National Science Teachers Association / Toshiba

1999 Laptop Grant

Amusement Park Physics

and the

Calculator Based Laboratory (CBL)

Abstract | Laptop Rationale | Student Learning Objectives | Ties to Curriculum | Number of Laptops | Time Requirement | Required Materials | Lesson Description | Assessment | References | Lesson Suggestions | Footnotes |

Abstract:

The Calculator Based Laboratory (CBL) with a single or triple axis accelerometer allows the student to record and analyze acceleration data collected while riding amusement park attractions. A traditional spring accelerometer is, at best, a fair approximation of the acceleration that one feels. The subjective data is not quantifiable and provides very limited details about the acceleration one experiences. In addition, the thrill and excitement of many of the newer attractions makes watching the spring accelerometer nearly impossible. By using the CBL system, the student is able to concentrate on the effect of the acceleration on their body while collecting the data. After the completion of the ride, the students can analyze the data to determine the acceleration at particular points of the ride. The students can better relate the "feeling" of the acceleration to the graph of the data that allows them to interpret acceleration vs. time graphs.

Laptop Rationale:

The amusement park activity requires a laptop computer to upload and store data recorded from the CBL system. The TI-83 calculator is capable of storing meaningful triple axis accelerometer data collected for a maximum of two 30 second portions of an amusement park ride. The 99 pixel width of the calculator screen also makes viewing amusement park rides requiring at least 300 data points difficult. By uploading the data to an advanced graphing software package on the laptop, students are better able to view and analyze the data in the park and on the return trip.

Student Learning Objectives:

After completing the Amusement Park Acceleration Activity, students will be able to:

1. sketch and explain distance vs. time graphs, velocity vs. time graphs, and acceleration vs. time graphs after observing an object in motion.
2. describe the position of a person on a ride and the acceleration the person experiences at a given point of an acceleration vs. time graph.
3. provide appropriate mathematical models for data collected with a CBL system including but not limited to concepts in linear, quadratic, exponential, sinusoidal, and piece-wise functions.
4. relate acceleration to gravitational forces such as 0g, 1g, 2g ....

Ties to the Curriculum:

This amusement park lesson plan creates the opportunity for grade 9-12 students to integrate math, science and technology as suggested in both the NCTM Standards and AAAS Benchmarks. In particular, the lesson is best described in the Standards 2000 which state that students must "learn to deal with complex problems that involve multiple aspects of mathematics. They must be able to analyze and solve problems that they encounter, without knowing a priori which areas of mathematics apply, because neither in the real world nor in abstract mathematics do problems come cleanly labeled as requiring the methods of algebra or geometry. Indeed, most meaningful problems require drawing upon multiple areas of mathematics for their solutions and can be approached from various directions. When working on complex problems, either alone or collaboratively, students must be able to apply varied subject matter knowledge and varied reasoning and problem solving skills, in integrated fashion." ¹

Number of Laptops:

The ideal ratio of laptops to students would be one computer for every four students. The minimum number would be one. With a single computer, students working at the park could concentrate on the collection of data and writing a summary of the ride's motion. The data can be quickly uploaded to the laptop and students return to a ride to collect more data. Hence, one laptop positioned at a central spot in the park could serve to store the data until it can be analyzed. This would allow the maximum amount of data to be collected during the field trip. Multiple computers would allow for more places around the park to store data. Using a word processor, students could more quickly and legibly record the type of ride, what portion of the ride the data came from, and the sensations experienced. Students may also analyze the data on the way home if each group had their own computer. This would be particularly useful for schools with lengthy travel times.

Time Requirement:

The first time requirement is learning to use the CBL system and analyze data graphs collected from the activities. Prior to attending the park, students will need to learn to operate the programs and the CBL system. This can be accomplished by having students wear the CBL system and run up/down steps, swing the CBL system in a circle, or attach the accelerometer to a pendulum or spring in harmonic motion. Students may also travel to a local park and practice on swings, merry-go-rounds etc. For students familiar with the CBL system, this task will take 1-2 hours and may be accomplished through prior lab activities.

The second time requirement is the travel time to/from the park and the actual collection of data. If one is at an amusement park, data collection may take up the entire day. If an amusement park is not available, substituting travel to a local park with swings, slides, etc. will most likely take 2-4 hours depending upon the number of types of play apparatus and the number of CBL systems available. In a local park, each student may want to collect their own data to relate their experience to the graph. In an amusement park where all students ride in the same "car", one person can collect the data for the entire group. Students going to a local park may also check out the CBL system and collect the data in an evening or weekend.

The final block of time is for the analyzing of the data and student presentations. Depending upon the types of data curves collected and the math background of the students, this may take 3 to 4 days of preparation and presentation. Students may discover mathematical concepts in linear, quadratic, exponential, sinusoidal and piece-wise functions.

Required Materials:

For each student:

	1-	Texas Instruments TI-83 Graphing Calculator (Any programmable model capable of linking to the CBL may be used.)
	1-	Texas Instruments Link Cable
	1-	Park map. Each student should mark the location of the bus pickup point and the "command center" on the map.
	1-	Lab notebook and writing utensil

For each group:²

	1-	Laptop computer
	1-	Texas Instruments Calculator Based Laboratory (CBL).
	1-	Fanny pack configured to contain the CBL.
	1-	Vernier Single or Triple Axis Low-g Accelerometer
	1-	Texas Instruments Graph-Link cable and software
	1-	Acceleration software for the TI-83. The programs with the accelerometers will work, but we have modified them for this particular activity. The modified software package is available on our web site at: http://lhs.lps.org/instruct/. Software for collecting acceleration for most models of TI calculators is available from Vernier at http://www.vernier.com/.
	1-	Schematic drawing/sketch of the amusement park ride/attraction with pertinent details such as heights, lengths, and times. The education coordinator or publicity department of the park may be able to provide these drawings. Our sample notebook is available in pdf form.
	1-	Stopwatch with rubber band for wrist strap.

For the entire group:

	1-	Extension cord with multiple outlet strip to power the computers throughout the day.
	1-	Video Camera to tape the rides for review at a later time. (optional)
	Optional Software:
		Students with a background in precalculus and calculus may find that additional analysis of the data can be achieved using the Graphical Analysis software by Vernier or the DataStudio software by Pasco. Larger graphs can also be obtained by exporting the data to any commercial spreadsheet package such as Microsoft Works, Microsoft Excel, ClarisWorks, etc.

Lesson Description:

1. Divide students into groups of four students. An even number works better as most park attractions seat pairs of riders. Students fearful of heights or susceptible to motion sickness are not required to ride all of the attractions. Each group of students should have at least one student willing to ride any attraction available at the park. Provide a worksheet for students to work on during the ride to the park. Review mathematical calculations, energy concepts, graph types, etc.
2. At the park, establish a "command center" where the laptops will be readily accessible to transfer, save and analyze data. An ideal location is near food, restrooms, tables, and an electrical outlet.
   1. One member of each group must report to the command center once every two hours with a minimum of one hour between reports. Students can upload data to the computer, look at graphs, and get assistance with specific questions at any time.
   2. Each member of the group must report at least one time during the day. These visits are recorded into the lab notebook for the activity. All members of the group must report together at least one time prior to the meeting at the conclusion of the day. Perhaps the entire class could stop for lunch or a mid-afternoon snack for a de-briefing session.
3. Provide a suggestion of which rides/attractions and what sections of the rides may be most appropriate for data collection. Students are required to collect acceleration data from at least four different rides.
4. After observing the ride in operation, each group of students will:
   1. make a sketch of the position (height) of the rider as a function of time.
   2. make a sketch of the apparent velocity vs. time graph.
   3. decide upon a portion of the ride to collect acceleration data.
   4. determine length of time and number of data points to be collected. The time interval between data points is the total collection time divided by the number of data points.
5. Program the CBL system for the proper settings as discussed above using the program ACC1TRIG or ACC3TRIG. Complete instructions for calibrating and using the software package are available on the web site http://lhs.lps.org/instruct/.
6. Secure the CBL to the student using a belt/strap. Board the attraction and press the Trigger button on the CBL at the appropriate place on the ride.
7. After exiting the attraction, use the program GETACC to download the data from the CBL to each student's calculator. Graph the acceleration vs. time data and save to a program if data is acceptable.
8. Record the data and observations about the ride. If ride lines are long, students should go to the next line and begin the boarding process. During the wait, students should use a notepad to record the name of the stored data, the attraction from which the data was collected, the number of data points, the time interval and the point on the attraction where data sampling began. Make a sketch of the graph. Mark on the sketch what motion was occurring at each significant point such as a local maximum or local minimum acceleration and values where the acceleration is zero. Describe the "feeling" you had at this point on the ride. Discuss possible mathematical models and make notes for evaluation on the way home.
9. Repeat the process on the same ride or a different attraction. When students have full calculators of data or have questions about the process or analyzing of their data, proceed to the "command center" and use the laptop computers to store the data using the TI Graph-Link cable and software.
10. Ideas for further investigation:
    1. Is there a difference in being in the front versus the back car? Have two groups of students ride the same attraction. One group sits in the front car and the other in the back car. At a pre-determined point, the rider in the front car lowers his hand and both students trigger their CBL. Both groups of students get together at the end of the ride to share and discuss the results.
    2. As a culminating activity and a way of gathering all of the students together at the end of the day, meet at a specified time for the purpose of mapping the acceleration on an entire ride. Pick the longest ride in the park such as a roller coaster. Time the length of the entire ride and divide the time proportionately among the number of CBL's. Program the CBL with an additional 2 seconds of time. For example, if 20 seconds is required, record data for 22 seconds or more. Board the attraction positioning each student with a CBL in consecutive rows on the ride along with a timing partner. At the starting point, the passenger in the first car drops their hand. The person in the first car starts their CBL and all other passengers start their stopwatch. During the ride, the passenger watches the stopwatch and assists the person carrying the CBL with triggering the equipment. In our example of 20 seconds, the second car would trigger at 20 seconds elapsed time, the third car at 40 seconds, and so forth. When finished, upload all of the data to a spreadsheet. Delete the duplicates at the start or end of the collection for each CBL to graph the acceleration for the entire ride. How did it turn out?
11. The return trip to school will allow the students to prepare a presentation of a selected ride for the class to promote discussion of the graphs and data collected and analyzed. Each group is given a description and drawing of a mythical amusement park attraction including various components of rides studied during the day. Students will begin to formulate a sketch of the position vs. time, velocity vs. time, and acceleration vs. time graph for the ride. Students frequently name this ride the "Nightmare".

Assessment:

The assessment strategy involves three specific projects with the following expectations:

1. Student Lab Activity Notebook
   1. Sketch of distance vs. time, velocity vs. time, and acceleration vs. time for a minimum of four rides.
   2. Sketch of the recorded data with the methodology for data collection.
   3. Interpretation of the acceleration data relating position on the attraction.
2. Group presentations and explanations of data including one of the four rides and an assigned portion of the class activity (mapping the complete acceleration of a roller coaster).
   1. Explanation of all graphs and the collection methods.
   2. Mathematical models presented where appropriate. Models may include equations such as linear, quadratic, sinusoidal, and exponential functions. Students may choose to use piece-wise functions to describe the collected data.
   3. Where models may be difficult to derive, other concepts such as force diagrams, motion maps, period, amplitude, and frequency may be used.
   4. Observations such as, does position in a ride have an effect upon the data, how did the data match the feeling experienced on the ride and how does the acceleration match the sketch predicted prior to boarding the ride?
3. The mythical amusement park roller coaster evaluation of the "Nightmare" will consist of a sketch of the same graphs in part 1a for a ride
   1. dropping from a height and returning to a position about one-half as high.
   2. traveling through a vertical loop and nearly horizontal loop.
   3. rolling up an incline to a stop.

References:

Clemens-Walatka, Bernadette, Amusement Park Inquiry, The Science Teacher, January 1998.

Energy in Motion, Physics in the Park, Knott's Berry Farm Amusement Park Education Department.

Gastinaue, John Physics with CBL, Vernier Software, 1998

Honig, Carlye "The Ups and Downs of Roller Coaster Design", Exploratorium Quarterly, Summer 1987

Morely, Nina, Physics Day at Six Flags Great America, Joliet West High School Student Handout.

Unterman, Nathan Amusement Park Physics, J. Weston Walch Publishers 1990

Lesson Suggestions:

1. If possible, attend the park on a "Physics Day" where the park is expecting physics students collecting data and studying the rides.
2. Contact the park's Education Coordinator and/or Safety Officer several months ahead of time noting the kind and type of equipment you will be bringing. Many parks will allow individuals to wear the CBL system as long it is securely fastened to the body and will not fly off during the ride.
3. A heavy rubber band strap should be used on the stopwatch instead of a string or rope. The band will prevent the stopwatch from flying off the wrist. However, if the watch should become lodged in the ride, the rubber band should slip off or break before serious injury occurs.
4. Be aware of all school policies regarding field trips.
5. Invite an administrator to join the students on the fun and educational trip.

Footnotes:

¹ NCTM Principles and Standards for School Mathematics: Discussion Draft, October 1998, pg. 272
²See note in Lesson Suggestions regarding safety issues.

Amusement Home | Lesson Plan | Planning | The Trip | Ripcord | Assessment | Final Exam