Graphing and Extrapolating Data
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1 Barbie Bungee Jumping Graphing and Extrapolating Data Team members have been hired to work for the Evil Knievel Entertainment Company. This company provides rock climbing, sky diving, extreme skateboarding, and hang gliding adventures to the public. The current market research indicates that the company should add bungee jumping to its list of entertainment services. As part of the preliminary research, the management assigned teams the task of working out the details of the jump that will ensure a safe yet thrilling experience. The company has several sites planned for bungee jumping and each site is at a different height. PURPOSE To ensure a safe and thrilling jump you will determine the relationship between the jump height and the number of rubber bands used to make the bungee cord. You must allow your action figure to come as close to the floor as possible without sustaining any injuries or fatalities. MATERIALS meter stick rubber bands, 7 to start Barbie dolls or other action figures balance graphing calculator or computer graphing software Safety Alert 1. Wear safety goggles. 2. Use extreme caution during jumps. PROCEDURE 1. Use one rubber band to secure Barbie s ankles together and to serve as a point of attachment for the bungee cord. Use a small rubber band to tie back Barbie s hair if it is not already in a ponytail. 2. Mass Barbie on the balance. Record the mass in Data Table Construct a bungee cord composed of 2 rubber bands and attach it to Barbie s ankles. Barbie will fall freely from a standing position, plunging head first throughout this activity. Measure the initial length of the 2-band bungee you constructed once it is attached to Barbie s ankles. Test drop Barbie several times to practice taking readings. Repeat this jump two more times and record the data. 4. Add a rubber band to your attached bungee cord. Measure the new cord length. Drop Barbie three times and record the data. 578 Laying the Foundation in Middle Grades Chemistry and Physics
2 28 5. Repeat step 4 until you have a total of 6 rubber bands. Record the data each time. Additional trials may be performed if time permits. You may have to devise a way to take measurements that are longer than 1.0 meter. 6. Calculate the average of the data and record it in the data table. 7. Using a graphing calculator or graphing software, construct a graph of drop distance vs. number of rubber bands. Run a linear regression on the data and write your regression equation in y = mx + b format in the space provided in the data table. 8. Use the regression equation to predict how many rubber bands will be needed in order for Barbie to perform a safe, yet thrilling jump for each location that your teacher specifies. Your teacher will set the boundaries for both Barbie s safety and her thrill factor. Laying the Foundation in Middle Grades Chemistry and Physics 579
3 Name Period Barbie Bungee Jumping Graphing and Extrapolating Data DATA AND OBSERVATIONS Mass of Barbie = Data Table Number of Rubber Bands Initial Length of Bungee (m) Maximum Drop Distance Trial 1 Trial 2 Trial 3 Average Linear Regression Equation: 580 Laying the Foundation in Middle Grades Chemistry and Physics
4 28 CONCLUSION QUESTIONS 1. What is the significance of the y-intercept in your regression equation? 2. Use your regression equation to predict how many of your rubber bands would be needed to allow Barbie a successful, yet thrilling jump from a height of 100 feet. Show all calculations in the space below. 3. Calculate the stretch coefficient for the trial that used 4 rubber bands by using the following formula: Amount of stretch Stretch factor = mass of Barbie Laying the Foundation in Middle Grades Chemistry and Physics 581
5 4. Ken wants to jump and have some fun too. Barbie loans Ken her bungee cord, but warns Ken that this may not be a safe plan. Why may it be a bad idea for Ken to use Barbie s bungee cord? 5. A student measured the mass of Barbie before attaching the first rubber band that secures Barbie s ankles to the bungee cord. How will this error affect the calculated value of the stretch factor? Your answer should state clearly whether the stretch factor increases, decreases, or remains the same and must be mathematically justified. 582 Laying the Foundation in Middle Grades Chemistry and Physics
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