pendulum motion with that of a simple pendulum. 

Revolution 

The ride consists of a large, vertical beam that is swung back and forth like 

a simple pendulum. At the bottom of the beam, a large circular ring type of 

arrangement is attached. The riders sit along the outer rim of the ring. As the 

pendulum swings, the ring rotates. You will measure the period of oscillation of the 

vertical beam and the period of the circular motion of the ring. 

23

Revolution 

DATA: Length of the vertical beam: L= 7.25 m. (added dimension is 10.24 meters) 

Radius of the ring: r= 4.26 meters 

The Theory 

A. The Pendulum 

As you may recall from your physics class, a simple pendulum consist of a mass 

hanging at the end of along string or rod. The period of the motion is the time 

required to swing through one complete cycle from point A to point B and back to 

A. See the diagram below. 

A 

B 

The period T is given by 

T = 2 

Where L is the length of the pendulum and ‘g’ is the acceleration due to gravity. 

G = 9.90 m/s 2 

B. Centripetal Force 

24

Revolution 

Whenever an object of mass ‘m’ is moving on a circular path of radius ‘r’ with a 

speed ‘v’ there is a centripetal force ‘F’ acting on the object and it is given by the 

formula: 

F =mv 2 / r 

This force is always directed toward the center of the circle. The passengers on 

the ride are seated around the circumference of a circle. As the ring rotates, the 

passengers feel a centripetal force given by equation number 2. 

V = 

Where T is the period (time to complete one cycle). 

The Procedure 

A. Pendulum Motion 

1. When the ride begins, use a stopwatch to measure the time it takes for the 

system to complete 4 cycles of the pendulum type motion. From this time, 

calculate the time for one cycle (the period T). 

Time for 4 cycles = ________________________________seconds 

T = ____________________________________________seconds 

2. Solve equation number 1 for the length L of a simple pendulum that has the 

same period as the revolution pendulum. Compare this length to the length of 

the actual vertical beam. 

B. Rotational Motion 

25

Revolution 

3. When the ride begins to move, measure the time it takes for the passengers 

to complete 4 rotations. From this time, calculate the time required for one 

rotation. From this time and equation number 3, calculate the speed ‘v’ of 

the riders. Using equation number 2 to calculate the force on a rider (use 

your own mass ‘m’) 

Time for 4 cycles = __________________________seconds 

T = _______________________________________seconds 

V = ______________________________________m/s 

F = ______________________________________N 

4. From the force ‘N’, calculate the ratio of the force ‘F’ to the weigh ‘mg’. 

This would be the so-called ‘g’ force acting on the rider. 

F /mg = ________________________________ 

26

If there was one scientist who would love modern amusement parks, it 

would probably be Galileo Galilei. The freefall condition he studied so 

carefully richly experience in this modern day environment. Advanced 

technology had made experiencing freefall not only safe, but exciting as 

well. We will analyze freefall in this laboratory activity. 

Dominator at Dorney Park is two different rides built on one common 

tower. One side launches you upward at 22 m/s and allows you almost 

four seconds of freefall condition while you decelerate and return to the 

launch point. The other side lifts you to 52 meters and launches you 

downward at nearly 18 m/s where YOU bounce on an air cushion to 

almost half of the initial height. The two different versions of the ride will be used to analyze 

two different aspects of motion. Launch side will 

look at basic kinematics and accelerated motion while the Drop side will 

examine momentum/impulse and work/energy conditions. 

Launch Side and Kinematics: To study the basic kinematics of Dominator, 

you will need to observe the following details: 

Sketch Dominator and mark in 

relative positions and time data. 

Time of launch acceleration_______ seconds (observe the bodies of riders 

to see when acceleration begins and ends) 

Time of freefall condition _______________ seconds (observe between 

acceleration and deceleration periods) 

Time of deceleration ____________________ seconds 

(watch when arms and legs drop) 

When you ride, you may also take acceleration data with your force meter 

and log them below: 

launch acceleration force reading ____________ 

freefall acceleration force reading ____________ 

deceleration force reading __________________ 

With the motion data collected, you will be able to find the following values: 

Since in a frictionless environment (which we will assume since air drag is minimal) 

V up =-V down V = V down - V up = 2 V up = g T freefall 

27

Since we are on Earth, g = 9.8 m/s/s downward and the delta V value is negative (your 

instructor may ask you to show that!), we can find the Velocity by using the previous equation. 

Vup = g * _______________=______________ m/sec 

With this value, we can find the acceleration and deceleration you experience at the start and 

end of the ride. Note you may get a 4g reading, but the calculations below will be much less. 

Don’t worry; trust the numbers, differences will be discussed in question #3. 

Aup= Vup / Tup= _____________m/s/s / _______________sec.= ________________m/s/s 

Adown=Vdown/Tdown=Vup/Tup=______________m/s / ____________sec.=__________m/s/s 

Convert these two accelerations to g’s or Force Factor readings by dividing by 9.8 m/s/s. 

FFup=Aup/9.8m/s/s=_____________ “g’s”, FFdown=Adown/9.8m/s/s=___________”g’s” 

Questions 

1. How do the force factors or “g” readings compare? What are sources of error? 

2. What is wrong with the advertising statement? 

Riders reach speeds of nearly 50 mph almost instantly after takeoff then experience 

negative gravity before they plummet back towards earth. 

3. The specifications for Dominator are a 4.g launch and landing. You probably noticed the 4g 

reading but did not find 4g’s in your calculations, why? (Hint: average vs. constant 

accelerations) 

4. How do the average and maximum values compare? Did you observe linear or nonlinear 

accelerations? If they are linear with zero as one end point you can use the numeric 

average. Did that work here? 

28

Dominator Part II, The Drop Side: or Work/Energy on the bounce…… 

By using the inclinometer and standing at some convenient distance from the base of 

Dominator, find the angle of incline for the maximum height and height after the first bounce. 

Angle at maximum height ____________________________(note this is 52 meters of altitude) 

Angle where riders begin deceleration=____________________________ 

Angle at max height after first bounce ___________________________ 

By using trigonometry, calculate the height where deceleration begins and after first bounce. 

The Law of Sine’s works well or use a scaled drawing and find the distance from the ride to 

your measuring location. 

Height where deceleration begins=__________________ 

Height after first bounce ______________________ 

First measure a total time for the drop, then measure the time the riders are decelerating by 

watching their bodies. Arms and legs are a good cue to see when deceleration is occurring. 

T(drop)=_____________ seconds 

T(decel)= ____________seconds 

Calculate your energy at these two positions. The maximum Mechanical Energy is the sum of 

the potential energy at the top and kinetic energy gained during the launch. The ride applies 

g/2 acceleration for approximately 10 meters. The remainder is covered in the PE calculation. 

ME(max) = PE + F * d = mgh + mg/2*10m = 

___________________(units also) 

PE (first bounce) = m g hbounce=____________________________________(units also) 

29

1. How much energy was lost from maximum height to first bounce height? 

2. What is the efficiency of the pneumatic spring used to bounce you? (remember it 

should not be very elastic, they want you to stop eventually) 

3. Did you notice your fall was not “freefall” soon after launch? The pneumatic system 

begins your deceleration soon after launch. If it were not for that, what would your final 

speed be before the 10-meter main deceleration? Use KE=PE + Work to find your 

velocity. 

30

4. Compare this velocity with an approximation based on landing time and average 

deceleration of 2g’s. How do they compare? 

5. Since we know the distance the riders came to rest in, using the fact that change in 

energy is due to work done we can find the average force on you. Find F given 

F=Energy / distance (work/energy theorem). 

6. Compare this to the force found by change in momentum divided by time. (application 

of impulse/momentum calculations) 

7. In all cases above, we have used average values. Calculus students should use the linear 

change in acceleration and reanalyze questions 5 and 6 using the appropriate F/t and 

F/d graphs in the area below. This question is meant to be open ended. It is safe to 

assume the force varies linearly with distance increasing from 0 to the 4g force. Be 

careful when looking at the time values due to the distance/velocity relationship. 

31

The Sea Dragon 

(Part 1) 

The following two activities involve the use of the 

conservation of mechanical energy and Newton's Second Law to 

determine the maximum speed of the Sea Dragon. It is 

recommended that the student first observe the motion of the ride to 

determine when and where the ride undergoes the motion of a 

physical pendulum. The portion of the ride studied should be while 

the boat is traveling freely. 

Activity I - Maximum Speed Using Energy 

Objective: To determine the maximum speed of the Sea Dragon using the principle of 

conservation of mechanical energy. 

Procedure: 

1. Use the inclinometer to measure the maximum angle, , that the ride makes with 

the vertical. 

Maximum angle, _________________ 

32


(Part 1) 

2. The length of the swing arm, L is 10.7 m. (See diagram above.) Knowing this and 

that the maximum angle determines the maximum height, h, use the following 

guide to find h. 

h = 10.7(l - cos) meters 

Maximum height, h_________________ 

3. Assuming that mechanical energy is conserved, the potential energy at the 

maximum height is equal to the kinetic energy, KE, at the lowest point. The 

lowest point is where the boat is traveling freely with maximum speed, v. 

PE = KE 

mgh = 1/2(m)v 2 

Solve mgh = ½ (m)v 2 for v and then calculate the maximum speed, v. 

33


Maximum speed, v_________________ 

(Part 1) 

Activity 2 – Maximum Speed Using Newton’s Second Law 

Objective: To determine the maximum speed of the Sea Dragon using Newton's Second 

Law and to compare this value to the speed found in Activity 1. 

1. Ride the Sea Dragon. Using a hand held vertical accelerometer measure the 

"g's" at the lowest point of the ride's swing. Remember that 1 g means you feel 

the seat exerting a force, FN, on you that is equal to your normal weight, making 

you feel you normal. Two "g's" mean that you feel like you weigh is twice your 

normal weight in that the seat exerts a force, FN, on you equal to twice your 

weight. 

Number of g’s at the lowest point: _________________ 

2. Since the motion of the ride near the bottom of the swing is approximately 

uniform circular motion, Newton’s Second Law predicts that 

FN -Fg = (mv 2 )/r 

where, 

FN is your support force (the force that the seat exerts on you) 

Fg is your weight 

m is your mass 

v is your speed and is a maximum value 

r is the radius of curvature (10.7 m) 

Solve this equation for maximum speed, v. 

What is the maximum speed equation, solved for v =_________________ 

3. Determine your support force by multiplying the number of “g’s” by your 

weight. 

34


What is the support force, FN_________________ 

(Part 1) 

4. Determine your mass using Newton’s Second Law. 

m= Fg/g 

Where g is the acceleration due to gravity 

What is your mass, m_________________ 

5. Calculate the maximum speed, v, using the equation in #2 of this Activity. 

What is your maximum speed, v_________________ 

6. Compare the two speeds using a percentage difference. If the speeds do not 

agree, discuss possible sources of error. 

What is the comparison of two speeds_________________ 

35


(Part 2) 

The following activity involves the use of oscillatory motion concepts. It is 

recommended that the student first observe the motion of the ride to determine when and 

where the ride undergoes the motion of a physical pendulum. The portion of the ride 

studied should be while the boat is traveling freely. 

Objective: To determine the period of oscillation of the Sea Dragon in two different 

ways. 

Procedure: 

1. Using a stopwatch, measure the period of oscillation of the Sea Dragon. 

1. period of oscillation, T (first way)_________________ 

2. Assume that the ride behaves like a simple pendulum and calculate the period using 

the following equation: 

T =2(L/g) 1/2 

where, 

T is the period of oscillation 

L is the length of the pendulum (10.7 m) 

g is the acceleration due to gravity 

2. period of oscillation, T (second way)_________________ 

3. Compare the two periods using percentage difference. Is the Sea Dragon a simple 

pendulum? 

36

White Water Landing 

Observations: 

White Water Landing will give you an opportunity to use 

the concepts of momentum and impulse to determine the forces 

acting on you during the “splashdown.” 

1a. After observing a number of boats “splashing down,” does 

the size of the splash vary or is it fairly constant? 

_____________________________ 

1b. If it varies, what observable factors seem to influence the size of the splash? 

2a. Is there any time during the ride that riders appear to lunge forward? 

2b. If yes, where and why does this occur? 

Activity 1 

Determining the magnitude of the velocity of the boat before 

and after “splashdown" 

Potential Energy PE = mgh mass (x) gravitational field (x) height 

(Top of the incline) 

Kinetic Energy KE = 1/2 mv 2 1/2 mass (x) velocity squared 

(Bottom of the incline) 

gravitational field g = 9.8 m/s/s at Dorney Park 

height of incline 25 meters 

Potential Energy Joules (J) 

Length of Boat 5.2 m 

Part (a) Velocity immediately before splashdown 

37


To find the approximate velocity of the boat immediately before splashdown, we 

can make the assumption that the Potential Energy of the boat at the top of the incline is 

completely converted to Kinetic Energy at the bottom. 

Find the Potential Energy of a passenger at the top of the incline: 

PE=___________ 

Lets assume that all of the Potential Energy becomes Kinetic Energy at the bottom of 

the incline. Use the information already obtained to find the velocity at the bottom of 

the incline. 

Part (a): Before splashdown 

your mass 

(kg) = _______________ 

Hint: To find your mass in kg, you may find it useful to know that the 

weight of a 1 kg mass on earth is approximately 2.2 pounds. 

height of incline 

gravitational field 

Potential Energy at top of hill 

Kinetic Energy at bottom of hill 

25 meters 

9.8 m/s/s 

(J) =_______________ 

(J) =_______________ 

Velocity at bottom of the incline (m/s) = _______________ 

Part (b): After splashdown 

Measure the time for the complete boat to pass under the bridge (after it has completed its 

“splashdown”). Observe at least three boats and find the average time for a boat to pass 

under the bridge. Use the information concerning the length of a boat to find the average 

final velocity of the boat. 

Data Chart for Finding Velocity of the Boat Before and After “Splashdown” 

Time to pass 

under the 

bridge 

Trial 1 Time (s) Trial 2 Time (s) Trial 3 Time (s ) Average Time (s) 

Velocity after 

splashdown (m/s) 

38


Activity 2 

Determining momentum change and impulse acting during the “splashdown” 

Momentum is defined as the mass of an object times its velocity. 

Physicists represent the quantity of momentum with the letter p. 

momentum = mass x velocity 

or 

p = mv 

Use your own mass to determine the momentum of a passenger riding in a boat 

both before and after splashdown. As a result of the boat splashing down, the 

momentum of each passenger changes. Find the change in momentum of the abovementioned 

passenger. 

momentum change = momentum after splashdown - momentum before splashdown 

or 

p = pafter - pbefore 

(the symbol delta means change) 

Data Chart for Finding Momentum Changes 

pbefore 

(kg m/s) 

pafter 

(kg m/s) 

p 

(kg m/s) 

Momentum of an object is changed by the application of an impulse. 

Impulse is defined as the product of an applied force and the time that the force acts: 

Impulse = Force x Time for force to act 

or 

J = F t 

The impulse applied to the passenger is equal to the momentum change for the 

passenger. 

J = p 

39


The time that the force acts to change the momentum is approximately the same 

as the time that the “splash” lasts, since the splash is a result of the water applying an 

impulse to the boat and the boat applying an impulse on the water. 

Observe at least three “splashdowns” and time how long each splash lasts to find 

an average splash time. From this information, determine the size of the force required 

to change the momentum of a passenger with your mass. 

If mass is in kg and acceleration is in m/s/s, then the unit for force is a newton 

(symbol N). 

Data Chart for Finding Forces Acting 

Trial 1 

Splash time 

(s) 

Trial 2 

Splash time 

(s) 

Trial 3 

Splash time 

(s) 

Average 

Splash time 

(s) 

p 

(kg m/s) 

 

Impulse 

(kg m/s) 

FA = Average Applied 

Force - FA(N) 

Activity 3 

Comparing Forces 

You can now determine how the force applied to the rider to slow down compares 

with other forces. A common force with which to compare is your weight. Determine 

how the force applied compares to your weight by using the following: 

Force Factor = Applied Force/Weight 

Data Chart 

If mass is in kg and acceleration is in m/s/s, then the unit for force is a newton (symbol N). 

FA (N) 

Applied Force from 

Activity 2 

Fw (N) 

Your Weight = mass * 

9.8 m/s/s 

Force Factor 

40



1. Compare your force factor with other students’ of different mass. Explain your 

observations. 

2. Predict the size of the force acting on the entire loaded boat (the boat has a mass of 

approximately 1000 kg when empty). Estimate the total mass of riders and boat. 

41

The Scrambler 

Introduction: 

The Scrambler consists of two sets of arms, the upper 

sweep arms and the lower arms, that have different radii 

and revolve around different points of rotation to 

produce varying forces. You will be studying the paths of 

these arms and the cars attached to them, along with 

their properties, such as angular velocity, tangential 

velocity, and centripetal force. 

Apparatus: 

Stopwatch, calculator 

Part I: 

Procedure 

Stand at some point around The Scrambler so that you can see the entire ride. 

Watch the ride rotate several times. 

1. What direction do the sweep arms appear to be rotating? (clockwise or 

counter-clockwise) 

_____________________ 

2. What direction do the lower arms appear to be rotating? (clockwise or 

counter-clockwise) 

_____________________ 

Do you notice anything about the ride that seems to be cyclical? Try focusing on 

one particular car or one spot along the outside of the ride. 

You may notice that each sweep arm returns to the same point along the outside 

of the rides’ path every revolution, but each lower arm (and attached car) does 

not. 

Before the ride starts, find a car that is closest to the fence surrounding The 

Scrambler. It should be pointing almost directly at you. Remember this car, as 

you will be following its motion. 

Laboratory courtesy of Andrew Snyder, Materials Engineering, Rensselaer Polytechnic Institute Page 42

The Scrambler 

3. As the ride is rotating, what do you notice about the group of 4 cars to which 

the car you picked out belongs? 

4. How many revolutions does it take for that car to return to the same point 

that it started at? 

____________________ 

5. What is the length of the sweep arms and what is the circumference of their 

path? 

Length: _________________ 

Circumference: ____________________ 

6. What is the length of the lower arms and what is the circumference of their 

path? 

Length: _________________ 

Circumference: ____________________ 

Part II: 

Now you will need your stopwatch and calculator. When the ride is up to full 

speed, record the time it takes for the ride to rotate 3 times. The easiest way to 

do this is record the time it takes for one of the sweep arms to pass you 3 times. 

Then divide by 3 to calculate the time of one revolution. 

Time of 3 revolutions: _______________________ 

Period (time of 1 revolution): _______________________ 

Now calculate the angular velocity, keeping in mind that each revolution is 

2*pi radians and your period has the units seconds/revolution. 

Angular velocity (in radians/second): 

________________________________ 


The Scrambler 

The tangential velocity is simply the speed that the object is travelling in its 

circular path. This can be obtained by multiplying the angular velocity by the 

radius of the path, or the length of the sweep arms. 

Tangential velocity (in meters/second): 

_______________________________ 

The next part is a little trickier. Your task is to calculate the time it takes for the 

group of 4 cars to rotate one revolution. The easiest way is to orient yourself to 

the ride the same way you were before, lined up with the closest car to the 

outside, and to time 4 rotations of the upper arm, while counting how many 

times the group of 4 cars spins in a full circle. (Remember: the car completes 

one spin every time it is swung to the outside of the fence, at the point furthest 

away from the middle of the ride) 

Time of 4 revolutions: ______________________ 

Number of spins in 4 revolutions: _______________________ 

Period (time of 1 spin): _____________________ 

You can now calculate the angular and tangential velocities for the lower 

arms attached to the cars using the same method you used for the sweep arms. 

Angular velocity (radians/second): _________________________ 

Tangential velocity (meters/second): _________________________ 

Part III: 

Now that you have calculated the velocities of both sets of arms it’s time to use 

them to reveal some interesting things about The Scrambler. Do the cars on The 

Scrambler have a higher speed when they are closer to the center of the ride or 

when they are closer to the outside of the ride? Hopefully, your answer was 

they travel faster when they are closer to the inside of the ride. Why is this? The 

speed of the cars is a product of the tangential velocity of both sets of arms. 

The sweep arms are moving clockwise, while the lower set of arms are moving in 

a counter-clockwise motion. This causes the tangential velocities of each set 

of arms to work together when the cars are closer to the center of the ride and 

offset each other when the cars are at their furthermost point from the center. 


The Scrambler 

Given the information provided above you should now be able to calculate the 

maximum and minimum speeds of the cars when the ride is at full speed. An 

important thing to remember when doing these calculations is that while the 

angular velocity is always constant, the tangential velocity varies as a 

function of the radius, or the distance of the object from the point of rotation. 

Also, remember that when the tangential velocities are opposing each other 

you need to make one positive and one negative. 

Radius of the lower arm at the point of maximum speed: 

__________________ 

Radius of the sweep arm at the point of maximum speed 

(distance of the car from the point of rotation of the sweep arm): 

_____________________ 

Tangential velocity of the car due to the lower arm at the point of 

maximum speed: 

_______________________ 

Tangential velocity of the car due to the sweep arm at the point 

of maximum speed: 

_______________________ 

Maximum speed of the car: _______________________ 

Radius of the lower arm at the point of minimum speed: 

__________________ 

Radius of the sweep arm at the point of minimum speed 

(distance of the car from the point of rotation of the sweep arm): 

_____________________ 


The Scrambler 

Tangential velocity of the car due to the lower arm at the point of 

minimum speed: _______________________ 

Tangential velocity of the car due to the sweep arm at the point 

of minimum speed: _______________________ 

Minimum speed of the car: ___________________ (does this answer 

surprise you?) 

Part IV: 

The final part of this exercise is to calculate the centripetal force on the rider 

at the innermost and outermost points on the ride’s path. This must be done 

similarly to the way you calculated the tangential velocity of the car at both 

points, as centripetal force is also a radius dependant value. The centripetal 

force always points toward the center of rotation for each set of arms, so be sure 

to make one positive and one negative, if needed. 

The equation for centripetal force is Force = mass * radius * (angular 

velocity) 2 . You can use your own mass (in kg) in this calculation. (1 kg = 2.2 

lbs.) 

Centripetal force on the rider at the innermost part: 

_______________________ 

Centripetal force on the rider at the outermost part: 

_______________________ 

Length of Sweep Arm: 4.23 meters 

Length of Lower Arm: 3.65 meters 

Pivot arm from pivot to car: 1.82 meters 


The Wave Swinger 

A SWINGING TIME 

Introduction: 

The Wave Swinger is a fairly simple ride, but it does 

have some interesting aspects. The rate of the rotation of 

the ride is constant and there are only two forces acting on 

the swing itself. This allows the easy analysis used in Part 

IV. However, because the ride tilts, the plane of swing is 

not horizontal. This adds some interesting possibilities to 

the motion of the swing and rider. 

Part I 

Theory 

Shown below is a crude picture of a rider on the swing seat. The swing seat and 

rider will be treated as one object. 

Since the forces F 1 and F 2 (actually there are four) are in the same direction, they can be 

considered as a single force F 1 and F 2 = F. This is shown below. 

Procedure: 

Place all answers where indicated within the procedures. 

1. Is the force of the chain F or mg? ________________________ 

47


2. The force mg is the force due to what phenomena? 

____________________________________________________ 

3. Draw the diagonal across the parallelogram. 

4. The diagonal of the parallelogram is the magnitude of what force? 

____________________________________________________ 

____________________________________________________ 

5. The direction of the force in number 4 is the same as the: 

speed or acceleration of the object? 

____________________________________________________ 

6. If the speed is constant, which acceleration is equal to (0), the tangential 

acceleration or radial acceleration? 

______________________________________________________________ 

7. Is v 2 /r the tangential or radial acceleration? 

Note: radial is another name for centripetal. 

______________________________________________________________ 

8. Noting that the diagram in #3 shows the net force (thus acceleration) to be slightly 

up, would you conclude that the swing is at a low or high spot in its rotational path? 

48


Part II 

Observations relating to the theory 

Procedure: 

Make the following observations of the ride. 

1. Using the outside swings only, does the weight on the swing effect the angle of the 

chains? 

____________________________________________________ 

 

Note: comparing an empty swing to a loaded one can do this. 

2. Do the riders on the inside swings travel at a faster or slower speed than those riding 

on the outside swings? 

____________________________________________________ 

3. Use the inclinometer (as shown in the diagram below) to measure the angle that the 

chains make with the vertical for when the swings are at their highest point and 

lowest point. Within experimental error, are they the same or different? 

____________________________________________________ 

4. Which swings have the greater angle from the vertical? The outside swings or the 

inside swings? 

____________________________________________________ 

49


Part III 

Observations to be made on the ride 

1. Watch the chain as the ride begins. Which way does it move relative to you? 

____________________________________________________ 

2. As you ride, how does the force of the seat on your “bottom” feel at a low point as 

opposed to that at the high point in your rotational path? 

Note: This force variation is indicative of the force variation in the chain. 

____________________________________________________ 

Objective: 

Part IV 

Numerical Analysis 

To determine whether the radial (centripetal) acceleration is equal to the acceleration 

value of g (tan ) where is the angle that the chains make with the vertical. 

Procedure: 

1. Use the inclinometer to measure the angle that the outer swings make 

with the vertical as shown in the figure of Part II, Procedure step 3. If 

you feel there is significant difference between the angle when the swings 

are at a low point and high point, record both angles. 

Angle Value (low point) ________________________________________________ 

Angle Value (high point)________________________________________________ 

2. Time the ride for five complete revolutions. ________________________ 

*The radius used is given as 9.0 meters. 

50


Analysis: 

1. Calculate the predicted acceleration using g(tan ), where g= 9.8 m/s 2 . If 

you used two different angles do this, perform calculation twice. 

____________________________________________________ 

2. Find the period of the swing. (This is the time for one revolution.) 

____________________________________________________ 

3. Calculate the acceleration using a = 4 2 r/T 2 . 

____________________________________________________ 

4. Compare the accelerations in Parts 1 and 3 using percent difference. 

____________________________________________________ 

5. Bonus: Based on the force diagram and a vertical component of the chain 

force equal to mg, show how Newton's Second Law produces an 

acceleration of g(tan). 

51

The Physics of 

Since the Gravity Rides of the 1500’s, the 

concept of the roller coaster has been a 

thrilling challenge for both rider and engineer. 

In this lab, you will have the chance to test the design of Steel Force, the “longest, 

tallest, fastest coaster in the East.” This laboratory is divided into 3 sections. Each 

section is a necessary step to evaluate the next section, so work in order and go as far as 

your instructor requires. The sections will help you examine kinematics, work/energy 

theorem, and curvilinear motion. The diagram below shows the parts of the ride we 

will analyze. 

Data Point A: 

is anywhere about half way up the first hill. At this point, the 

chain drive system is pulling the train uphill at a constant velocity. 

Data Point B: is at the bottom of the first hill. At this point, there is a tunnel 34 

meters long. You will use the length of the tunnel to find the speed 

at this point on the ride. 

Data Point C: 

Data Point D: 

Data Point E: 

is at the top of the second hill, 49.1 meters above the ground. You 

will use the length of the train to find its speed here. 

is the spiral curve at the far end of the coaster. You will measure 

the time to go around the curve for one full revolution. The radius 

of this turn is 31 m. 

is the return camelback’s first “hump.” You will use the train 

length to find its speed at this point. 

All data can be logged on the Steel Force Data Sheet, which follows this lab. The data 

will help you complete the computations for all of the following sections. 

52

Steel Force 

Section #1 

Koaster Kinematics...... 

One of the primary measurements we must take in physics is the motion value called 

speed. In this section, we will compute the speed and acceleration values at the five 

points of interest on Steel Force. 

In general, we will use: 

v =d /t and a = v /t. 

Speed at points A, C, and E: 

At these points you will compute speed by using train length divided by time 

taken to pass a point. The train is 19.6 meters long. Check your Steel Force Data 

Sheet for the time to pass a point on the track at each of these locations. Use the 

measured times and complete the calculations in the chart on the next page for 

each of the points A, C and E. 

Speed at point B: 

This is the tough one! The tunnel is 34 meters long. If you measure the time 

through the tunnel, it will be short and you can compute the speed by the basic 

equation in chart line #4. 

Can you think of a way of measuring this more accurately? If you can, take the 

measurement your way and the way described above, then compare. If not, see if 

you can find another group who has done this. 

Hint: the train is 19.6 meters long and its length will increase the time of passing a 

point. 

Speed at curve D: 

Your measure of the time around the curve, along with the distance traveled, will 

give you this solution in line #5. 

Acceleration on first hill: 

Now apply your acceleration equation to solve for the average acceleration on the 

first hill. This is done in line #6. You will need the velocity at the top and bottom 

of the hill (Data points A and B) and also the time down the hill. Measure the 

time from when the center of the train passes the top of the hill to when that point 

enters the tunnel. 

53

Steel Force 

Deceleration on second hill: 

Using the same type of calculation, find the deceleration rate when going up to 

point B in line #7. 

Line 1 

Line 2 

Line 3 

Line 4 

Line 5 

Line 6 

Line 7 

VA=19.6m/____________ seconds = ______________ 

don't forget units 

VC=19.6m/____________ seconds = ______________ 

units 

VE=19.6m/____________ seconds = ______________ 

units 

VB=34 m/____________ seconds = ______________ 

units 

VD=*62 m/_________ seconds = ______________ 

units 

Ahill=V/t =(________-_________)/____________ = ______________ 

units 

Ahill=V/t =(________-_________)/____________ = ______________ 

units 

Section #2 

Using the Work/Energy Theorem...... 

Once you have been lifted to the top of the first hill, your trip is entirely 

controlled by a simple concept in physics, work/energy. The motor drive system simply 

is designed to propel you to the top of the first hill. This motor/chain drive acts on you 

and the train but, for this example, we will only work with you (all other parts like the 

train and passengers are proportionately larger). We will work on the assumption that 

friction is negligible to make our calculations easier. 

54

Steel Force 

Up the first hill: As you are pulled up the hill, the motor system must apply a 

force parallel to the hill in order to move you along. This hill is at an angle of 25 

degrees. 

8. Find the force on you as you go up the hill: 

F parallel =__________________ 

Note: Recall the equation F par = mg sin 

 

This force will be applied up the entire length of the hill, 144 meters. 

9. What work is done on you during this part of the trip? 

Work = ___________________ 

Before going further, how much power is required to pull you up, if you reach the top in 

the amount of time that you found? 

Find this in both Watts and Horsepower. 

P = #9_______/_______ (time) = _____________watts = _____________hp 

(10) 

Now, back to Work... The work done on you in a frictionless environment would 

remain as part of the total mechanical energy. 

11. At the top of the hill, what two types of energy do you have? 

12. List them and compute their values for you below. 

Use your mass for this analysis: 

(11) E (total mechanical energy) = _______________+________________ 

name of one 

name of the other 

(12) E (total mechanical energy) = _____________+____________ = 

compute P 

compute K 

Since this value will remain nearly constant between the first and second hills, find the 

values for the stored part of the energy at points B and C. Note the first hill (at B) is 

below the starting level by 1.5 meters. 

(13) P at B = _____________ 

(14) P at C = _____________ 

55

Steel Force 

The work done to get you to the top of the 61 meter hill can be found the same way as finding the 

stored energy. 

15. Using this type of calculation, what is the stored energy at the top of the hill? 

P at Top = _______________ 

Does this compare favorably to your calculation from calculation #9? Why? 

_____________________________________________________________ 

_____________________________________________________________ 

_____________________________________________________________ 

If we assume E initial =E final , we can use the equation: 

_______________ (value from 12) = P + K. 

With this we can solve for velocity at two points of interest, points B and C. 

E (12) = P + K therefore K = E (12) - P 

Find the values for the motion energy at B and C; then compute the velocity from the equation K 

=1/2 m v 2 . 

K B = _______________ therefore V B = _________________ 

K C = _______________ therefore V C = _________________ 

We have measured the velocity at points B and C. Using Work/Energy we have 

predicted it. Compare the two values. How do they compare? What sources of error exist and 

how bad were they? In the blocks below, assuming the actual measures from Section #1 to be 

accurate, compute experimental error and explain. 

Data Analysis at Point B 

Data Analysis at Point C 

56

Steel Force 

Section #3 

Curvilinear Motion and Vectors 

reaction forces 

The basic motion we experience on roller coasters was 

explained in the sixteenth century. We will look at these 

principles using the physics and trigonometry studied in class. 

When you are traveling in the train, your body is 

moving in a straight line until the track or gravity changes 

your motion. We will start by looking at changes in the 

horizontal motion that your train travels. 

Mg 

F c 

When you travel through the far point spiral, you are traveling at a speed calculated in 

equation. You have the radius and speed, so find the centripetal acceleration. 

a centripetal = V 2 /R = _______ 2 /31 meters = _________________ 

The average angle of the track at this spiral is 44 o . Compare this to a vector 

diagram of the track’s gravitational force verses its centripetal force. Fill in the values 

and draw scaled reaction forces with resultant on the drawing above. What do you 

notice? Discuss below: (include not just values, but what you felt, which way the forces 

acted on you, etc.) 

57

Steel Force 

Points B, C and E are other interesting 

positions. In these areas, you have a combination of 

forces acting on you in the vertical directions. If we 

assume a person to be ideally viewed as shown, create 

a free body diagram (FBD) including the seat and 

gravitational forces on the rider. Use the dot to the 

right for your FBD. 

gravity 

seat force 

At point B, we will define the upward force of the seat to be N for normal force. The 

centripetal force is also upward and gravity is downward. From this, we can predict the 

seat force on you by applying Newton’s Second Law as follows: 

F = m a 

The values, that we can see from the FBD, expand to the following: 

N - m g = m v 2 /r, or N = m(g+v 2 /r) 

16. Since these values are all known, we can easily find the force on your body. The 

radius of the tunnel curve is 34m. Using your value for speed from (4) and your 

mass, find the seat force N. 

N = ___________________ 

17. Divide this (16) by your weight and compare to your accelerometer reading. 

N/mg =_____________ g’s compared to ___________________ g’s 

58

Data Point A, You are looking for the 

velocity of the train going up the hill. 

Find the time for the train to pass a 

point on the hill. 

t =________________ 

Data Taking Sheet for 

Side 1, Kinematics 

Data Point C, The velocity at the 

top of the second hill is again found 

using train length and 

Time, t, =_________________ 

Data Point B, Finding the velocity at the 

bottom of the big hill. Use the time it takes 

the train to go through the tunnel. Be 

careful, it will be a very short interval...... 

t =____________________ 

Data Point E, The top of the first 

Camelback Hump will be used as 

a reference. Measure the time it 

takes the train to pass the very 

top point. 

t =_________________ 

59 

Data Point D, To find the speed 

through the curve, use the 

circumference and time to pass a 

vertical point through one 

revolution. 

t =_______________

Data Taking Sheet for 

Side 2, Curvilinear Motion and Vectors 

Data Point A, As you go up the hill, 

which way do you feel a force? 

Using your accelerometer, find the 

acceleration you are experiencing. 

a=_______________ 

Data Point A to B, as you accelerate down 

the hill, you should see your accelerometer 

reading change. Find the acceleration 

going down the hill and at the bottom. 

a down =__________ a bottom =__________ 

Data Point E, What is the 

acceleration at the peak of this 

hump? Take a reading and listen 

to the train on the track. What do 

you notice? 

a=________________ 

60 

Data Point D, We will need 

acceleration through this curve. 

Use your accelerometer to 

measure this value. 

a=________________

Energy Curves for Steel Force 

Objective: To investigate a rider’s energy curves for a portion of the Steel Force ride 

Equipment: stopwatch, scaled photo of Steel Force’s second hill (see Diagram 1 in data section), 

small ruler 

Note: In this investigation the x-axis runs along the track. 

Procedure: 

1. Determine the speed of the coaster at position A (0 meter). To do this, time how long it 

takes the 19.6 meter long train to pass position A and record. (See Diagram 1 in data 

section). 

2. Repeat step # 1 for each of the remaining positions (B through L). 

3. Record your weight in pounds. 

4. Using Newton’s Second Law and the fact that 1 pound equals 4.448 Newtons, calculate 

the rider’s mass in kilograms and record. Show your work in the analysis section. 

5. Determine the rider’s kinetic energy at each position and record. 

6. Using Diagram 1 with its provided scale (the 20 m width), determine the distance each 

position is from position A (0 meters) and record. Note: This distance is equal to the 

magnitude of the position, x. 

7. Using Diagram 1 with its provided scale (the 20 m width), determine the height each 

position is from the ground and record. 

8. Determine the potential energy of the rider at each position and record. Show your work 

in the analysis section. 

Special thanks to Jeff Wetherhold 61


Data: 

A, 0 m 

B 

C 

D 

E 

F 

G 

H 

height of hill = 46 

m 

I 

J 

K 

L 

20 m 

Diagram 1 

Length of train = 19.6 meters 

Rider’s weight = _____ pounds 

Rider’s mass = ______ kilograms 



Position 

mark 

Position,x 

(m) 

A 0 

Position,y 

(m) 

Time to 

pass 

position 

mark 

Speed at 

position 

mark 

(m/s) 

Kinetic 

energy at 

position 

mark, K 

(J) 

Potential 

energy at 

position 

mark, U 

(J) 

Total 

energy at 

position 

mark, E 

(J) 

B 

C 

D 

E 

F 

G 

H 

I 

J 

K 

L 



Analysis: 

1. Show work for finding the rider’s mass. 

2. Show work for finding the rider’s kinetic energy. 

3. Show work for finding the rider’s potential energy. 

4. Using the provided graph paper, graph the kinetic energy, the potential energy, and the 

total energy as a function of the position, x. Plot the energies on the same set of axes. 

5. Based on analysis # 4 results, construct the corresponding net force vs. position graph 

(use the same piece of graph paper that you used for analysis # 4). 

6. According to the net force vs. position graph, what is the net force on the rider at the 

top of the hill? Does this make sense to you? Explain. 

7. Is the mechanical energy of the rider conserved? If not, what happens to the lost 

mechanical energy? 


Centripetal Force and Steel Force 

Objective: To determine the centripetal force on a person riding Steel Force 

Equipment: stopwatch, scaled photo of Steel Force’s second hill (see Diagram 1 in data section), 

small ruler 

Procedure: 

1. Have someone ride the Steel Force and measure, with the vertical accelerometer, 

the “g-force” at the top of the second hill (see Diagram 1) and record. 

2. Time how long it takes the 19.6 meter long train to pass the top and record. 

3. Record the rider’s weight in pounds. 

4. Using Diagram 1 and its scale, determine the radius of the curvature of the hill at the top 

and record. 

Data: 

TOP 

20 m 

Diagram 1 


Centripetal Force and Steel Force 

g-force at top of hill = _______ g 

length of train = 19.6 meters 

time for train to pass top = ______ seconds 

rider’s weight, W = ______ pounds 

radius of curvature of the second hill at the top, r = ______ meters 

Analysis: 

1. Draw a force diagram for the rider at the top of the hill. The forces involved include the 

normal force, F N and weight, W. 

2. Knowing that 1 pound equals 4.448 Newtons, determine the rider’s weight, W in Newtons. 

3. Knowing the g-force on the rider, determine the normal force on the rider at the top. For 

example, if the rider measured 2 g’s, then the normal force on the rider would be equal to 

two times the rider’s weight. 

4. Using Newton’s Second Law and the fact that 1 pound equals 4.448 Newtons, calculate 

the rider’s mass, m in kilograms. 

5. The centripetal force on the rider is equal to the net center directed force, Σ F on the 

rider. Use this fact to determine the centripetal force, F c on the rider at the top. 

6. Knowing the length of the train and the time for the train to pass the top, determine the 

speed, v of the rider at the top of the hill. 

7. Knowing that acceleration of the rider at the top is given by the equation ac = 

v 2 , 

r 

determine the rider’s acceleration. 

8. From Newton’s Second Law, the centripetal force on the rider is also equal to the rider’s 

mass times the rider’s acceleration or F 

= māc . Use this fact to determine the 

c 

centripetal force on the rider at the top. 

9. Using a % difference, compare the centripetal forces you found in analysis # 5 and # 8. 


The Talon will allow the opportunity to study the forces that act as your body goes through a variety of 

loops and curves. Before riding, spend some time looking at the ride. If possible watch a number of trains 

going through the complete circuit. 

1. Describe what your body would expect to feel at the following points on the ride: 

(See the accompanying diagram to identify these points) 

o Bottom of the first hill: 

o Top of the vertical loop (when you are upside down): 

o As you pass through the top of the Zero “g” Roll 

(the title of this element may be helpful!): 

o The middle of the horizontal Spiral: 

Mass in kg = 

Formulas required for these activities: 

Weight in pounds/2.2 

Magnitude of velocity = Distance traveled/time interval or v = d/t 

Centripetal acceleration = Velocity squared divided by radius or a C =v 2 /r 

Centripetal Force = Mass times centripetal acceleration or F = ma c 

Force due to gravity 

(weight) = 

Mass times gravitational acceleration or F g =mg (g = 9.8 m/s/s at 

Dorney Park) 

Force Factor = Seat Force/Force of Gravity or FF = F s /F g 

67

Most of the required measurements can be taken while observing the Talon from the area around the 

Antique Carousel near the Main Gate. 

Part 1 - Determining the magnitude of the velocity at key points on the ride. 

Observe some cars traveling through the ride. Find the magnitude of the velocity of the cars as they pass 

each of the following locations. To find the velocity, use the length of the train (12.2 meters) and measure the 

time it takes the complete train to pass a certain point. Be sure to collect data for at least three trials and average 

your results. Measure time in seconds (s) and calculate the velocity in meters per second (m/s) 

Bottom of the first hill: 

Length of Train = 12.2 m 

Time for train to pass the point = _______________ 

Magnitude of the velocity of train = ____________________________ 

Top of the vertical loop (when you are upside down) 

Length of Train =12.2 m 



At the peak of the Zero “g” Roll 




In the middle of the horizontal Spiral 




68

Part 2 - Determining the accelerations and forces acting on a rider at key points: 

You will need to have your mass in kg determined: Your mass = ___________kg 

The accelerations and forces experienced moving through a curve or loop can be considered by using 

the principles of circular motion. 


Radius of curve= 25.0 m 

Centripetal Acceleration = ____________ 

velocity (from part 1) = ______________ 

Centripetal Force = _________________ 

Top of the vertical loop (when you are upside down): 


velocity (from part 1) = _____________ 



Radius of curve= 18. 0 m 





Centripetal Force = ________________ 





69

Part 3: Determining the force that a rider feels at key points and calculating expected “g” forces. 

In addition to moving along the curve, a force is also required to “hold you up”. This additional force 

would be an upward force equal in amount to your weight. The centripetal forces that you calculated in Part 2 

are simply a combination of the force that the seat exerts (Fs) and the force due to gravity (Fg). The force due 

to gravity is often referred to as your weight. Calculate your weight in Newtons. 

Force due to gravity (weight) = ____________________N 

Bottom of loop. 

Fc is up, so 

F c =F s -F g 

Seat Force F s = F c +F g 

Fs 

Top of loop. 

This situation works for top 

of vertical loop and top of 

Zero “g” roll 

Fc is down, so 

F c =F g +F s 

Seat Force F s = F C -F g 

Fs 

Fg 

Fg 

Your weight in newtons = __________________N 


Centripetal Force (from part 2)= ____________N 

Seat Force = ____________________N 



Seat Force = ____________________N 

70



Seat Force = ____________________N 

Analysis of the forces in the horizontal spiral requires knowledge of vector mathematics. This analysis may 

be optional. 

The forces in the horizontal spiral are a bit more complicated, the centripetal force is a combination of the force 

required to hold you up (opposite of force of gravity) and the seat force, both of which are vectors. 

Since these are vectors that are not parallel to one another you need to use vector addition techniques. 

Seat Force 

(Fs) 

Force holding you 

up = your weight 

(Fg) 

From the Pythagorean Theorem: 

Centripetal Force 

(Fc) 

Fs 2 = Fg 2 + Fc 2 



Seat Force = ____________________N 

Part 4: Calculated “g” Forces: 

Of interest to many roller coaster enthusiasts are the “g” forces experienced at various places on the ride. 

Use the calculations you have just completed to find the Force Factor (or “g” forces) that you can expect at 

the key points on the ride. 


Seat Force (from part 3)= ____________N Predicted Force Factor (“g” force) = ______________ 







71

Part 5: - Measuring “g’s” 

Someone in your group needs to ride the roller coaster. Using your vertical accelerometer (long tube) 

measure the g's at the points being studied. Remember 1 g means that you feel forces equal to your weight, 

2 g’s mean that you feel forces that are double your weight, etc. To measure g forces, hold the accelerometer 

parallel to your body (perpendicular to the lap bar). As you ride, try to remember the readings as you pass 

through each of the key points, do not attempt to write down the readings in the midst of the ride!!! 


Measured “g” Force = ______________ 







72


1. Which of the four points has the rider traveling at the greatest speed? Explain why this is the fastest of 

the four points. Dorney Park ads say that Talon reaches speeds of 58 mph, how do your results compare 

to this claim? (either convert your results to mph or convert 58 mph to m/s to do the comparison) 

2. Compare the calculated force factors at each point to the measured force factors. Why may there be 

some differences? 

3. Why do they refer to the third element studied as the Zero “g” Roll? Do your results seem to agree with 

this claim? 

4. Why is the radius of the vertical loop so much smaller at the top than at the bottom? How do you think 

the experience of Talon would be affected if the vertical loop had a large radius at the top (like it does at 

the bottom)? 

5. Describe what factors make Talon exciting and different from other coasters like Steel Force or 

Hercules? If you studied another coaster, compare the results and explain what makes the other coaster 

exciting and different from Talon. 

73

Inclined Spiral 

Immelman 

Zero “g” Roll 

Horizontal Spiral 

Vertical Loop 

Bottom of First Hill

Thunderhawk 

An Enlightening Lab 

Introduction: 

Thunderhawk is the original roller coaster for Dorney Park. Although it looks small compared to 

Steel Force it is an excellent ride in design and function. As with all wooden type coasters the vibrations 

are part of the experience. It is for this reason this lab has no measurements taken on the ride though it is 

highly recommended you ride it to experience the usual thrills and also the decrease in energy as you 

move from beginning to end. 

Purpose: 

To measure the lost mechanical energy from the top of the first hill to the small hump near the 

end of the ride. 

Theory: 

There are no blueprints of this 1923 ride so all measurements must be determined by you. 

Position yourself in the vicinity of the ride called, Possessed so that you have an unobstructed view of the 

first hill of the Thunderhawk. In line with the top of the hill and approximately twelve feet off the 

ground you will see a red spot. Notice that this spot is the same height as the small hump behind the hill. 

See figure one. This small hump is near the end of the ride. This height will be zero potential energy, 

thus when the coaster goes over the small hump it will have all kinetic energy and no potential energy. 

Note: potential energy is based on position relative to a zero reference level. Any height below 

the red spot would be a negative potential energy and the kinetic energy would be more than our value. 

Top of hill 

6 ft 

Top of hump 

Red dot 

Figure 1 

75

Thunderhawk 


You will find the mechanical energy you have left at the top of the small hump as a percentage of 

the mechanical energy you have at the top of the first hill. Since energy is conserved this "lost" 

mechanical energy is actually converted to small molecular motions associated with thermal energy. 

This percentage is in a sense a measure of our coaster's efficiency. 

Equations: 

1. Top of the first hill: 

Total MechanicalEnergy PE KE mgh 1 mv 2 

2 

2. Top of the hump: 

Total MechanicalEnergy KE 1 2 mV 2 

3. Fraction of Mechanical Energy Remaining 

 

 

1 

2 mV2 

mgh 1 2 mv2 

1 

2 V 2 

gh 1 2 v2 

(mass cancels) 

V 2 

 

2 gh v 2 (multiplyby two) 

4. Percentage of Mechanical Energy Remaining 

 

 

 

 

 

 

V 2 

 

2gh v 2 100 

 

76

Thunderhawk 


Procedure and Data: 

1. Using the red spot as h = 0 determine the height of the first hill given that the vertical boards are 6 feet 

long. Notice we will be using English units, so g = 32 ft/s 2 . Also the nearest whole foot will be uncertain 

so generally we will be working with two significant digits. 

Estimated height of hill as measured from the red spot 

h = _____ feet 

2. The trains are 40 ft long. Measure the time it takes the entire train to pass a vertical rail at the top of 

the hill. 

time = _________ seconds 

3. Now measure the time it takes an entire train to pass over the small hump behind the first hill. This is 

near the end of the ride. You can use the top of the hump as the reference point. You can move your 

position to line up a vertical board with this spot. 

time = _________ seconds 

Calculations: 

1. Calculate the speed v in ft/s as the train passes over the first hill. 

2, Calculate the speed V in ft/s as the train passes over the hump. 

3. Use equation 4 from the theory to calculate the percentage of the energy remaining near the end of the 

ride. 

77

Thunderhawk 


Want an "A”? Answer the following: 

1. If the weight of the train is 4000 pounds find the potential energy at the top of the first hill. Note: the 

unit "pounds" is weight, therefore mg = 4000 pounds so just multiply by h. 

The unit will be ft-lb. 

2. Find the mechanical energy "LOST" during the ride. 

3. If this energy were heat what would be the temperature increase of a cup of water (0.52 lbm) if the 

specific heat of the water were 1 BTU / ( lbm o F). Assume no heat was used to heat the container. 1 BTU 

= 778 ft lb A BTU is a British Thermal Unit 

78

The Hydra 

Introduction: This experiment is written in three different parts. Lab 1 will be using the speed of the 

Hydra train at various places on the ride along with the radius of curvature of the track at those locations 

to calculate the force factor that the rider experiences. Lab 2 will also calculate force factor but this time 

the track is banked which makes the problem a little more challenging. Lab 3 will be calculating the total 

amount of energy at various places looking at the amount of energy lost throughout the ride. 

Preliminary Data: 

The information found in the Preliminary Data section will be used throughout the Hydra Labs. 

Equipment needed: 

Stopwatch 

Vertical accelerometer 

Special thanks to Brent Ohl 79

The Hydra 

C 

D 

A 

B 

G 

E 

F 

Measure the time it takes the train to pass the reference points shown below. Start the stopwatch when 

the front of the train reaches the reference point and stop the stopwatch when the back of the train reaches 

that point. The pictures will help you find the reference points. It is recommended that at least two 

people measure the time and take the average for more accurate results. Enter the values of time in Table 

#1. 

Point A: 

The bottom of the first hill. Look for the red dot on the middle of the track. 


The Hydra 

Point B: 

The top of the zero-g roll. Use the track junction as the reference. 

Point C: 

Point D: 

The bottom of the hill just after the zero-g roll. Look for the red dot. 

The middle of the cobra roll (a.k.a. Happy Face). Use the support post as the reference 

point. 

Point E: 

The top of the camel back just after the train passes the station. Use the support post as 

the reference point. 

Point F: The middle of the spiral near the end of the ride. Use the support post as the 

reference point. 

Point G: 

The end of the ride just before entering the breaking segment. Use the first vertical post 

on the handrail as the reference point. 

Now ride Hydra and measure the force factor at Points A-F using the vertical accelerometer holding it 

parallel to your upper body. Once again, it would be best if at least two people measure the force factor 

and compare them for more accurate results. Enter the values for the force factor in the table below. 

In the table below use the descriptors; lighter, heavier, or same to describe the sensation you experienced 

at the designated locations in reference to how you feel motionless, upright. 


The Hydra 

Knowing the that the length of the train is 12.298 meters long, ∆x, and 

train at the designated locations. 

x 

v , calculate the speed of the 

t 

Table #1 

Track 

Section 

A 

Time, ∆t 

(seconds) 

Train Speed, v 

(m/sec) 

Force 

factor 

Sensation 

(lighter, heavier, 

same) 

B 

C 

D 

E 

F 

G XXX XXX 

This information will be used throughout the three labs for Hydra. 

Your weight in lbs, Fw = ________________ x 4.45 N = __________________N 

lbs 

Your mass in kg, m = 

F w 

g 

______________________ kg 


The Hydra 

Lab 1—Force Factor Analysis 

Using the orientation represented in the picture for each location, draw the force diagram of the rider. 

Then use Newton’s laws to calculate the force of the seat and force factor experienced by the rider. The 

radii of curvatures are given for each part. The speed of the train was calculated in table #1. 

Part A 

Radius of the track, r = 26.25 m 

Calculate the seat force using: 

F 

seat 

F 

w 

mv 

 

r 

2 

F 

force factor 

F 

seat 

w 

___________ 

Part B – top of zero-g roll 



F 

w 

F 

seat 

mv 

 

r 

2 

Fseat 

force factor ___________ 

Fw 

Part C – After zero-g Roll 



F 

seat 

F 

w 

mv 

 

r 

2 


The Hydra 

F 

force factor 

F 

seat 

w 

___________ 

Part D—Cobra Roll (a.k.a. Happy Face) 



F 

seat 

F 

w 

mv 

 

r 

2 

F 

force factor 

F 

Part E—Camel Back 



seat 

w 

F 

___________ 

w 

F 

seat 

mv 

 

r 

2 

F 

force factor 

F 

seat 

w 

___________ 


The Hydra 

Questions: 

1. How do the force factors you experienced while riding compare to the force factors you 

calculated using Newton’s laws? Why are the values not exactly the same? 

2. The force factors experienced from the Camel Back and the Zero-g Roll are the same, but 

the orientation of the rider is very different. Why is this the case? 

Lab 2: Force 

Factor on the 

Spiral—The 

Banked Curve of 

This activity is designed for the Honors/Advanced Placement Physics student. 

The radius of curvature of the spiral is 16.1 m. 

Using the diagram below, draw the force diagram of the rider while on the spiral (Point F) described in 

the preliminary data section. Assume there are no forces applied to the rider that are parallel to the seat. 


The Hydra 

Front view of the rider 

Using the force diagram along with force factor and speed of the train you found in the preliminary data 

section, generate the equation for the banking angle of the spiral. 

Calculate the banking angle of the spiral: 

Banking Angle, θ = _______________________ 

According to your force diagram, generate another equation to calculate the banking angle of the spiral 

and solve for it. 

Banking Angle, θ = ____________________ 


The Hydra 

Analysis: 

According to the force diagram, we made the assumption that there are no parallel forces applied 

to the rider by the seat. This means that the banking angle of the track is perfect. When dealing with 

roller coasters, this typically does not happen. This way the train “searches” for equilibrium, and the 

train will wobble from side to side while traveling around the curve similar to that of a passenger train. 

So, engineers correct this problem by not making the banking angle perfect. Does your data verify this? 

Explain. 


The Hydra 

Lab 3: Work/Energy 

considerations using 

Equipment needed: 

Stopwatch 

Inclinometer 

Power of the chain lift: 

Hold the inclinometer parallel to the lift hill and record the angle of the lift hill below: 

Angle of incline: _________________ 

Calculate the force of the chain lift, F|| to get the 12,560 kg train to the top of the hill assuming the train 

moves up the hill at constant speed. 

F|| 

θ 

mg 

θ 

mg sinθ 

F|| = mg sinθ = ___________________ 

Measure the total time the front car of the train takes to make it up the lift hill. 

Time, t = ______________________ 

Calculate the average speed v of the lift hill chain knowing the hill is 69.5 m long. 

d 

v = _________________ 

t 

Calculate the amount of work done by the chain to lift the train up the hill. 


The Hydra 

W = F|| d = ______________________ 

Calculate the power output of the chain lift motor in watts and horsepower knowing there is 746W/hp. 

P = 

W 

t 

_______________Watts = ___________________hp 

Compare the power found above to the power calculated by using the following equivalent equation: 

P = F|| v = ______________________ 

Total Energy of the train at various locations along the track (NOTE: All track height measurements 

will be in reference to the bottom of the first hill) 

Keeping in mind that gravitational potential energy is represented by the following equation: 

and kinetic energy is given by the equation: 

PE = mgh 

You can now find the total energy at any given point on the track by 

1 KE mv 

2 

2 

Where mass m is the mass of the train. 

TE = PE + KE 

Calculate the energy at the top of the lift hill: The lift hill is 32.1m. 

PE = _________________________ 

KE = __________________________ 

TEinitial = ______________________________ 

Calculate the energy at Point A: The height at A is 0 m above the bottom of the lift hill. 

PE = _________________________ 

TEA = _________________________ 

KE = __________________________ 

TEinitial - TEA = ______________________ 


The Hydra 

Calculate the energy at Point B: The height at B is 20.2 m above the bottom of the lift hill. 

PE = _________________________ 

TEB = _________________________ 

KE = __________________________ 

TEinitial – TEB = ______________________ 

Calculate the energy at Point C: The height at C is 5.5 m above the bottom of the lift hill. 

PE = _________________________ 

TEC = _________________________ 

KE = __________________________ 

TEinitial – TEC = ______________________ 

Calculate the energy at Point D: The height at D is 8.5 m above the bottom of the lift hill. 

PE = _________________________ 

TED = _________________________ 

KE = __________________________ 

TEinitial – TED = ______________________ 

Calculate the energy at Point E: The height at E is 10.1 m above the bottom of the lift hill. 

PE = _________________________ 

TEE = _________________________ 

KE = __________________________ 

TEinitial – TEE = ______________________ 

Calculate the energy at Point F: The height at F is 6.1 m above the bottom of the lift hill. 

PE = _________________________ 

TEF = _________________________ 

KE = __________________________ 

TEinitial – TEF = ______________________ 

Calculate the energy at Point G: The height at G is 7.3 m above the bottom of the lift hill. 

PE = _________________________ 

TEG = _________________________ 

KE = __________________________ 

TEinitial – TEG = ____________________ 


The Hydra 

The work energy theorem Wbrakes = KE can be used to calculate the average force needed to stop the 

train when it reaches the braking section of the ride. 

The kinetic energy of the train just before the brakes are applied is the KE at Point G. 

The kinetic energy of the train when the train stops is 

KEG = ________________________ 

KEstop = _______________________ 

Calculate the amount of work needed to stop the train: 

Wbrakes = _____________________ 

Calculate the average force applied to the train by the brakes knowing W = Fd and the distance the brakes 

are applied to the train is 6.2 m. 

Fbrakes = _______________________ 

Questions: 

1. Is the total energy the same at every point on the track you measured? Should it be the 

same—Explain. 

2. How much energy was lost on the ride? What is the cause of this loss of energy? 

3. It was mentioned previously that the brakes apply an average force to the train. Explain 

why it is an average force and not an instantaneous force. 


The Hydra 

4. You calculated the total amount of energy of the train at the top of the lift hill. Where did 

that energy come from? 

Critical Thinking Problem: 

Try to calculate the average frictional force applied to the train starting at the top of the lift 

hill to Point G given the length of the track being approximately 810 m. 

Lab 4: The JoJo 

Roll of. . . 

This is a short conceptual activity using the JoJo Roll of the Hydra. The JoJo roll is the first element 

when leaving the station. This element is quite unique to roller coasters. 

Part 1 

Go to the Cobra Roll side of the ride facing the "happy face" to get a front view of the train 


The Hydra 

passing through the JoJo Roll. 

Question: 

1. Estimate your force factor just before entering the roll. Explain your reasoning. 

2. Estimate your force factor when you are upside down in the roll. Explain your reasoning. 


The Hydra 

Part 2: 

While riding through the JoJo Roll, hold one vertical accelerometer upside down, hold one horizontally 

left, hold one horizontally right, and hold one right side up. 

Questions: 

1. What was the difference in force factor during the JoJo Roll? Explain your reasoning. 

2. Compare the JoJo roll to other roller coasters that go upside down with regards to the 

weightless feeling and the force factor. 

3. Since you are going upside down, can you do something to the ride to create a weightless 

feeling on the JoJo roll? Why/Why not. 

4. The JoJo is considered a heartline roll. By watching the train pass through the roll, explain 

the meaning of heartline roll. 


Interpreting Graphs 

Part I: - Directions: Using Graph 1 and 2 below answer the questions found below the graphs. 

Graph 1: Dominator: Shot Downward 

Questions: 

1. A. If you and a friend were watching and waiting in line to ride the Dominator, 

at what point of the drop would you tell him/her on the ride that they will 

experience a feeling of weightlessness? 

B. At what time interval does this occur at according to the graph? 

____________________________________ 

2. If zero altitude is your starting position on the Dominator, according to the 

graph how high does the Dominator climb before dropping you? 

__________________________________ 

3. The same friend you advised in question #1 is afraid that the Dominator is 

going to drop straight to the ground. According to graph 1, how much distance 

is between the ground and the lowest point on the first drop? 

__________________________________ 

95


4. From the graph of The Dominator, notice that the ride lasts longer than 120 

seconds. From your interpretation of the first 120 seconds of the ride, and after 

looking at the ride in the park, draw what you think the altitude and the x- 

acceleration due to gravity would look like if the graph actually took into 

account the ENTIRE ride. 

Hint: Take a stop watch and see how much longer the ride actually goes and 

how many more up and down motions the ride will experience after the 120 

seconds represented on the graph. 

Graph 2: Revolution 

5. According to graph #2 (Revolution), how many revolutions actually occurred in 

the 120 seconds? 

______________________________________________ 

6. What is the correlation between the altitude and the G forces acting on the x- 

axis according to the data obtained from Revolution? 

_______________________________________________ 

7. If you think of Revolution as a pendulum, at what point would you experience 

the greatest G forces? The highest peak or at the lowest point in the ride? 

___________________________________ 

96


Explain how you determined this by using specific references to the graph. 

______________________________________________________________________________ 

______________________________________________________________________________ 

______________________________________________________________________________ 

______________________________________________________________________________ 

________________________________________________ 

8. After viewing the ride “Revolution” compare the graph to the actions of the 

actual ride. Notice again that the entire ride is not present on the graph. If 

“Revolution” runs an identical path each time it operates, do you think the g- 

force shown on the graph has reached its highest peak? If not, how many more 

peaks would there be before it reaches its highest peak? 

______________________________________________________________________________ 

______________________________________________________________________________ 

____________________________________________________________ 

Part II 

Directions: For the following Graphs A – J, match the graph with the ride in 

Dorney Park. Answer the questions after all the graphs. 

Graph A 

97


Graph B 

Graph C 

98


Graph D 

Graph E 

99


Graph F 

Graph G 

100


Graph H 

Graph I 

Graph J 

101


Dorney Park Ride 

Apollo 2000 

Wave Swinger 

Thunderhawk 

Steel Force 

The Hydra: Revenge 

Talon 

Enterprise 

Music Express 

Dominator: Being Shot Up 

Sea Dragon 

Matching Graph Letter 

____________________________ 

____________________________ 

____________________________ 

____________________________ 

____________________________ 

____________________________ 

____________________________ 

____________________________ 

____________________________ 

____________________________ 

Analysis 

1. Write a brief statement that describes your reasoning for selecting the graph you 

did for Thunderhawk? Were there specific details on the graph that made you 100% 

sure that this graph was the graph for Thunderhawk? 

____________________________________________________________________________________ 

____________________________________________________________________________________ 

________________________________________________ 

2. Which graphs to rides interpretations were the hardest to make? For what reasons 

were they the most difficult? 

____________________________________________________________________________________ 

____________________________________________________________________________________ 

________________________________________________ 

3. Which rides had the most similar graphs? Why do you think they have similar 

graphs? 

____________________________________________________________________________________ 

____________________________________________________________________________________ 

____________________________________________________________________________________ 

____________________________________ 

4. On graph I, what trend do you notice about the G forces when the altitude is at its 

peak versus when the altitude has reached its low point? 

____________________________________________________________________________________ 

____________________________________________________________________________________ 

____________________________________________________________________________________ 

_________________________________ 

102

Possessed 

Preliminary Data: 

Your weight in pounds = ________________lb X 4.45 N/lb = ___________________N 

weight in Newtons 

Your mass, m in kilograms = 

___________________kg 

2 

9.8m 

sec 

Mass of loaded train = 13,065 kg 

Length of the train = 15.75 m 

Measure the time it takes for the train to do its first launch (L1) from rest. Suggestion: Use the center of 

the train as your reference point. This is the time it takes the train to be accelerated by the LIMs (linear 

induction motors). You may want to stand back from the ride to get a better overall view of the station to 

take your measurements. 

tL1 = ____________________sec 

Measure the time it takes for the train to pass through the second boost which is the same time it takes to 

pass through the station after the first launch. 

here (x = 60 m) here 

tL2 = ____________________sec 

103

Possessed 

Measure the time it takes for the train to pass through the first braking pass in the station. 

tB1 = ____________________sec 

Measure the time it takes for the train to pass through the second braking pass in the station. 

tB2 = ____________________sec 

Section 1: Linear Acceleration 

1. Since the distance that the train is traveling during its first launch is 48 m and the train starts from 

rest, use the linear equation given to calculate the average constant acceleration of the first launch. 

Remember that you measured the time. 

1 2 

x v 

i t at 

2 

Acceleration of the launch, a = ____________________m/sec 2 . 

2. Assuming no friction, calculate the average net force you experience. 

Favg = ma _______________________N 

3. Calculate the average amount of work the LIM’s do on you during the launch knowing the 

distance traveled during the launch given in #1. 

W = Fdcos______________________J 

4. Calculate your force factor you experience while launching. 

104

Possessed 

ff = 

F avg 

weight 

______________________ 

5. Using a linear equation given, calculate the speed of the train upon reaching the vertical section 

of the track. 

2 2 

v v 2ax 

OR v v at 

f 

i 

f 

i 

vL1 = _________________________m/sec 

6. For the students with the CENCO lateral accelerometers, get in line and ride POSSESSED. 

While in line, secure and familiarize yourself with the lateral accelerometer. When on the ride, 

have your lateral (horizontal) accelerometer ready for launch. Position the accelerometer as 

instructed by your teacher. Measure the average lateral force factor of the first launch by 

recording the average location of the BB’s in the tube. 

ff = ____________________ 

Alt. 6. For students with the PASCO or handmade lateral accelerometers, get in line and ride 

POSSESSED. While in line, secure and familiarize yourself with your version of the inclinometer (used 

as a lateral accelerometer). When on the ride, have your inclinometer ready for launch. Position the 

accelerometer as instructed by your teacher. Measure the average angle of the first launch. 

Calculate the accelerating force, FN on you by using the following: 

θ 

θ 

Fnety = may 

FN cosθ – w = may 

FN cosθ – w = 0 

FN cosθ = w 

w 

Calculate your force factor while launching. 

ff = 

F N 

weight 

_____________________ 

Compare your results with that calculated in #4 elaborating on reasons for errors. 

105

Possessed 

Section 2: Work/Energy considerations for the Launch and Boost 

7. Using the conservation of energy and the speed of the train after the initial launch found in 

procedure 5, calculate the height of the train on the spiral section of the track. 

KEL1 = PEvert. 

1 

mv 

2 

 

2 

L1 

mgh vert 

h = _________________________m 

8. Using the work/energy theorem and the values found in #6, calculate the average amount of work 

the LIM’s do on you during the first launch using the 

W 

LIM 

WLIM = KE 

1 2 1 

mvL 

1 

mvi 

2 2 

2 

W = _______________________J 

9. Now calculate the average amount of work the LIM’s do on the train during the first launch. 

WLIM = KE 

1 2 1 2 

WLIM 

mvL 

1 

mvi 

2 2 

W = _______________________J 

106

Possessed 

10. Calculate the average power delivered by the LIMs to the train during the first launch. 

P = 

W 

t L1 

_______________________W 

OPTIONAL: 11. Calculate the average current supplied by the LIMs during the launch. The voltage 

provided to each LIM during launch is 240 V and assuming there are 4 LIMs operating at any given time. 

(NOTE: This is an over simplified version as to what actually is occurring electrically during the 

launch.) 

P = current x voltage 

Current = _______________________amperes 

12. Assuming no friction, the speed of the train at the end of the first launch must the same as the 

speed of the train at the beginning of the second boost because of the conservation of energy. 

Knowing the speed of the train at the end of the first launch given in procedure 5, the distance 

(xL2 = 60.0 m) of the train during the boost (see picture on page 1), and the time it takes for the 

second boost from the initial data, calculate the acceleration and speed of the train after the 

second boost using the given linear equation. 

1 2 

xL2 

vL 

1t 

at AND vL2 

vL 

1 

at 

2 

aL2 = _________________________m/sec 2 and vL2 = _____________________m/sec 

12. Using the work energy theorem, calculate the average amount of work on the train to accelerate it 

through the second boost. 

WLIM = KE 

1 2 1 2 

WLIM 

mvL2 

mvL 

1 

2 2 

W = _______________________J 

13. Calculate the average net force on the train for the second boost using the equation. 

107

Possessed 

F 

ma 

OR 

W F( 2)cos 

net 

x L 

F = _______________________N 

14. Compare the force of the second boost to that of the first launch. Are they same or different and 

why? 

15. Using the conservation of energy and the speed of the train after the second boost, calculate the 

height of the train on the straight vertical section of the track. 

KEL1 = PEvert. 

1 

mv 

2 

 

2 

L2 

mgh vert 

h = _________________________m 

108

Possessed 

Section 3: The Vertical Braking 

The train gets stopped for 1 second by standard mechanical clamp brakes when it reaches its highest 

point of approximately 37 m as measured from the center of the train on the straight vertical section of 

the track. 

16. How energy does the train have while held 

stationary by these brakes at this height? 

PE train 

mgh 

W = ________________________J 

17. How much power is delivered by the brakes at this 

point? 

PEtrain 

P 

t 

P = _________________________W 

18. How much force must the brakes be applying to the train to keep it held in this vertical position? 

Force = ________________________N 

Section 4: Stopping the train at the end of the ride 

19. Using the conservation of energy, calculate the speed of the train upon entering the station after 

the vertical brake. 

PE KE 

mgh 

vert. 

brake 

vert. 

brake 

 

1 

2 

station 

mv 

2 

station 

109

Possessed 

vstation = ___________________________m/sec 

20. You know the distance and the time, tB1, for the train to pass through the braking pass while 

passing through the station. You also know how fast the train is moving upon entering the station 

along with the initial speed upon entering the station from procedure 19. Calculate the 

acceleration and speed of the train at the end of the first braking pass through the station by using 

the equations. 

1 2 

xstation 

vstationt 

at AND vB 

1 

vstation 

at 

2 

aB1 = _____________________m/sec 2 and vB1 = _______________________m/sec 

21. Calculate the amount of work required to slow the train in the first braking pass. 

W 

LIM 

WLIM = KE 

1 2 1 

mvB 

1 

mv 

2 2 

2 

station 

WB1 = ________________________J 

22. Calculate the average force the LIMs apply to the train to slow it down during the first braking 

pass. 

ma OR W F( x)cos 

F net 

Favg = __________________________N 

110

Possessed 

23. Since the train stops during it second braking pass through the station, calculate the amount of 

work required to slow the train in the second braking pass. 

WLIM = KE 

1 

WLIM 

mv 

2 

2 

0 

B1 

WB2 = ________________________J 

24. Calculate the average force the LIMs apply to the train to slow it down during the second braking 

pass. 

W F x 

cos 

 

Favg = __________________________N 

25. Compare the work done or force applied by the LIMs to launch the train at the beginning of the 

ride to that in braking the train. Be sure to explain your reasoning. 

111

Possessed 

Section 4: Vertical Sections of the Ride 

. In this section of the lab, you will be looking at the vertical sections of the track to see if the spiral 

vertical section of the track affects freefall. Secure the vertical accelerometer as shown in the 

diagram below. This orientation is for when you are on the spiral vertical section of the track. 

Reverse the accelerometer for the straight vertical section of the track. You will need to orient the 

accelerometer so that the weight hangs suspended by the spring when the train is on these sections 

of the track. 

Spiral side 

straight side 

When the train is at the highest on these sections of the track, record the force factor. Be sure you 

are not recording the force factor while the train is being stopped on the straight vertical section of 

the track. 

If you do not have a vertical accelerometer, you can use a stopwatch to measure the time it takes 

for the train to freefall on these sections. 

Vertical Spiral section of track 

ffspiral or time = ________________ 

Vertical straight section of track 

ffstraight or time =________________ 

112

Possessed 

Explain any differences in the force factor on these two sections of track. Should there be a difference? 

Why or why not? 

Section 5: The Upward Curved Sections and Centripetal Force 

In this section of the lab you will calculate the radius of each vertical curve by using the force factors 

and speeds that you measure. This section can be done as a stand-alone activity or can utilize the 

data from the previous sections. You can use the speeds from the previous sections. It would be 

helpful if you have several students taking measurements at the same time. 

Measure the time the train takes to pass the lone vertical support post outside of the station on each side 

of the station shown in the picture. If time permits, measure the speed at these points for one, 

two, or three passes. The more data you have, the more accurate your calculations. Enter the data 

into the table below. 

By knowing the length of the train given in the preliminary data at the beginning of the lab, calculate the 

speed of the train just as it enters the vertical curves. Enter the data in the table below. 

Secure the vertical accelerometer and measure the force factor you experience while passing through the 

curves for each pass you predetermined. Be sure you are measuring the force factor that 

corresponds to the time you measured. Also, be sure that you are holding the vertical 

accelerometer parallel to your body as shown in the picture on the next page. 

113

Possessed 

Pass 

time 

(sec) 

Spiral side 

speed 

(m/sec) 

force 

factor 

radius 

(m) 

time 

(sec) 

Vertical Side 

speed 

(m/sec) 

force 

factor 

radius 

(m) 

1 

2 

3 

According to the free-body diagram and the two expressions given, 

Fseat 

ac 

F 

ff 

w 

F 

seat 

seat 

w 

mv 

r 

2 

w 

1. Derive an expression for calculating the radius of curvature of the track. 

2. Calculate the radius of curvature for each curve and enter the data into the table on the 

previous page. 

QUESTIONS: 

1. Compare the radius on the straight side and the spiral side of the ride. 

114

Possessed 

2. As the speed increased, explain what happened to the force factor. 

3. As the speed increased, explain what happened with the radius? 

4. If the radius was smaller, what would happen to the force factor? Speed? Support your answer. 

115

Coaster Quest 

Pennsylvania Standards in Science and Technology 

Unifying Themes 

Academic 

Standard 

Standard 

Category 

3.1.10 C 

Standard 

Statement 

C. Apply 

patterns as 

repeated 

processes or 

recurring 

elements in 

science and 

technology. 

Content 

Descriptors 

Examine and 

describe physical 

patterns in motion. 

Performance 

Tasks and 

Associated 

Learning 

Activities 

Antique Carrousel 

Apollo 2000 

Enterprise 

Ferris Wheel 

Revolution 

Sea Dragon 

Steel Force 

Wave Swinger 

White Water 

Landing 

Unifying 

Themes 

3.1.10 D 

3.1.12 C 

3.1.12 D 

D. Apply scale as a 

way of relating 

concepts and 

ideas to one 

another by 

some measure. 

C. Assess and 

apply patterns in 

science and 

technology. 

D. Analyze scale as 

a way of relating 

concepts and 

ideas to one 

another by 

some measure. 

Apply dimensional 

analysis and scale as a 

ratio. 

Assess and apply 

recurring patterns 

in natural and 

technological 

systems. 

Compare and 

contrast structure and 

function relationships 

as they relate to 

patterns. 

Assess patterns in 

nature using 

mathematical 

formulas. 

Assess the use of 

several units of 

measurement to the 

same problem. 

Analyze and apply 

appropriate 

measurement scales 

when collecting data. 


Dominator 

Enterprise 

Sea Dragon 

Steel Force 


Apollo 2000 

Dominator 

Enterprise 

Ferris Wheel 

Revolution 

Sea Dragon 

Steel Force 

Wave Swinger 



Apollo 2000 

Dominator 

Enterprise 

Ferris Wheel 

Revolution 

Sea Dragon 

Steel Force 

Wave Swinger 


116

Coaster Quest 


Inquiry and Design 

Academic 

Standard 

Standard 

Category 

3.2.7 A 

3.2.4 B 

Standard 

Statement 

A. Explain and apply 

scientific and technological 

knowledge. 

B. Describe objects in the 

world using the 

five senses. 

Content 

Descriptors 

Answer “What if” questions based 

on observation, inference or prior 

knowledge or experience. 

Recognize observational 

descriptors from each of the five 

senses (e.g., see-blue, feel-rough). 

Use observations to develop a 

descriptive vocabulary. 

Performance 

Tasks and 

Associated 

Learning 

Activities 


Apollo 2000 

Dominator 

Enterprise 

Revolution 

Sea Dragon 

Steel Force 

Wave Swinger 


Apollo 2000 

Dominator 

Enterprise 

Sea Dragon 

Steel Force 

Wave Swinger 

Inquiry and 

Design 

3.2.7 B 

3.2.10 B 

B. Apply process 

knowledge to make and 

interpret observations. 

B. Apply process 

knowledge and organize 

scientific and 

technological phenomena 

in varied ways. 

Measure materials using a variety 

of scales. 

Describe relationships by making 

inferences and predictions. 

Communicate, use space / time 

relationships, define operationally, 

raise questions, formulate 

hypotheses, test and experiment, 

Design controlled experiments, 

recognize variables, manipulate 

variables. 

Interpret data, formulate models, 

design models, and produce 

solutions. 

Develop appropriate scientific 

experiments: raising questions, 

formulating hypotheses, testing, 

controlled experiments, recognizing 

variables, manipulating variables, 

interpreting data, and producing 

solutions. 


Apollo 2000 

Dominator 

Enterprise 

Ferris Wheel 

Revolution 

Sea Dragon 

Steel Force 

Wave Swinger 



Apollo 2000 

Dominator 

Enterprise 

Ferris Wheel 

Revolution 

Sea Dragon 

Steel Force 

Wave Swinger 


117

Coaster Quest 



Academic 

Standard 

Inquiry and 

Design 

Standard 

Category 

3.2.12 B 

3.2.10 C 

3.2.12 C 

Standard 

Statement 

B. Evaluate experimental 

information for 

appropriateness and 

adherence to 

relevant science 

processes. 

C. Apply the elements of 

scientific inquiry to solve 

problems. 

C. Apply the elements of 

scientific inquiry to solve 

multi-step problems. 

Content 

Descriptors 

Evaluate experimental data 

correctly within experimental 

limits. 

Judge that conclusions are 

consistent and logical with 

experimental conditions. 

Interpret results of experimental 

research to predict new information 

or improve a solution. 

Generate questions about objects, 

organisms and/or events that can be 

answered through scientific 

investigations. 

Evaluate the appropriateness of 

questions. 

Conduct a multiple step 

experiment. 

Organize experimental information 

using a variety of analytic methods. 

Judge the significance of 

experimental information in 

answering the question. 

Suggest additional steps that might 

be done experimentally. 

Generate questions about objects, 

organisms and/or events that can be 

answered through scientific 

investigations. 

Evaluate the appropriateness of 

questions. 

Organize experimental information 

using analytic and descriptive 

techniques. 

Evaluate the significance of 

experimental information in 

answering the question. 

Project additional questions from a 

research study that could be studied. 

Performance 

Tasks and 

Associated 

Learning 

Activities 


Apollo 2000 

Dominator 

Enterprise 

Ferris Wheel 

Revolution 

Sea Dragon 

Steel Force 

Wave Swinger 



Apollo 2000 

Dominator 

Enterprise 

Revolution 

Sea Dragon 

Steel Force 

Wave Swinger 


Apollo 2000 

Dominator 

Enterprise 

Ferris Wheel 

Revolution 

Sea Dragon 

Steel Force 

Wave Swinger 


118

Coaster Quest 



Academic 

Standard 

Standard 

Category 

Standard 

Statement 

Content 

Descriptors 

Performance 

Tasks and 

Associated 

Learning 

Activities 

Inquiry and 

Design 

3.2.10 D 

3.2.12 D 

D. Identify and apply the 

technological design 

process to solve 

problems. 

D. Analyze and use the 

technological design 

process to solve 

problems. 

Examine the problem, rank all 

necessary information and all 

questions that must be answered. 

Assess all aspects of the problem, 

prioritize the necessary information 

and formulate questions that must 

be answered. 


Apollo 2000 

Dominator 

Enterprise 

Sea Dragon 

Steel Force 

Wave Swinger 


Apollo 2000 

Dominator 

Enterprise 

Sea Dragon 

Steel Force 

Wave Swinger 

119

Coaster Quest 


Physical Science 

Academic 

Standard 

Standard 

Category 

Standard 

Statement 

Content 

Descriptors 

Performance 

Tasks and 

Associated 

Learning 

Activities 

Physical 

Science 

3.4.4 C 

C. Observe and 

describe different 

types of force and 

motion. 

Describe various 

types of motions. 

Compare the relative 

movement of 

objects and describe 

types of motion 

that are evident. 

Describe the 

position of an object 

by locating it relative 

to another object or 

the background (e.g., 

geographic direction, 

left, up). 


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3.4.7 C 

C. Identify and 

explain the 

principles of force 

and motion. 

Explain various 

motions using models. 

 


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Physical Science 

Academic 

Standard 

Physical 

Science 

Standard 

Category 

3.4.10 C 

3.4.12 C 

Standard 

Statement 

C. Distinguish 

among the 

principles of force 

and motion. 

C. Apply the 

principles of motion 

and force. 

Content 

Descriptors 

Know Newton’s laws 

of motion 

(including inertia, 

action and 

reaction) and gravity 

and apply them to 

solve problems 

related to forces and 

mass. 

Determine the 

efficiency of 

mechanical systems 

by applying 

mathematical 

formulas, concepts 

through words, 

models and 

mathematical 

symbols. 

Analyze the 

principles of 

translational motion, 

velocity and 

acceleration as they 

relate to free fall and 

projectile motion. 

Analyze the 

principles of 

rotational motion to 

solve problems 

relating to angular 

momentum, and 

torque. 

Interpret a model 

that illustrates 

circular motion and 

acceleration. 

Describe inertia, 

motion, equilibrium, 

and action/reaction 

concepts through 

words, models and 

mathematical 

symbols. 

Performance 

Tasks and 

Associated 

Learning 

Activities 


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121

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Technological Devises 

Academic 

Standard 

Technological 

Devises 

Standard 

Category 

3.7.7 A 

3.7.7 B 

3.7.10 A 

Standard 

Statement 

A. Describe the 

safe and 

appropriate use of 

tools, materials 

and techniques to 

answer questions 

and solve 

problems. 

B. Use appropriate 

instruments and 

apparatus to study 

materials. 

A. Identify and 

safely use a variety 

of tools, basic 

machines, materials 

and techniques to 

solve problems and 

answer questions. 

Content 

Descriptors 

Identify uses of 

tools, machines, 

materials, 

information, people, 

money, energy and 

time that meet specific 

design criteria. 

Describe safe 

procedures for using 

tools and materials. 

Assess materials for 

appropriateness of 

use. 

Select appropriate 

instruments to 

measure the size, 

weight, shape and 

temperature of living 

and non-living 

objects. 

Apply knowledge of 

different 

measurement systems 

to measure 

and record objects’ 

properties. 

Select and safely 

apply appropriate 

tools, materials and 

processes necessary 

to solve complex 

problems. 

Apply advanced tool 

and equipment 

manipulation 

techniques to solve 

problems. 

Performance 

Tasks and 

Associated 

Learning 

Activities 


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Academic 

Standard 

Technological 

Devises 

Standard 

Category 

3.7.10 B 

3.7.12 A 

Standard 

Statement 

B. Apply 

appropriate 


apparatus to 

examine a variety 

of objects and 

processes. 

A. Apply advanced 

tools, materials 

and 

techniques to 

answer complex 

questions. 

Content 

Descriptors 

Describe and use 

appropriate 

instruments to gather 

and analyze data. 

Compare and 

contrast different 

scientific 

measurement 

systems; select the 

best measurement 

system for a specific 

situation. 

Explain the need to 

estimate 

measurements within 

error of various 

instruments. 

Apply accurate 

measurement 

knowledge to solve 

everyday problems. 

Select and safely 

apply appropriate 

tools, materials and 

processes necessary 

to solve complex 

problems that could 

result in more than 

one solution. 

Evaluate and use 

technological 

resources to solve 

complex multi-step 

problems. 

Performance 

Tasks and 

Associated 

Learning 

Activities 


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Academic 

Standard 

Technological 

Devises 

Standard 

Category 

3.7.12 B 

Standard 

Statement 

B. Evaluate 

appropriate 


apparatus to 

accurately 

measure 

materials and 

processes. 

Content 

Descriptors 

Apply and evaluate 

the use of 

appropriate 

instruments to 

accurately measure 

scientific and 

technologic 

phenomena within the 

error limits of the 

equipment. 

Evaluate the 

appropriate use of 

different 


(macro and micro). 

Evaluate the utility 

and advantages 

of a variety of absolute 

and relative 


for their appropriate 

application. 

Performance 

Tasks and 

Associated 

Learning 

Activities 


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Enterprise 

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Revolution 

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124

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