Physics and
Astronomy Night
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 9 a.m. to 8:00 p.m with activity booths starting around 4 p.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
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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 aid in determining vertical and horizontal Figure A 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. String Protractor Suppose the height h of the Total Tower Weight Figure B
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must be determined. First the distance L is estimated by pacing it h off or by some other suitable methods. Sight through the soda L straw at the top of the tower and read the angle from the protractor. Then since Figure C tan h L h is given by h L � (tan )
A similar device can be used to measure horizontal distances that cannot be easily paced off. Using a moveable pin d 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 measured. Pace off or estimate the baseline L shown a b 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 your line of sight from pin a to c extends to the other Figure D end of the unknown distance d. Figure E shows that triangles aop and abc are similar. Thus, p d bc c d L ab o or a b � bc � L d �� �� L Ł abł � 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 h close to the structure, the following technique can be used. Suppose the height 1 2 h in Figure F is to be determined. Standing back at some distance from the object, D measure the angle 1. Walk directly toward the object a distance D and measure angle Figure F 2. Knowing 1, 2, and D, the height h
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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 v ave 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 d n � circumference n2R v ave 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 d length of train v ave 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 hA B principle of conservation of total mechanical hB energy it follows that 1 mghA 1 mv2A mghB mv 2B 2 2 Figure G Solving for vB:
2 v B 2g(hA hB ) v A 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.
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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 forces on mass (either up or down) is a 0-5 newton spring scale with a when scale is 100 gm mass attached. When measuring vertically right side up: upward accelerations such as at the bottom of the Tower Fs of Doom, the spring scale is held vertically as in Figure Fs H. The forces on the mass are as drawn, where Fs is the reading on the scale. Applying Newton’s second law, mg
Fs mg ma Thus the acceleration, a, of the mass (and also of the m person holding the scale), is given by Figure H F mg F a s s g m m forces on mass If the person is holding the scale upside down (for example, at the when the scale is top of the loop of the Side Winder), the forces on m are as upside down: diagrammed in Figure I. Again applying Newton’s second law , mg the acceleration of the mass m is given by
� F a � s g �� Fs Ł m ł In either situation then, the acceleration can be calculated by knowing 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.
1. Attach the rubber band to the center of the top of th e rubber tube’s lid. You might use tape or a paper clip. band
2. Screw the lid to the top of the tube. sinker 3. Mark on the outside of the tube the location of th e -1g bottom of the rubber band. Identify this mark as “-1g”. 0g 4. Remove the lid and permanently attach one sinker t o 1g 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”.
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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 Direction of acceleration and held so that the weight can swing Acceleration freely. See Figure J. As the accelerometer is accelerated the weight swings through an angel . Applying Newton’s second law to the horizontal and T vertical components of the forces on the weight, we get Forces on Weight � F T cos mg 0v mg � Fh T sin ma where T is the tension in the string and a is the unknown acceleration. Solving these for a, we get 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 a 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.
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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 3- points: 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
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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?
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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?
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Mind Eraser
Name(s)______Name(s)______
Part 2 Equipment – stopwatch, calculator Write complete answers to each of these following questions on your own paper.
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.
Total length of track (m) . Average Speed (m/s) = 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 Describe how you estimated this distance.
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.
Times measured: ______s ______s ______s
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.
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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.
Times measured: ______s ______s ______s
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?
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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
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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?
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TOWER OF DOOM
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TOWER OF DOOM
Name(s)______Name(s)______
Part 1: Write complete answers to each of these following questions on your own paper.
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. 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? Why do you say so?
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TOWER OF DOOM
Name(s)______Name(s)______
Part 2 Equipment: stopwatch, calculator Write complete answers to each of these following questions on your own paper.
1. Estimate the distance that the seats drop during the ride. Estimated distance of fall ______m Describe how you estimated this distance.
2. Using repeated measurements, determine the time it takes the seat to “fall” that distance.
Times measured: ______s ______s ______s
Average time to fall = ______s
3. Calculate the Average Speed of the fall using the formula.
Distance traveled (m) . Average Speed Falling (m/s) = 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.
Times measured: ______s ______s ______s
Average time to rise = ______s
7. Calculate the Average Speed of the rise using the formula.
Distance traveled (m) . Average Speed Rising (m/s) = Average time for trip (s)
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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
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TOWER OF DOOM
Name(s)______Name(s)______
Part 3 Equipment: stopwatch, calculator
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. 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?
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BIG WHEEL
Name(s)______Name(s)______
The Big Wheel is a quiet and relaxing ride, unless you are afraid of heights!
Part 1 Write complete answers to each of these following questions on your own paper.
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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?
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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 than, equal to) the gravitational weight.
c. Going down (Point 3): I predict that the apparent weight would be (greater than, less than, equal to) the gravitational weight.
d. At the bottom (Point 4): I predict that the apparent weight would be (greater than, less than, equal to) the gravitational weight
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BIG WHEEL
Name(s)______Name(s)______Part 2 Equipment: stopwatch, calculator Write complete answers to each of these following questions on your own paper.
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 Describe how you estimated this distance.
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)
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BIG WHEEL
Name(s)______Name(s)______
Part 3 Equipment: stopwatch, calculator, accelerometer
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. 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.
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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 than, equal to) the gravitational weight.
b. At the top (Point 2): I predict that the apparent weight would be (greater than, less than, equal to) the gravitational weight.
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c. Going down (Point 3): I predict that the apparent weight would be (greater than, less than, equal to) the gravitational weight.
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.
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CAROUSEL
Name(s)______Name(s)______
Part 1 Write complete answers to each of these following questions on your own paper.
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?
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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?
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CAROUSEL
Name(s)______Name(s)______
Part 2
Write complete answers to each of these following questions on your own paper. Equipment: stopwatch, calculator
1. Using repeated measurements, measure the time for a horse to make several continuous revolutions. Number of revolutions =______Time for all revolutions = ______s ______s ______s Average time for one revolution = period = ______s Average number of revolutions/second = frequency = ______rev/s
2. Estimate the radius of the Carousel from the center to an outside horse Estimated radius to outside horse ______m Describe how you estimated this distance.
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 Describe how you estimated this distance.
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
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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
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CAROUSEL
Name(s)______Name(s)______
Part 3 Equipment: stopwatch, calculator, accelerometer
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)
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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)
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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?
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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 Write complete answers to each of these following questions on your own paper.
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)?
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THE SEA DRAGON
Name(s)______Name(s)______
Part 2
Equipment: stopwatch, calculator Write complete answers to each of these following questions on your own paper.
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 Describe how you estimated this distance.
4. Estimate the length of the seating area. Estimated length ______m Describe how you estimated this distance.
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
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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. Describe how you could estimate this mass.
9. Estimate the maximum height attained by the middle of the seating area from the bottom of the arc. Estimated height ______m Describe how you estimated this distance.
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?
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THE SEA DRAGON
Name(s)______Name(s)______
Part 3 Equipment: stopwatch, calculator, accelerometers
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. 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)]
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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
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THE SIDEWINDER
Name(s)______Name(s)______
Part 1 Write complete answers to each of these following questions on your own paper.
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. a. Describe the sensations. b. What would happen to a rider without the seat harness?
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THE SIDEWINDER
Name(s)______Name(s)______
Part 2
Write complete answers to each of these following questions on your own paper. 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.
Estimated height ______m Describe how you estimated this distance.
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?
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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.
Times measured: ______s ______s ______s
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. Estimated height ______m Describe how you estimated this distance.
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.
Times measured: ______s ______s ______s
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. Describe how you could estimate this mass.
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)
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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
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THE SIDEWINDER Name(s)______Name(s)______
Part 3 Equipment: stopwatch, calculator, accelerometer
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. 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?
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THE DRAGON WING
Name(s)______Name(s)______
Part 1 Write complete answers to each of these following questions on your own paper.
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?
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THE DRAGON WING
Name(s)______Name(s)______
Part 2 Write complete answers to each of these following questions on your own paper. Equipment: stopwatch, calculator
1. Using repeated measurements, determine the time to complete several continuous revolutions of the ride. Number of revolutions =______Time for all revolutions = ______s _____ s ______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 radius of the horizontal circle in which each passenger vehicle moves when it is moving most rapidly. Estimated radius ______m Describe how you estimated this distance.
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)
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THE DRAGON WING
Name(s)______Name(s)______
Part 3 Equipment: calculator, accelerometer, protractor
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. 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. a) When the ride is moving without a tilt? b) When the ride is moving with a tilt?
3. What values were recorded using the accelerometer a) When the ride is moving without a tilt? b) When the ride is moving with a tilt?
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.
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TROIKA
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TROIKA
Name(s)______Name(s)______
Part 1 Write complete answers to each of these following questions on your own paper. 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.
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TROIKA
Name(s)______Name(s)______
Part 2 Write complete answers to each of these following questions on your own paper. Equipment: stopwatch, calculator
1. Estimate the length of the primary (arm) axis.
Estimated length ______m Describe how you estimated this distance.
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.
Estimated length ______m Describe how you estimated this distance.
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. Number of revolutions =______
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Time for all revolutions = ______s ______s ______s Average time for one revolution = period = ______s Average number of revolutions/second = frequency = ______rev/s
6. Using repeated measurements, determine the time for the secondary (cluster) axis to make several continuous revolutions. Number of revolutions =______Time for all revolutions = ______s ______s ______s Average time for one revolution = period = ______s Average number of revolutions/second = frequency = ______rev/s
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:
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.
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TROIKA
Name(s)______Name(s)______
Part 3 Equipment: calculator, accelerometer
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.
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:
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.
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Physiology of Amusement Park Rides Physiology of Amusement Park Rides
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 6. Enlarges eye pupils 10. Fast breathing 3. Tense muscles 7. Trembling 11. Stomach Butterflies 4. Unable to move 8. Sweaty hands 12. Other
Ride Pulse Rate Breathing Rate Symptoms Before After Before After 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. 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? 2. Based on your observations, how could an amusement park design a ride to give greater illusion of speed and danger? 3. On a separate sheet, describe a ride that you would design.
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For Teacher Reference Only Ride Specifications
Carousel Period of Revolution 19.5 s Radius 27 ft PLEASE DO The Mind Eraser
Total time of ride 1 min 45 sec NOT SHARE Height of first hill 125 ft THESE Mass of train 7500 kg Track length 740m PAGES Track gauge 1217 mm Lift motor 129 kW DC WITH Length of train 15 m
Capacity STUDENTS
number of trains 2
coaches per train 10
passengers 2 per coach
passenger mass 150 kg per coach
Power usage 300kVA
Big Wheel
Period of revolution 24 sec Diameter 80 ft Capacity
number of gondolas 20
passengers 6 adults or 8 children per gondola passenger mass 583 kg/gondola Drive motors 8 x 7.5 hp = 60 hp Power Requirements total 130 kW drive 70 kW lights 60 kW
Line voltage 220 V, 3 phase, 60 Hz PLEASE DO Lighting voltage 110 V NOT SHARE
Boomerang THESE Track length 662 m Track gauge 1219 mm PAGES Train length 18.5 m Capacity WITH number of trains 1 STUDENTS coaches per train 4 passengers 4 per coach passenger mass 300 kg per coach Power Usage 190 kVA
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Dragon Wing Capacity number of vehicles 16 passengers 2 per vehicle passenger mass 154 kg per vehicle PLEASE DO average ride speed 8.6 rpm ride duration 3 min 55 sec NOT SHARE Max diameter at full rpm 27.43 m Drive motors 5 x 460 V, 3 phase, 60 THESE Hz Power requirements PAGES total 160 kVA WITH drive motors 60 kVA hydraulic motors 75 kVA STUDENTS lights 7 kVA Lighting (neon) voltage 110 V Hydraulic pump motor 100 hp Sea Dragon Length of support arm 40 ft Length of ship 35 ft 6 in Max speed 35.7 ft per sec Power requirements: motor 75kW lights 25kW Sidewinder Diameter of loop 30 ft Height at top of loop 60ft Height of station 50 ft Acceleration at start 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 10,120 Hot Dogs 232,640 Hamburgers 303,000 Ketchup 2,862 gallons Mustard 891 gallons Funnel Cakes 96,912
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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
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