Physics and Astronomy Night At Elitch Gardens

Transcription

Physics and
Astronomy Night
At Elitch Gardens
This curriculum book is developed by:
DEPARTMENT OF PHYSICS AND ASTRONOMY
Accelerate into your future in science!
Begin now - www.du.edu/physastron
INTRODUCTION
Welcome to Physics and Astronomy Night at Elitch Gardens! The park will be open
to physics/physical science students and their teachers from 4 p.m. a.m. to 8:00 p.m
with all day access to the park starting at 9 a.m.
In this booklet, we provide a variety of materials for teachers and students to take advantage of
some of the many educational opportunities at Elitch Gardens. Feel free to duplicate any of these
materials. Please do not distribute information in Section 5. It contains ride
specifications—these often contain the actual values that students are asked to estimate or
calculate. We have tried to provide materials that will give maximum flexibility for in use in the
classroom.
1. Suggestions for Making Measurements. In this section are some ideas on measuring time,
distance, angles, and accelerations related to various rides, as well as some suggestions for
equipment that can be built in the classroom and brought to Physics Night. NOTE!!!
Accelerometers will not be allowed on any ride on which the rider is inverted. e.g. Mind
Eraser, Sidewinder, Boomerang.
2. Estimation Problems –Fermi Questions. This section invites students to make order of
magnitude estimations concerning quantities at the park. Students will need to make some
assumptions about quantities (e.g., number of hot dogs consumed per person) to determine
the magnitude of some of the quantities. Answers are not provided, but the quality of the
assumptions made and the consideration of influencing factors should be reflected in the
teacher-based grading.
3. Ride-related activities. The activities for each ride are divided into three parts.
Part 1 – These questions generally do not require any calculations or estimations. The
questions ask for information about sensations and other observables. These questions should
be appropriate for all students regardless of physics background.
Part 2 – These questions generally require the students to make estimates or timings. For
estimates, students are asked to describe their method. The calculations generally involve
substituting into provided equations. This section would be most appropriate for physical
science students or students in a physics course that does not emphasize mathematics.
Part 3 – These questions generally provides minimal guidance for calculating quantities. It
relies on a student’s understanding of physics relationships and vectors including
trigonometric relationships. This section would be most appropriate for physics students.
Data for Parts 1 and 2 need to be collected during Physics Night; however, the calculations
and descriptions could be completed later at school. Part 3 information often relies on data 1
Introduction from Part 2 and often requires that some measurements using accelerometers or
protractors be made at the park. Much of the analysis of the data could be done at a later
time.
4. Physiology of Amusement Park Rides. Questions on this page invite students to be
thoughtful about a variety of physiological responses to typical rides.
5. Specifications for Elitch Gardens Rides - Data for several rides at Elitch Gardens
are presented in this section. These data are provided to assist teachers in designing
studies for their students, including the use of the activities materials provided in this
booklet. Because some of these data may be relevant to Physics Night Challenges,
we request that teachers do not give these data sheets to students.
Many teachers who use these materials have their students work in teams to gather data and
complete the activity sheets. No student should be forced to participate in any ride. Most
activities can be completed without actually riding the ride. Estimates and measurements can be
made from the ground. Safety is a concern of Elitch Gardens and should be for your students as
well.
This booklet is the result of significant work done by Steven Iona at the University of Denver,
Department of Physics and Astronomy 2112 E. Wesley Ave. Denver, CO 80208. It built on
earlier drafts done by Rob Davies and activities drawn from similar manuals used at
Kennywood, Wyandot Lake and Riverside theme parks. Gretchen Swanson, Columbine High
School, Albert Thompson, Ponderosa High School, and Herschel Neumann, University of
Denver provided editorial review.
The entire Physics and Astronomy Night program including this booklet is a work in progress.
Your comments and suggestions can improve the program. Please send your remarks to:
Angela Wilson
303.572.4502
[email protected]
Special Events
Elitch Gardens Theme Park & Water Park
299 Walnut Street
Denver, CO
Tickets can be purchased online at ElitchGardens.com
Contents
Suggestions for Making Measurements
Estimation Problems - Fermi Questions
The Mind Eraser
Tower of Doom
Big Wheel
Troika
Carousel
The Sea Dragon
The Sidewinder
The Dragon Wing
Physiology of Amusement Park Rides
Ride Specifications (Please do not distribute this information to the students.)
Further Curriculum Resources
4
Suggestions For Making Measurements
Time
The times that are required in the amusement park problems can easily be measured using
a watch with a sweep second hand or a digital watch having a stopwatch function. When
measuring the period of a ride like the Tilt-a-Whirl, measure the time for several
repetitions of the motion. This will give you a better estimate of the period of the motion
than just measuring one repetition. When measuring a single event on a ride (for example
the time required for the Boomerang Coast-to-Coaster to complete one loop), measure the
time for several trains and average them.
Distance
Since you cannot interfere with the normal operation of the rides, you will not be able to
directly measure heights, diameters, etc. All but a few of the distances needed in the
following problems will have to be measured remotely. Following are a few suggestions
on how to obtain reasonable estimates of needed distances.
Pacing – Determine the length of your stride by walking at your normal rate over
a
measured distance, for example, the length of the football field at school.
Count the
number of steps you take to cover this distance. Knowing the distance and the number of
steps taken, the average distance covered per step can be determined.
Knowing you
distance per step, horizontal distances can be paced off and estimated.
This technique
can be used, for example, to determine the diameter of the Big Wheel.
Ride structure – Distance estimated can be
made by noting regularities in the structure of
d
d
the ride.
For example, the track on the
Twister II has regularly spaced cross-members
as shown in Figure A. The distance d can be
estimated and by counting the number of
cross-members, distance along the track can
be determined.
Such an estimate of the
distance between the supporting members can
Figure A
aid in determining vertical and horizontal
distances, which can also be used to determine
the angle of inclines. In the past, some students have taken photographs of a structure
and knowing one distance in the photograph, used scaling techniques to determine other
distances along the ride.
Soda Straw
Triangulation – For measuring heights by
triangulation, a device such as that shown
in Figure B can be constructed. As will be
discussed later, this gadget also can be
used as an accelerometer. The way this
gadget is used is shown in Figure C.
Suppose the height h of the Total Tower

Protractor
String
Weight

Figure B
2
must be determined.
First the
distance L is estimated by pacing it
off or by some other suitable
methods. Sight through the soda
straw at the top of the tower and
read the angle
 from the
protractor. Then since
tan   h
h

L
Figure C
L
h is given by
h  L � (tan )
A similar device can be used to measure horizontal
moveable pin
d
distances that cannot be easily paced off.
Using a
piece of cardboard (a shoebox top works well) and
three straight pins, the triangulator shown in Figure
c
D can be made.
Suppose the distance d is to be
b
measured. Pace off or estimate the baseline L shown
a
in Figure E. Sight along fixed pins a and b toward
fixed pins
one end of the distance d. While the triangulator is
in this position, line up the moveable pin c so that
Figure D
your line of sight from pin a to c extends to the other
end of the unknown distance d. Figure E shows that triangles aop and abc are similar.
Thus,
p
d bc

L ab
or


a
c
d
o
b
� bc �
d  ��
�� L
Ł abł�
L
Figure E
If it is difficult to measure or estimate the
length of the base line, L, (in Figure C or
Figure E) because it is impossible to get
close to the structure, the following
technique can be used. Suppose the height
h in Figure F is to be determined. Standing
back at some distance from the object,
measure the angle 1. Walk directly toward
the object a distance D and measure angle
2. Knowing 1, 2, and D, the height h
h
1
2
D
Figure F
3
can be calculated using the expression
sin 1 � sin  2 
h =Œ
œ� D
 sin(2  1 ) 
Speed
The average speed of an object is given by
d
t
where d is the distance traveled in time t. This is pretty straight forward since d and
t can be measured as discussed above. However, there are two basic types of speed
computations. First there are problems in which the speed is fairly constant, and second,
those in which the speed is changing. When the speed is constant , a fairly long t can be
measured. For example, on the Big Wheel, the speed of rotation is constant so if
n
revolutions occur in time t, the speed is given by
v ave 
d n � circumference n2R


t
t
t
When the speed is changing and the speed needs to be estimated at a particular point
along the ride, the time interval should be as short as possible. This involves determining
how far the object moves in this short interval of time. On the Mind Eraser for example,
the speed at a certain point along the track must be found. One simple way of doing this
is to measure the length of the train and the time required for the entire train to pass a
certain point on the track. The train’s speed then is given by
v ave 
v ave 
length of train
d

t time to pass point
In a situation where it can be assumed that the total mechanical energy is conserved, the
speed of an object can be calculated using
A

energy considerations. Suppose the speed at
point B is to be determined on The Mind
Eraser (see Figure G). Then from the
B
hA
hB
principle of conservation of total mechanical
energy it follows that
1
mghA  1 mv2A  mghB  mv 2B
Figure G
2
2
Solving for vB:
v B  2g(hA  hB )  v2A
Thus, by measuring the speed of the train at point A and the heights hA and hB, the speed
of the train at point B can be calculated.
4
Acceleration
(NOTE!!! Accelerometers will not be allowed on any ride on which the rider is
inverted. e.g. Mind Eraser, Sidewinder, Boomerang)
A simple device for measuring vertical accelerations
(either up or down) is a 0-5 newton spring scale with a
100 gm mass attached. When measuring vertically
upward accelerations such as at the bottom of the Tower
of Doom, the spring scale is held vertically as in Figure

H. The forces on the mass are as drawn, where Fs is the
reading on the scale. Applying Newton’s second law,
Fs  mg  ma
m
Thus the acceleration, a, of the mass (and also of the
person holding the scale), is given by
F  mg F
a s
 sg
m
m
If the person is holding the scale upside down (for example, at the
top of the loop of the Side Winder), the forces on m are as
diagrammed in Figure I. Again applying Newton’s second law ,
the acceleration of the mass m is given by
a  � � F s  g ��
Łm
ł
In either situation then, the acceleration can be calculated by
knowing Fs.
forces on mass
when scale is
right side up:
Fs

Fs
mg
Figure H
forces on mass
when the scale is
upside down:

mg
Fs
Figure I
For those who do not have a spring scale to build the accelerometer shown in Figure H, a
similar device can be built out of a clear plastic tube (such as a tennis ball container), a
rubber band, and three fishing sinkers.
rubber
1. Attach the rubber band to the center of the top of th e
band
tube’s lid. You might use tape or a paper clip.
2. Screw the lid to the top of the tube.
sinker
-1g
3. Mark on the outside of the tube the location of th
e
0g
bottom of the rubber band. Identify this mark as “-1g”.
1g
4. Remove the lid and permanently attach one sinker t o
the bottom of the rubber band.
2g
5. Screw the lid back on and mark on the tube th
e
location of the bottom of the rubber band. Identify thi s
mark as “0g”.
6. Temporarily add a second sinker to the bottom of the rubber band, and again mark
the tube at the location of the bottom of the rubber band. Identify this mark as
“1g”.
7. Temporarily hang a third sinker. Mark the location of the bottom of the rubber
band as “2g”.
5
8. Remove the 2nd and 3rd sinkers, fasten the lid on the tube and it is ready for use.
To use this accelerometer hold it vertically. Read your vertical acceleration by noting the
location of the bottom of the rubber band relative to the scale written on the outside of the
tube. Note that upward accelerations are positive and downward are negative.
The triangulation device discussed earlier can also be
used to measure horizontal centripetal (e.g. Tea Cups)
and horizontal start/stop accelerations (e.g.
Sidewinder). The device is held with the soda straw
horizontal, aligned along the direction of the
acceleration and held so that the weight can swing
freely. See Figure J. As the accelerometer is
accelerated the weight swings through an angel
.
Applying Newton’s second law to the horizontal and
vertical components of the forces on the weight, we
get
� F  T cos
� F  T sin
 mg  0v
 ma
h
where T is the tension in the string and a is the
unknown acceleration. Solving these for a, we get
Direction of
Acceleration

T

Forces on
Weight

mg
Figure J
a  g tan 
Thus, by noting the angle  during the acceleration a fairly decent estimate of the
acceleration can be made.
The acceleration of a person on a ride can also be determined by direct calculation. The
acceleration calculations required in the following problems are of two basic types:
acceleration down an inclined plane and centripetal acceleration of an object moving with
uniform circular motion.
Inclined Plane – The average acceleration of an object is defined as
v v  vo
ave
t
t  to
where v is the speed at time t and vo is the speed at some initial time t o. Simply stated
then, the average accelerations is just the change in the speed of the object in the time
interval t – to. Suppose the acceleration of the Mind Eraser train down the first big hill is
to be calculated. It can be estimated by finding its average acceleration. First determine
vo, the speed of the train just as it starts down the hill, by measuring the time it takes the
length of the train to pass a fixed point as discussed previously. Find v, its speed at the
bottom of the hill, using the same method. Also, since t – to is just the time required to the
train to change its speed from vo to v, this is the time elapsed as the train moves from the
top to the bottom of the hill. Measure this time and calculate the acceleration using the
equation above.
a

6
ESTIMATION PROBLEMS - FERMI QUESTIONS
These questions require that you make some estimates. These are not guesses, they are estimates
based on information you believe to be true. Generally, you will need to use several bits of
information and perform calculations to arrive at an answer. Please justify your estimates and
show your work.
Some information that might assist you:
.
· Elitch Gardens is open about 120 days a year
.
· Elitch Gardens is open 10 hours a day on average
JUSTIFY ALL YOUR ANSWERS (Give reasons for your answers!)
1. MILK BOTTLE STAND. Estimate how many baseballs are thrown at the milk bottles in the
course of one day.
2. OBSERVATION TOWER. Estimate the volume of air inside the entire Observation Tower
complex.
3. PICNIC TABLES
a) Estimate the number of picnic tables at Elitch Gardens.
b) If a gallon of paint covers an area of 500 ft2 (46.38 m2), estimate how many gallons of
paint would be needed to paint all the picnic tables in Elitch Gardens?
4. Estimate the number of PEPPERONI SLICES that are used per day at the Wild Fire
Pizza restaurant in the park?
5. Estimate the number of FRENCH FRIES sold per day at the Fresh Cut
Fries stand.
6. Estimate the distance traveled by the STATIONARY TIGER on the outside edge of Carousel in
one year.
7. Estimate the number of FUNNEL CAKES sold per day at the park.
8. Estimate the total number of PASSENGERS THE MIND ERASER could carry during one
year of operation.
9. Estimate the number of SHINGLES on the roof of the Carousel entrance building.
10. Estimate the number of GRAINS OF SALT that are on all of the soft pretzels sold per day at
Elitch Gardens.
11. Estimate the total DISTANCE WALKED by all the guests at Elitch Gardens this
year.
12. Assume that a serving of COTTON CANDY could be completely unwound into a single
very long thread. Estimate the length of the Cotton Candy thread.
13. CORN DOGS are sold throughout the park.. Estimate the total surface area of all the corn
dogs sold at the park during the last year.
14. Many people order some type of food covered in melted cheese. These foods include pretzels,
french fries, and taco chips. Estimate the number of gallons of MELTED CHEESE
used in one season at Elitch Gardens.
15. Estimate the number of incandescent LIGHT BULBS in use at Elitch Gardens.
16. Estimate the number of gallons of WATER that evaporate into the air, in one season, from
the clothing, shoes, and hair of people that get wet on the Disaster Canyon ride.
17. Estimate the number of DIPPINDOTS servings sold at Elitch Gardens during the
season?
18. Estimate the number of PAPER CUPS that are used at Elitch Gardens in one
season?
19. Estimate how many TRASH CAN LINERS are used at Elitch Gardens in one
season?
20. How many gallons of WATER are used to flush Elitch Gardens' toilets in one
season?
Suggested Scoring Rubric
Developed by Ed Henke Langley, HS Pittsburgh, PA
1-point: No attempt to answer the question
2-points: Attempted to answer, but the answer is just numbers. The process is not clear 3points: Identifies more than half the numbers. Shows calculations. Process is clear
4-points: Identifies most numbers. Shows most calculations. Explains calculations with a word
equation or dimensional analysis. Process is clear
5-points: Identifies all numbers. Shows all calculations. Explains calculations with a word
equation or dimensional analysis. Process is cle
8
Mind Eraser
10
Mind Eraser
Mind Eraser
Name(s)__________________________ Name(s)__________________________
Part 1
The Mind Eraser combines the physics concepts of work, potential energy, kinetic energy,
power, centripetal force, and acceleration to provide for maximum excitement.
Write complete answers to each of these following questions on your own paper.
Things to notice as you ride or watch:
1. How does the size of the hills change during the ride?
2. Why is the first hill higher than the second?
3. As the car goes up the second hill, does it gain or lose speed?
4. As the car goes down the second hill, does it gain or lose speed?
5. As you go up a hill, do you feel heavier, lighter, or the same?
6. As you roll over a large hill, you are (pushed into / pulled out of) your seat by the seat
belt?
7. As you move down a roller coaster hill, do you feel (weightless / heavier / lighter)?
8. When the ride makes a turn, do you feel like you are pushed into the turn or away from
it?
9. When the ride makes a turn, on what part of your body do you feel the force?
10. When the ride makes a turn, what object is exerting the force on your body?
11. Do the curves slope toward the inside or toward outside of the turn?
12. When you go around a turn on the roller coaster, you body is moved (toward the inside /
toward the outside) of the circle.
13. Which law(s) of motion explains why you are moved in this direction?
11
14. Using letters from the diagram, label the following:
I. Place(s) with increasing
Gravitational Potential energy
_____
II. Place(s) with maximum
Gravitational Potential energy
_____
III. Place(s) with increasing kinetic
energy _____
IV. Place(s) with maximum kinetic
energy _____
15. Riders are most often scared as they travel down the first drop.
a. Describe the sensations.
b. What would happen to a rider without the seat harness?
c. Were the fluid contents of your stomach on the bottom of your stomach or on the top
of your stomach as you travel down the first hill? Explain your answer.
16. Is there a difference in sensation, speed, or anything else when you ride in the front car
versus when you ride in the back car? Why do you think this is true?
17. Some people feel dizzy immediately following the ride. After a few minutes, the feeling
goes away. What might be happening in their inner ear during this recovery period?
18. The roller coaster pushes hardest on the track when the rider feels the most force. Most
tracks creak, squeak, or groan at this time. As you are waiting, listen to the track sounds
and notice the noisiest places. Then, when you ride the coaster, describe whether the
strong forces and the loudest noises come at the same places.
19. Why is the first hill always the highest?
20. Try sitting on one of your hands during the ride. Where on the ride does your hand feel
the most pressure?
21. Where on the ride do you feel as if you are going to be moved out of your seat?
12
Mind Eraser
Name(s)__________________________ Name(s)__________________________
Part 2
Equipment – stopwatch, calculator
1. Using repeated measurements, determine the Average Time for the ride from the moment
the train begins to move until the time the ride comes to its final stop.
Times measured: ________ s ________ s ________ s
Average time for total trip ________ s
2. Estimate the total length of the track.
Estimated total length of track ______________ m
Describe how you estimated this distance.
3. Calculate the Average Speed of the train using the formula.
Average Speed (m/s) =
Total length of track (m) .
Average time for total trip (s)
4. Estimate the height of the first hill from the bottom of the first hill.
Estimated height of first hill ______________ m
5. The acceleration due to gravity for a free falling object is 9.8 m/s2. Use this value to
calculate the predicted maximum speed of the Mind Eraser at the bottom of the first
hill
Predicted Maximum speed (m/s) =
Square root [2 * (acceleration due to gravity (m/s2)* height (m)]
6. Using repeated measurements, determine the time for a cart to travel from the bottom
to the top of its first hill.
Average time to travel from the bottom to the top of the first hill = ________ s
7. The mass of the train is 7500 kg.
Describe how you could estimate this mass.
13
8. Calculate the energy to raise the train to the top of the first hill; the power
required, in watts; and the power required, in horsepower.
Energy used (J) = mass of train (kg) * acceleration due to gravity (m/s2) * height (m)
Power (W) = Energy used (J) / time of travel up first hill (s)
Power (hp) = Power (W) / 746 W/hp
9. Using repeated measurements, determine the time for a cart to travel from the top to
the bottom of its first hill.
Average time to travel from the top to the bottom of the first hill = ________ s
10. Estimate the speed of the train at the top of the first hill.
Estimated speed at top of hill = ________ m/s
Describe how you determined this speed.
11. Calculate the acceleration of the cart during its travel down the first hill.
Acceleration (m/s2) =
[Max speed at bottom of hill (m/s) – speed at top of hill (m/s)] / time down the hill (s)
12. If you accidentally drop your 1-pound shoe and your 1-ounce candy bar at the same time
from the top of the first hill. Answer the following
2
2
Questions. (Recall: g = 9.8 m/s , and distance d = (1/2) gt . Neglect air resistance.)
a) How long will it take your shoe to reach the ground?
b) How long will it take the candy bar to reach the ground?
14
Mind Eraser
Name(s)__________________________ Name(s)__________________________
Part 3
Equipment: stopwatch, calculator, accelerometer/force-meter
Show all your work, any assumptions you made, the reasoning you used, and any
measured or estimated values, Write complete answers to each of these following questions
on your own paper.
1. Identify three sources of friction.
2. What is your mass ____ kg
3. What is your Gravitational Potential energy at the top of the first hill? _________ Joules
4. How much power is used to get you up the first hill? __________ Watts
5. What force is applied to get you up the first hill? _________ Newton
6. What is the average speed of the train on the first hill from A to C?
Average speed AC (m/s) = ________ m/s
7. What is the average speed of the train at the bottom of the first hill?
Average speed at C (m/s) = ________ m/s
8. What kinetic energy does this speed give for you at the bottom of the first hill?
Kinetic Energy at C = __________ (J)
9. What was your Gravitational Potential energy at the bottom of the first hill?
Gravitational Potential Energy at C = _________ J
15
10. Compare the change in Gravitational Potential energy to the change in kinetic energy as
the train moves from the top to the bottom of the first hill. Within experimental error,
how does your data show that energy was conserved?
11. If there had been no friction, what would be the maximum speed at the bottom of the first
hill?
12. Calculate the ratio of the speeds determined these two ways (from #7 and #11) at bottom
of the first hill.
13. Find a percentage difference based on the average of the two calculated values.
14. Using your accelerometer, record the following for the first hill:
a. Accelerometer readings (good luck!) At A, just before descending __________ m/s2
b. At B, about halfway down __________ m/s2
c. At C, bottom of hill __________ m/s2
15. Where does the accelerometer read closest to zero? How do you feel at this point?
16. What does the near-zero reading tell you about the shape of the track at that point?
17. Where does the meter give a maximum reading? Why is it a maximum here?
18. to move the carts requires 70 kW of electrical power. How does this value compare with
your calculations? Why might the values not be the same?
16
TOWER OF DOOM
17
TOWER OF DOOM
Name(s)__________________________ Name(s)__________________________
Part 1:
1. While you are riding the elevator, put your hands between your thighs and the seat. (Note: if
you don't wish to ride the elevator, answer these questions by imagining what you would
experience. Indicate if you participated in the ride or imagined the sensations. )
a. While the elevator is moving upward, at what point do you feel the greatest
force? (Circle one) (i) Near the bottom (ii) in the middle (iii) near the top of the
motion Why?
b. While the elevator is moving downward, at what point do you feel the least force?
(Circle one) (i) Near the bottom (ii) in the middle (iii) near the top of the motion
Why?
2. Riders are most often scared as they travel downward.
c. Were the fluid contents of your stomach on the bottom of your stomach or on the top
of your stomach as you travel down? Why do you say so?
18
TOWER OF DOOM
Name(s)__________________________ Name(s)__________________________
Part 2
Equipment: stopwatch, calculator
1. Estimate the distance that the seats drop during the ride.
Estimated distance of fall ______________ m
2. Using repeated measurements, determine the time it takes the seat to “fall” that distance.
Average time to fall = ________ s
3. Calculate the Average Speed of the fall using the formula.
Average Speed Falling (m/s) =
Distance traveled (m) .
Average time for trip (s)
4. The maximum speed is equal to twice the average speed if the seat starts at rest and
accelerates uniformly during the trip.
The maximum speed is = __________________ m/s
5. Calculate the acceleration of the cart as it moves down the tower.
Falling Acceleration (m/s2) =
[Max speed (m/s) – speed at top of tower (m/s)] / time to travel down the tower (s)
6. Using repeated measurements, determine the time it takes the seat to rise to the top of the
tower.
Average time to rise = ________ s
7. Calculate the Average Speed of the rise using the formula.
Average Speed Rising (m/s) =
19
Distance traveled (m) .
Average time for trip (s)
8. Calculate the acceleration of the cart as it moves up the tower.
Rising Acceleration (m/s2) =
[Speed at top of tower (m/s) – Max speed (m/s)] / time to travel up the tower (s)
9. What is your mass ______ kg (If you do not know your mass, use 60 kg)
10. Calculate your Maximum Kinetic Energy
Kinetic Energy at bottom (J) =
(0.5) * mass (kg) * Maximum Speed (m/s) * Maximum Speed (m/s)
11. Calculate your Maximum Gravitational Potential Energy (use acceleration due to gravity =
9.8 m/s2)
Maximum Gravitational Potential Energy at top (J) =
mass (kg) * acceleration due to gravity * distance the ride drops (m)
12. The distance traveled with constant acceleration starting from rest, can be determined using
d= (0.5) att2 ,
If the elevator were in free fall, about how long would it take to go from top to bottom (g =
9.8m/s2)?
____________ sec
20
TOWER OF DOOM
Name(s)__________________________ Name(s)__________________________
Part 3
measured or estimated values . Write complete answers to each of these following questions
on your own paper.
1. How could you convince someone that the maximum speed of the seat at the bottom of the
tower is equal to twice the average speed of the seat?
2. How does your calculated value of falling acceleration compare to the known acceleration
due to gravity (9.8 m/s2)?
3. What do you think is happening in the ride’s mechanisms to explain the different
acceleration?
4. How much work is done to lift a 75 kg person to the top of this ride?
5. Using the difference in heights between the top and bottom of the ride, predict the maximum
speed at bottom of the ride.
6. Compare the predicted speed at the bottom with the measured maximum speed at the bottom.
What is the percent difference based on the measured speed?
21
BIG WHEEL
Name(s)__________________________ Name(s)__________________________
The Big Wheel is a quiet and relaxing ride, unless you are afraid of heights!
Part 1
4
Assume the wheel turns smoothly.
a. While on the ride, sit on your hands to feel how your weight may change.
a. At what position in the above diagram would you feel a greater weight than normal?
b. At what position in the above diagram would you feel a smaller weight than normal?
c. At what position in the above diagram, would you expect to experience “stomach
butterflies”?
d. How do these “stomach butterfly” sensations relate to the effect of gravity on the material
(food, drink) inside your stomach?
b. While on the ride, close your eyes and keep them closed for what you feel are two
revolutions. Notice your position relative to the ground just before closing your eyes and
right after opening them.
a. How close were you to judging two revolutions?
b. How did you know when you were moving up or down, since you had your eyes
closed?
22
c. If you were to carry a pendulum onto the ride, would you expect its time to swing once back
and forth (period) to be longer / shorter / the same as that on the ground?
d. Apparent weight is how a scale would read if you were sitting on it during the ride. If the
bottom of the seat were pushing against your backside, the scale would read more. If the seat
were falling away, the scale would read less. Predict the magnitude of the apparent weight
while going up, at the top, coming down, and at the bottom.
a. Going up (Point 1): I predict that the apparent weight would be (greater than, less
than, equal to) the gravitational weight.
b. At the top (Point 2): I predict that the apparent weight would be (greater than, less
c. Going down (Point 3): I predict that the apparent weight would be (greater than, less
d. At the bottom (Point 4): I predict that the apparent weight would be (greater than, less
than, equal to) the gravitational weight
23
BIG WHEEL
Name(s)__________________________ Name(s)__________________________
Part 2
1. Measure the time for the ride takes to complete several continuous revolutions.
Number of revolutions =__________
Time for all revolutions = ______________ s
Average time for one revolution = ___________ s
Average number of revolutions/second = frequency = __________rev/s
2. If you stayed on this ride for 8 hours, how many revolutions would you complete?
3. Estimate the diameter of the wheel.
Estimated diameter ______________ m
4. Multiply the diameter by pi ( = 3.1416) to get the circumference of the Big Wheel.
Circumference = ________ m
5. Calculate the average speed of the Big Wheel using the following:
Average speed (m/s) = circumference (m) / average time for one revolution (s)
24
BIG WHEEL
Name(s)__________________________ Name(s)__________________________
Part 3
Equipment: stopwatch, calculator, accelerometer
measured or estimated values. Write complete answers to each of these following questions
on your own paper.
1. Where do the maximum and minimum accelerations occur?
2. What are the average linear and angular speeds of the passenger gondolas?
3. Calculate the frequency and period of rotation of the passenger gondolas.
4. Draw free body diagrams (force diagrams) for the rider at each of the positions.
4
5. Apparent weight is how a scale would read if you were sitting on it during the ride. If the
bottom of the seat were pushing against your backside the scale would read more. If the
seat were falling away, the seat would read less. Predict the magnitude of the apparent
weight while going up, at the top, coming down and at the bottom. (Explain your
answer using the force diagrams)
a. Going up (Point 1): I predict that the apparent weight would be (greater than, less
b. At the top (Point 2): I predict that the apparent weight would be (greater than, less
25
c. Going down (Point 3): I predict that the apparent weight would be (greater than, less
d. At the bottom (Point 4): I predict that the apparent weight would be (greater than, less
than, equal to) the gravitational weight
6. Centripetal force = mv2/r. If the wheel could go fast enough, there would be a speed at which
you would have no apparent weight? At what speed is this? (Note: Mass doesn’t matter).
How would this affect the ride for the passengers?
7. If the Big Wheel were twice the diameter, how would the experience be different for the
riders?
8. If the Big Wheel were twice the diameter, what speed would you have to reach to have no
apparent weight on this new ride?
9. Using an accelerometer, record the values at each of the four positions:
Point 1 __________ m/s2
Point 3 __________ m/s2
Point 2 __________ m/s2
Point 4 __________ m/s2
10. Compare the predicted accelerations you calculated in step #1 above with the actual
accelerations you measured with an accelerometer.
26
CAROUSEL
Name(s)__________________________ Name(s)__________________________
Part 1
1. Describe the direction of rotation of the horses as viewed from above.
2. Suppose you drop a coin onto the Carousel floor as you sit on one of the horses. Where
does it land relative to you (e.g., directly below, in front of, or behind you)?
3. Now suppose that you stand near the edge of the Carousel and drop a coin off the edge of
the Carousel. When the coin hits the ground, where does it land relative to you? (e.g.,
directly below, in front of, or behind you)?
4. Is the floor of the ride level? If not, which way does it tilt? Why?
5. If you were to throw a ball from position A on the diagram to someone at position B
while the ride was turning, where would you aim the ball?
27
6. Draw the path of the ball as seen by someone standing on the ground.
7. Draw the path as seen by a person on the ride at point B.
8. As the ride turns, is your body thrown slightly to the inside or outside?
9. Do all the animals on the Carousel go up and down at the same time?
10. Does the animal next to you move up and down as you do?
11. Do you feel slightly lighter or heavier when your horse is going up? Why?
12. Do you feel slightly lighter or heavier when your horse is going down? Why?
13. Do you feel different when riding a horse on the outside vs. the inside of the Carousel?
If so, describe the differences when on the outside horse versus the inside horse?
14. How does the angular velocity (number of degrees moved /second) of the outer horse
compare to that of an inner horse? (Are their revolution rates the same? If not, which is
larger?.)
15. Ata which number position on the diagram above would you have the greatest linear
speed?
16. At which number position would you have the smallest linear speed?
28
CAROUSEL
Name(s)__________________________ Name(s)__________________________
Part 2
1. Using repeated measurements, measure the time for a horse to make several continuous
revolutions.
Time for all revolutions = ______________ s _______ s _______ s
Average time for one revolution = period = ___________ s
2. Estimate the radius of the Carousel from the center to an outside horse
Estimated radius to outside horse ______________ m
3. Multiply the radius by two to get the diameter. Multiply the diameter by pi ( = 3.1416)
to get the circumference of the horse path.
Circumference at outside horse = ________ m
4. Calculate the average linear speed of an outside horse using the following:
Average linear speed on outside (m/s) =
circumference (m) / average time for one revolution (s)
5. Calculate the centripetal acceleration of an outside horse
Outside centripetal acceleration (m/s2) =
average speed (m/s) * average speed (m/s) / radius to the horse (m)
6. Estimate the radius of the Carousel to an inside horse
Estimated radius to inside horse ______________ m
7. Multiply the radius by two to get the diameter. Multiply the diameter by pi ( = 3.1416)
to get the circumference of the horse path.
Circumference of inside horse = ________ m
29
8. Calculate the average linear speed of an inside horse using the following:
Average linear speed (m/s) = circumference (m) / average time for one revolution (s)
9. Calculate the centripetal acceleration of an inside horse
Inside centripetal acceleration (m/s2) =
average speed (m/s) * average speed (m/s) / radius of inside horse (m)
10. Count the number of horses in the outer ring __________
Count the number of horses in the inner ring __________
11. What is the angle (number of degrees) between horses:
on the outer ring? __________o
on the inner ring? __________ o
30
CAROUSEL
Name(s)__________________________ Name(s)__________________________
Part 3
Show all your work, any assumptions you made, the reasoning you used, and any measured
or estimated values. Write complete answers to each of these following questions on your
own paper.
1. At position (A), draw an arrow representing the linear velocity at that instant. Also, draw
an arrow that represents the acceleration. (Label them v and a)
2. At position (B); draw an arrow representing the linear velocity and acceleration. (Label
the v and a)
3. Assume the following drawing shows you on the horse at position (B). Draw all the force
vectors that are acting on you at this point. (Free Body Diagram)
4. Your mass is ______ kg. (If you do not know your mass, use 60 kg)
31
5. Calculate the centripetal force acting on you while you are riding an outer horse.
Centripetal force = _________ N
6. Calculate the centripetal force acting on you while you are riding an on an inner horse.
Centripetal force = _________ N
7. Draw to scale a horizontal vector representing the centripetal force on your when you are
on an outside horse. Add to it a vertical vector equal in magnitude to your weight but
directed upwards. These are the components of the force applied on you by the Carousel.
Use a ruler and protractor and this diagram to find the net applied force.
8. Using your vector diagram, discuss what you expect to happen to the forces as you
change from an inner to an outer horse.
9. Accelerometer readings on:
a. Inner horse __________
b. Outer horse = __________
10. How do your measurements of acceleration/force compare with your expectations?
11. Hold the horizontal accelerometer perpendicular to a horse. Record the angle with the
vertical.
Inner horse _________ o Outer horse __________ o
12. Hold the vertical accelerometer upright and record the meter readings as the horse goes
up and down.
At bottom going up _______ o in middle going up _______ o arriving at top ________ o
At top starting down ______ o in middle going down _____ o arriving at bottom _____ o
13. How do the readings on the vertical force meter relate to the force sensations you
experienced?
14. How does the radial force meter reading on the inner horse compare with that on the
outer horse?
15. If you are moving in a circle, a force toward the center of the circle is needed to make
you move in that circle. Answer the following questions by using the a horizontal
accelerometer. Get on a horse that does not move up and down. Before the Carousel
starts, hold the string with your hand, in front of you, and let the weight hang beneath
your hand.
a. When the Carousel is starting up, which way does the weight move? (toward the
center of the Carousel or toward the outside the Carousel, in the direction the
horse is facing or the opposite direction to the way the horse is facing)
32
b. When the Carousel is moving at constant speed, does the weight move? ? (toward
the center of the Carousel or toward the outside the Carousel, in the direction the
horse is facing or the opposite direction to the way the horse is facing)
c. When the Carousel is slowing down and coming to a stop, which way does the
weight move? ? (toward the center of the Carousel or toward the outside the
Carousel, in the direction the horse is facing or the opposite direction to the way
the horse is facing)
d. When the Carousel is moving at constant speed, does the string pull the weight? ?
(toward the center of the Carousel or toward the outside the Carousel, in the
direction the horse is facing or the opposite direction to the way the horse is
facing)
16. How does the concept of centripetal force and Newton’s Second Law help explain these
observations?
33
THE SEA DRAGON
Name(s)__________________________ Name(s)__________________________
The Sea Dragon is a good example of a pendulum. However, you must admit it is a little
different from any you have seen at school.
Part 1
1
1. Using the diagram above answer the following:
a. At which location (1 or 2) might you feel “weightless”?
b. At which location (1 or 2) might you the greatest speed?
c. At which location (1 or 2) might you feel the heaviest?
2. At what point in the swing of the boat does it feel like the boat is moving the fastest?
3. For the biggest thrill, which seat on the boat would you recommend: near the end of the
boat, or near the middle of the boat? What reasoning can you give for your answer?
4. When you are at the highest place Point 1, you are traveling the (fastest/slowest)?
5. When the seating area changes directions, you feel (lightest/heaviest)?
34
THE SEA DRAGON
Name(s)__________________________ Name(s)__________________________
Part 2
1. Using repeated measurements, measure the time for the ride to complete several
continuous back and forth motions.
Number of round trips =__________
Time for all round trips = ______________ s ____ s _____ s
Average time for one round trip = ___________ s
Average number of trips/second = frequency = __________trips/s
2. If you stayed on this ride for 8 hours, how many round trips would you complete?
3. Estimate the length of the pendulum.
Estimated length ______________ m
4. Estimate the length of the seating area.
5. Using multiple measurements, determine the time for the seating area to pass by Point 2
at the bottom of the swing.
Time for train to pass Point 2 = ______________ s ____ s _____ s
Average time to pass point 2 = ___________ s
35
6. Determine the average speed of the seating area at Point 2.
Total length of seating area (m) .
Average Speed at Point 2 (m/s) = Average time to pass Point 2 (s)
7. Determine the centripetal acceleration of the seating area at Point 2.
Centripetal acceleration (m/s2) =
Average Speed at Point 2 * Average Speed at Point 2 / length of the pendulum (m)
8. The mass of the seating area is 1300 kg.
9. Estimate the maximum height attained by the middle of the seating area from the bottom
of the arc.
Estimated height ______________ m
10. Calculate the Kinetic Energy of the seating area at Point 2
Kinetic Energy at Point 2 (J) =
(0.5) * mass (kg) * Average Speed at Point 2 (m/s) * Average Speed at Point 2 (m/s)
11. Calculate the Gravitational Potential Energy of the Seating Area at Point 1 (use
acceleration due to gravity = 9.8 m/s2)
Gravitational Potential Energy at Point 1 (J) =
mass (kg) * acceleration due to gravity * max ht of middle of seating area (m)
12. Note: the initial Kinetic Energy of the seating area at the maximum height is 0 J.
13. Note: the Gravitational Potential Energy of the seating area at the bottom of the arc is 0 J.
14. Calculate the change in Kinetic Energy
Change in Kinetic Energy (J) =
Kinetic Energy at Point 2 – Kinetic Energy at max height
15. Calculate the change in Gravitational Potential Energy
Change in Gravitational Potential Energy (J) =
Gravitational Potential Energy at Pt 2 – Gravitational Potential Energy at max ht
16. Did the change in Kinetic Energy match the change in Gravitational Potential Energy?
Why would you expect them to have equal magnitudes?
36
THE SEA DRAGON
Name(s)__________________________ Name(s)__________________________
Part 3
Equipment: stopwatch, calculator, accelerometers
own paper.
1. Using the method discussed on the triangulation section of “Suggestions for Making
Measurements,” find the height of the Sea Dragon at its highest point.
Height = distance away * (Tan Ø)
Height =________ (m)
(Don’t forget the height of your eye above the ground)
Height of the Sea Dragon = Height from above + height of your eye from the
ground
Height of Sea Dragon =________ + ________ = ___________ m
2. The acceleration due to gravity for a free falling object is 9.8 m/s2. Use this value to
calculate the maximum predicted speed of the Sea Dragon at the bottom of the
swing
Maximum speed (m/s) =
Square root [2 * (acceleration due to gravity)* max ht of middle of seating area (m)]
37
3. Use the Equation:
to calculate the theoretical period of the pendulum. (L = length of pendulum, T =
period of swing, g = 9.8 m/s2.)
4. If a difference exists between the measured period and the theoretical period, what do
you believe is the reason for the difference?
5. Does this ride follow rules for a simple pendulum? Defend your answer.
6. Hold the accelerometer vertically.
The acceleration at Point 1 = __________
The acceleration at Point 2 = __________
7. Explain why the accelerometer reading at Point 1 is less than when the ride is not
moving.
8. Explain the differences you found between the accelerometer readings at Point 2 and the
centripetal acceleration calculated in Part 2.
9. When the seating area is full of people, how much energy needs to be supplied by the
motors to get the “dragon” swinging to its maximum height?
10. Did the change in Kinetic Energy match the change in Gravitational Potential Energy?
Why would you expect them to have equal magnitudes?
11. On the following diagram draw a free body diagram indicating all forces acting at this
location.
(A) At Point 2
(B) At Point 1
38
THE SIDEWINDER
Name(s)__________________________ Name(s)__________________________
Part 1
D
1. Describe your feeling at the top of the loop Point C.
2. At which point during the ride do you feel the heaviest?
3. Why doesn’t your money fall out of your pockets when you are upside down at the top of
the loop?
4. At which point during the ride do you feel you are moving the fastest?
5. At which point during the ride do you feel you are moving the slowest?
6. Riders are most often scared as they travel upside down.
39
THE SIDEWINDER
Name(s)__________________________ Name(s)__________________________
Part 2
Equipment: stopwatch, calculator, ruler
1. Measure the height of the station using two different methods:
Method 1. Measure the height of one step and count the number of steps to get the
height at the top of the ride:
Measure the height of one step = ___________m
Number of steps = __________
Height to top = __________m (Station at Points A and C)
Method 2. Use another method to estimate the height to the top of the ride.
2. Compare the two height calculations as follows:
Average of the heights based on Method 1 and Method 2
Average value = (height from Method 1 + height from Method 2) / 2
Percent difference:
Percent difference: =
(height from Method 1 – height from Method 2) / Average Value of height
3. Which height measurement do you think is more accurate? Why?
40
4. From a position on the ground, use multiple measurements to determine an average time
it takes the train to pass Point D on the diagram.
Average time for train to pass Point D ________ s
5. If the length of the train is 12 m, calculate the average speed of the train at Point D.
Calculate the Average Speed of the train at Point D using the formula.
Total length of train (m) .
Average Speed at Point D (m/s) = Average time to pass Point D (s)
6. Estimate the height of Point D.
7. From a position on the ground, use multiple measurements to determine an average time
it takes the train to pass Point C on the diagram.
Average time for train to pass Point C ________ s
8. If the length of the train is 12 m, calculate the average speed of the train at Point C.
Calculate the Average Speed of the train at Point C using the formula.
Total length of train (m) .
Average Speed at Point C (m/s) = Average time to pass Point C (s)
9. The mass of the train and passengers is 2100 kg.
10. Calculate the Kinetic Energy of the train at Point C
Kinetic Energy at Point C (J) =
(0.5) * mass (kg) * Average Speed at Point C (m/s) * Average Speed at Point C (m/s)
11. Calculate the Kinetic Energy of the train at Point D
Kinetic Energy at Point B (J) =
(0.5) * mass (kg) * Average Speed at Point D (m/s) * Average Speed at Point D (m/s)
41
12. Calculate the Gravitational Potential Energy of the train at Point C (use acceleration due
to gravity = 9.8m/s2)
Gravitational Potential Energy at Point C (J) =
mass (kg) * acceleration due to gravity * height of Point C
13. Calculate the Gravitational Potential Energy of the Train at Point D (use acceleration due
to gravity = 9.8 m/s2)
Gravitational Potential Energy at Point D (J) =
mass (kg) * acceleration due to gravity * height of Point D
14. Calculate the change in Kinetic Energy as the train moves from Point C to Point D
Change in Kinetic Energy (J) = Kinetic Energy at Point D – Kinetic Energy at Point C
15. Calculate the change in Gravitational Potential Energy as the train moves from Point C
to Point D
Change in Gravitational Potential Energy (J) =
Gravitational PE at Point D – Gravitational PE at Point C
16. Calculate the centripetal force on the train at Point C
Centripetal Force at Point C (J) =
mass (kg) * Avg Speed at Pt C (m/s) * Avg Speed at Pt C (m/s) / radius of loop (m)
17. Calculate the centripetal force on the train at Point D
Centripetal Force at Point D (J) =
mass (kg) * Avg Speed at Pt D (m/s) * Avg Speed at Pt D (m/s) / radius of loop (m)
18. Calculate the energy to raise the train to the top of the hill; the power required, in
watts; and the power required, in horsepower.
Energy used (J) = mass of train (kg) * acceleration due to gravity (m/s2) * height (m)
Power (W) = Energy used (J) / time of travel up hill (s)
Power (hp) = Power (W) / 746 W/hp
42
THE SIDEWINDER
Name(s)__________________________ Name(s)__________________________
Part 3
own paper.
1. How much work does it take a 75 kg person to climb the stairs to reach this ride?
2. How many times must the 75 kg person climb the stairs of this ride to “burn off” the
energy in a soft drink, french fries, and a hamburger, (Note: 1 food Calorie = 4200 J)
3. Using the measured speed at Point C and the difference in heights between points C and
D, predict speed at Point D.
4. Compare the predicted speed at the bottom (Point D) with the measured speed at the
bottom. What is the percent difference based on the measured speed?
5. Predict the initial speed of the train just after launch. Show how you made this
prediction.
6. If the train was launched using a spring, estimate the spring constant.
7. For the most exciting ride, at Point C the centripetal force should equal the gravitational
force. How did the values you calculated compare to this ideal situation?
8. What is the acceleration as the ride begins (launch)?
9. What force must be applied over the braking distance in order to stop the train?
43
THE DRAGON WING
Name(s)__________________________ Name(s)__________________________
Part 1
The suspended cars of the Bat Wing will swing out at some angle when they travel in a circle.
The angle depends upon the radius of the circular path and the speed of the wheel.
1. What sensations do you feel when the ride is moving, but not tilted?
2. What sensations do you feel when the ride is going up when tilted?
3. What sensations do you feel when the ride is going down when tilted?
4. What sensations do you feel as the speed increases?
5. Which goes higher----an empty swing or one with someone in it?
6. What happens to the seats as the speed increases?
7. During the ride, you feel several forces:
a) Where on your body to you feel those forces?
b) What object(s) exert those forces?
c) In what direction are the forces?
44
THE DRAGON WING
Name(s)__________________________ Name(s)__________________________
Part 2
1. Using repeated measurements, determine the time to complete several continuous
revolutions of the ride.
Time for all revolutions = ________ s _____ s _______ s
Average time for one revolution = ___________ s
2. If you stayed on this ride for 8 hours, how many revolutions would you complete? ()
3. Estimate the radius of the horizontal circle in which each passenger vehicle moves when
it is moving most rapidly.
Estimated radius ______________ m
4. Multiply the radius by 2 to determine the diameter.
5. Multiply the diameter by pi ( = 3.1416) to get the circumference of the largest horizontal
circle covered by the riders.
Circumference = ________ m
6. Calculate the average speed of the riders using the following:
Average speed (m/s) = circumference (m) / average time for one revolution (s)
7. Determine the centripetal acceleration of the seating area.
Centripetal acceleration (m/s2) =
Average Speed * Average Speed / radius of riders (m)
45
THE DRAGON WING
Name(s)__________________________ Name(s)__________________________
Part 3
Equipment: calculator, accelerometer, protractor
own paper.
1. What is the average linear and angular speed of the ride?
a) When the ride is moving without a tilt?
b) When the ride is moving with a tilt?
2. Determine the frequency and period of rotation.
3. What values were recorded using the accelerometer
4. Compare the calculated acceleration with the acceleration you measured with an
accelerometer.
5. The force diagram for the passenger vehicle looks like the figure. The horizontal
component of the cable tension is T * sin  = Fc. The vertical component is T * cos =
W. Using the maximum speed and radius calculated before along with data on the
vehicle and passenger mass to determine the centripetal force. Then calculate the value
of . Compare this to an actual value measured for the ride.
6. The electrical power required to operate the Bat Wing is approximately 128 kilowatts. (1
kilowatt = 1000 watts. 1 watt = 1 joule/second) If electrical energy costs 7.5 cents per
kWhr, calculate the electrical energy cost of one ride.
46
TROIKA
47
TROIKA
Name(s)__________________________ Name(s)__________________________
Part 1
This ride is made up of clusters of seats at the end of arms.
1. As viewed from above, is the motion clockwise or counterclockwise of:
The arms ____________________ Each cluster ____________________
2. Concentrate your attention on one rider, and follow this single rider's motion for at least
one full rotation of the ride around the primary axis at the center of the ride. Be sure to
choose your frame of reference be viewing the ride from above the ride.
Draw the path of the rider for one full turn of the primary axis.
3. Label the following on your drawing:
a. Points of greatest (GS) and lowest (LS) speed.
b. Points of greatest (GA) and lowest (LA) acceleration magnitude.
c. Points of greatest (GF) and lowest (LF) force magnitude.
48
TROIKA
Name(s)__________________________ Name(s)__________________________
Part 2
1. Estimate the length of the primary (arm) axis.
2. Multiply the radius of the primary (arm) axis by two to get the diameter. Multiply the
diameter by pi ( = 3.1416) to get the circumference of the primary (arm) axis.
Circumference at primary (arm) axis = ________ m
3. Estimate the length of the secondary (cluster) axis.
4. Multiply the radius of the secondary (cluster) axis by two to get the diameter. Multiply
the diameter by pi ( = 3.1416) to get the circumference of the secondary (cluster) axis.
Circumference at secondary (cluster) axis = ________ m
5. Using repeated measurements, determine the time for the primary (arm) axis to make
several continuous revolutions.
49
6. Using repeated measurements, determine the time for the secondary (cluster) axis to
make several continuous revolutions.
7. Calculate the average linear speed of objects at the end of the primary (arm) axis using
the following:
Average linear speed of primary arm (m/s) =
circumference of primary arm (m) / average time for one revolution (s)
8. Calculate the centripetal acceleration of objects at the end of the primary (arm) axis
Centripetal acceleration of primary arm (m/s2) =
average speed (m/s) * average speed (m/s) / radius primary (arm) axis (m)
9. Calculate the average linear speed of objects at the end of the secondary (cluster) axis
using the following:
Average linear speed of secondary cluster (m/s) =
circumference of secondary cluster (m) / average time for one revolution (s)
10. Calculate the centripetal acceleration of objects at the end of the secondary (cluster) axis
Centripetal acceleration of secondary cluster (m/s2) =
average speed (m/s) * average speed (m/s) / radius of secondary (cluster) axis (m)
11. What values would you predict for the maximum and minimum linear speeds for
passengers on the ride
Maximum linear speed = ___________ m/s
Minimum linear speed = ___________ m/s
12. Label the following on a drawing that shows the path of the passengers during one full
turn of the primary axis:
50
TROIKA
Name(s)__________________________ Name(s)__________________________
Part 3
Equipment: calculator, accelerometer
own paper.
Measure and record the maximum and minimum horizontal accelerometer readings as
directed along a radius of the cluster.
1. Is this acceleration inward or outward?
2. Maximum reading of accelerometer __________ m/s2
3. Minimum reading of accelerometer___________ m/s2
4. Where does the maximum and minimum acceleration occur?
5. Compare the calculated acceleration with the acceleration you measured with an
accelerometer.
6. What is the average linear and angular speed of the ride?
7. What values would you predict for the maximum and minimum linear speeds for
passengers on the ride
Maximum linear speed = ___________ m/s
Minimum linear speed = ___________ m/s
8. Label the following on a drawing that shows the path of the passengers during one full
turn of the primary axis:
51
For each of the rides listed below, measure your pulse rate and breathing rate before and after the ride. Indicate any
symptoms that you had by placing numbers of those appropriate from the list below.
Symptoms:
1. Dry Mouth
5. Cold hands/feet
9. Upset stomach
2. Dizziness
3. Tense muscles
4. Unable to move
6. Enlarges eye pupils
7. Trembling
8. Sweaty hands
10. Fast breathing
11. Stomach Butterflies
12. Other
Ride
Pulse Rate
Before
After
Breathing Rate
Before
After
Symptoms
Before
After
Troika
Boomerang
Tea Cups
Sidewinder
Sea Dragon
Big Wheel
Mind Eraser
Tower of Doom
Twister II
Shipwreck Falls
Spider
Tilt-A-Whirl
Dragon Wing
Questions:
1.
2.
3.
52
Amusement park rides are designed to give the illusion of danger and speed. Which rides,
based on the symptoms that you had, seem to give the greatest illusion?
Based on your observations, how could an amusement park design a ride to give greater
illusion of speed and danger?
On a separate sheet, describe a ride that you would design.
For Teacher Reference Only
Ride Specifications
Carousel
Period of Revolution
Radius
The Mind Eraser
Total time of ride
Height of first hill
Mass of train
Track length
Track gauge
Lift motor
Length of train
Capacity
number of trains
coaches per train
passengers
passenger mass
Power usage
19.5 s
27 ft
1 min 45 sec
125 ft
7500 kg
740m
1217 mm
129 kW DC
15 m
PLEASE DO
NOT SHARE
THESE
PAGES
WITH
STUDENTS
2
10
2 per coach
150 kg per coach
300kVA
Big Wheel
Period of revolution
Diameter
Capacity
number of gondolas
passengers
passenger mass
Drive motors
Power Requirements
total
drive
lights
Line voltage
Lighting voltage
24 sec
80 ft
20
6 adults or 8 children per gondola
583 kg/gondola
8 x 7.5 hp = 60 hp
130 kW
70 kW
60 kW
220 V, 3 phase, 60 Hz
110 V
Boomerang
Track length
Track gauge
Train length
Capacity
number of trains
coaches per train
passengers
passenger mass
Power Usage
53
662 m
1219 mm
18.5 m
1
4
4 per coach
300 kg per coach
190 kVA
PLEASE DO
NOT SHARE
THESE
PAGES
WITH
STUDENTS
Dragon Wing
Capacity
number of vehicles
passengers
passenger mass
average ride speed
ride duration
Max diameter at full rpm
Drive motors
16
2 per vehicle
154 kg per vehicle
8.6 rpm
3 min 55 sec
27.43 m
5 x 460 V, 3 phase, 60
Hz
Power requirements
total
drive motors
hydraulic motors
lights
Lighting (neon) voltage
Hydraulic pump motor
160 kVA
60 kVA
75 kVA
7 kVA
110 V
100 hp
Sea Dragon
Length of support arm
Length of ship
Max speed
Power requirements:
40 ft
35 ft 6 in
35.7 ft per sec
motor 75kW
lights 25kW
Sidewinder
Diameter of loop
Height at top of loop
Height of station
Acceleration at start
30 ft
60ft
50 ft
0 – 35 mph in 3 seconds
Tower of Doom
Time up
8s
Time down
4s
Height
260 ft
Power
480 kW
Concessions (number per
year)
Corn Dogs
Hot Dogs
Hamburgers
Ketchup
Mustard
Funnel Cakes
10,120
232,640
303,000
2,862 gallons
891 gallons
96,912
54
PLEASE DO
NOT SHARE
THESE
PAGES
WITH
STUDENTS
Resources
Nathan A. Unterman of Glenbrook High School has compiled an excellent list of Internet, print,
software, video and other resources. His list is at http://newton.dep.anl.gov/app/nau_links.htm.
Internet
Amusement Park Physics:
http://www.joyrides.com/links.htm http://www.coasterclub.org/
http://curie.uncg.edu/~mturner/title.html http://www.learner.org/exhibits/parkphysics/
http://www.Funderstanding.com/k12/coaster/
http://www.esc2.net/TIELevel2/projects/roller/default.htm
http://www.cinternet.net/~bowersda/history.htm
http://www.nsta.org/programs/laptop/lessons/h5.htm
http://www.learner.org/exhibits/parkphysics/
Annenberg site with simulations and opportunities to design rides. Background
information provided..
http://curie.uncg.edu/~mturner/title.html
Descriptions of experiments and activities on rides and playground equipment.
http://www.funderstanding.com/k12/coaster/
Design a roller coaster
http://www.vast.org/vip/book/home.htm
Complete book on roller coaster design
http://www.newton.dep.anl.gov/app/nau_links.htm
List of Internet sites related to amusement park physics
http://solomon.physics.sc.edu/~tedeschi/midway/bigtop.html
South Carolina book on-line
http://www.physics.emich.edu/amusement/
Eastern Michigan University lessons.
Books
Amusement Park Physics: A Teacher's Guide
Nathan A. Unterman / Paperback / Published 1990 J Weston
Walch; ISBN: 0825116813
http://www.vernier.com/cmat/amusementparkphysics.html
Amusement Park Physics
Carole Escobar (Editor) / Paperback / Published 1994 American
Assn of Physics Teachers; ISBN: 0917853539
Other
Amusement Park Physics Digitized Video Collection for Motion Analysis
Physics Curriculum & Instruction
22585 Woodhill Dr.
Lakeville, MN 55
55

Physics and Astronomy Night At Elitch Gardens

Transcription

Similar documents

SMART FUN in MIRABILANDIA ( )

Live Lakini`s Juice

Poster - Burn Fund

2016 Poster - Prostate Cancer Fight Foundation

Making SOMEDAY Into TODAY - Someday I`ll Do It, Why Not Today?

April - GWRRA Maryland Chapter "J"

INSIDE

Slinger Super Speedway Marketing Kit

Cybex Trazer

This 2 day dualsport ride for licensed, street