Barbie Bungee Jump Lab

Transcription

1 Cyriax, Pereira, Ritota 1 Georgia Cyriax, Sophia Pereira, and Michelle Ritota Mrs. Rakowski Honors Physics: Period 3 11 March 2014 Purpose: Barbie Bungee Jump Lab The purpose is to design a bungee jump ride for a Barbie doll. To do this we must find the correct number of rubber bands used to reach the distance from the top of the balcony in the science wing to 10 cm off the ground. Hypothesis: 1. If we create a scaled down version of the bungee jump from the balcony, we should be able to calculate how many rubber bands are needed to successfully achieve the right distance for Barbie s bungee jump. 2. If we use conservation of energy principles, then we will be able to calculate the number of bands that are needed to successfully achieve the right distance for Barbie s bungee jump. Procedure for Hypothesis 1: Independent variable number of rubber bands Dependent variable the distance the rubber bands stretch Controls Barbie s height, Barbie s mass, type of rubber bands

2 Cyriax, Pereira, Ritota 2 1. Gather materials needed for lab including Barbie, rubber bands, meter sticks, camera, and tape. 2. Attach two meter sticks to a wall or door with tape in a continuous line and two rubber bands to Barbie s ankles. See the picture of the apparatus to set up correctly. 3. Hold Barbie at the highest point of the meter sticks and drop her. Use a camera or phone to record the fall. 4. Once dropped, measure lowest point Barbie s head reaches on meter sticks using the recording and record data in the data table. 5. Perform two other trials and record the data. Then find average centimeters Barbie fell to. 6. Repeat steps 3 to 5 with three rubber bands and then four rubber bands. 7. Create an Average Distance vs. Number of Rubber Bands chart out of the recorded data. 8. Use a trendline to create an equation to calculate the number of rubber bands required for the bungee jump.

3 Cyriax, Pereira, Ritota 3 Procedure for Hypothesis 2: Independent variable Force applied on rubber bands (dependent on the mass of the weights) Dependent variable the distance the rubber bands stretch Controls Type of rubber bands 1. Measure Barbie's mass and height and record the data. 2. Determine the spring constant of the rubber bands by a. Setting up the apparatus shown below. b. Hang a weight of 0.05 grams on the rubber band and record the distance the rubber band stretched in meters. c. Repeat step b over with weights of 0.1, 0.15, 0.2, 0.25, 0.3, and 0.35 grams. d. Create a Force vs. Distance of Rubber Band chart with a linear trendline and

4 Cyriax, Pereira, Ritota 4 measure the slope. 3. Calculate the gravitational potential and elastic potential energy of Barbie before she jumps using the equation GPE= mgh. 4. Calculate how much the rubber bands will stretch using the equation EPE= ½kx^2. 5. Determine the number of rubber bands needed for Barbies bungee jump by using adding the distance of stretch or compression, Barbie s height, and 10 centimeters. Then subtract the numbers from the height of the balcony. Finally divide that number with the length of one rubber band to get the answer. Data/Observations: First Hypothesis: # of rubber bands Trial 1 (cm) Trial 2 (cm) Trial 3 (cm) Average (cm) Events Observed: We found it hard to measure the distance the rubber band stretched to because it happened in an instant. Even when recording the fall of Barbie and slowing down the video, exact measurement were almost impossible to achieve. We had trouble finding a suitable place to conduct the experiment. At first we tried to conduct it without a wall but finding the exact measurement to drop it from was too challenging. The solution to this problem was using the wall as the location, but even the wall had its flaws because it didn t allow the Barbie to drop like it would drop from a balcony.

5 Cyriax, Pereira, Ritota 5 Counting the number of rubber bands was a little off as well. There was part of the rubber band used to like together the next object and therefore creating some error within the experiment. Analysis of data: The range of the independent variable was 2 to 4 rubber bands. This was sufficient enough for the lab because the amount of data collected from the independent variables was used to increase the accuracy of the result. The values found for each trial were not consistent; instead they changed in small intervals either increasing or decreasing. Reproducing the data will be very difficult because replicating inconsistent data is impossible and the rubber bands always end up stretching out after being tested on. Second Hypothesis: Force (N) Distance Rubber Bands Stretched (m) Events Observed: As usual, getting exact measurement was tricky because the weights got in the way of the ruler.

6 Cyriax, Pereira, Ritota 6 We noticed that when adding the weights, the rubber band was slowly stretching out and, before we knew it, the length of the rubber band after was different from when we started. Analysis of Data: The range of the independent variables was 0.49 to 3.43 Newtons. This was sufficient enough for the lab because the amount of data collected from the independent variables was more than enough to increase the accuracy of the result. The values found for each trial were not consistent; instead they changed in similar but not accurate intervals either increasing or decreasing. Reproducing the data will be difficult because replicating inconsistent data is near to impossible and the rubber bands always end up stretching out after being tested on. Analysis of Data: First Hypothesis:

7 Cyriax, Pereira, Ritota 7 Average Distance (m) = 0.25(Number of Rubber Bands) The graph represents the relationship between the number of rubber bands used and average distance it stretched. The rubber band stretches about 0.25 meters per rubber band with the additional height of Barbie added. The correlation between the number of rubber bands used and average distance it stretched is that every time the number of rubber bands used is multiplied by 0.25 and is added to , it equals the average distance the Barbie will reach. Second Hypothesis:

8 Cyriax, Pereira, Ritota 8 Distance (m) = [Force (N)] The graph represents the relationship between the amount of force applied to the rubber bands used and distance it stretched. The rubber band stretches about meters per Newton applied. The correlation between the amount of force applied to the rubber bands used and distance it stretched is that every time the amount of force applied to the rubber bands is multiplied by and is added to , it equals the distance the rubber band will stretch. This data was used to find the spring constant of the rubber bands which is 10000/691. This was found by using the reciprocal of the slope from the graph. Calculations Using Data Collected: (see attached papers) Results: Hypothesis 1: 18-rubber bands - too short

9 Cyriax, Pereira, Ritota 9 Hypothesis 2: 25 rubber bands- too long Additional trials: 24 rubber bands - too long 23 rubber bands - just right Percent Errors: (see separate piece of paper) Conclusion: The purpose of this experiment was to design a bungee jump ride for a Barbie doll by calculating the number of rubber bands needed to reach the distance from the top of the balcony in the science wing to ten centimeters off the ground. We had two methods of conducting our experiment. One method was determining the relationship between the average drop height versus the number of rubber bands required. The second method was to use conservation of energy principles. In our first model, we hypothesized that we could create a scaled down version of the bungee jump from the balcony, we should be able to calculate how many rubber bands are needed to successfully achieve the right distance for Barbie s bungee jump. After creating the apparatus, we used different amounts of rubber bands to measure the distance the Barbie doll fell. We then created a graph and, using the equation of the graph, we calculated how many rubber bands were needed for Barbie s bungee jump. The independent variable of this experiment were the number of rubber bands we used. The dependent variable was the distance the rubber bands stretched. The controls of the experiment were Barbie s height, Barbie s mass, type of rubber bands. To ensure that our constants remain the same, we made sure that we had ample rubber bands of the same type stashed away and we chose the same barbie when

10 Cyriax, Pereira, Ritota 10 conducting the experiment. During this part of the experiment, we found it hard to measure the distance the rubber band stretched to because it happened in an instant. Even when recording the fall of Barbie and slowing down the video, exact measurement were almost impossible to achieve. We also had trouble finding a suitable place to conduct the experiment. At first we tried to conduct it without a wall but finding the exact measurement to drop it from was too challenging. The solution to this problem was using the wall as the location, but even the wall had its flaws because it didn t allow the Barbie to drop like it would drop from a balcony. Not only that but, counting the number of rubber bands was a little off as well. There was part of the rubber band used to like together the next object and therefore creating some error within the experiment. The range of the independent variable was 2 to 4 rubber bands. This was sufficient enough for the lab because the amount of data collected from the independent variables was used to increase the accuracy of the result. Moreover, the values found for each trial were not consistent; instead they changed in small intervals either increasing or decreasing. Reproducing the data will be very difficult because replicating inconsistent data is impossible and the rubber bands always end up stretching out after being tested on. The graph of this data represents the relationship between the number of rubber bands used and average distance it stretched. The rubber band stretches about 0.25 meters per rubber band with the additional height of Barbie added. The numerical version of this is Average Distance (m) = 0.25(Number of Rubber Bands) The correlation between the number of rubber bands used and average distance it stretched is that every time the number of rubber bands used is multiplied by 0.25 and is added to , it equals the average distance the Barbie will reach. Once calculated, we found out that the number of rubber bands needed was 18 rubber

11 Cyriax, Pereira, Ritota 11 bands. In our second method, we hypothesized that if we use conservation of energy principles, then we will be able to calculate the number of bands that are needed to successfully achieve the right distance for Barbie s bungee jump. We used various calculations to get the exact number of rubber bands needed for the Barbie jump. One part of the calculations was to calculate the spring constant of the rubber bands. To do this, we tested one rubber bands to see how far it will stretch when more weight was added. For that data, we created an force versus distance of rubber band chart and used the equation of the graph to find the spring constant. During this part of the experiment, we had getting exact measurements because the weights got in the way of the ruler. We also noticed that when adding the weights, the rubber band was slowly stretching out and, before we knew it, the length of the rubber band after was different from when we started. The range of the independent variable in our data table was 0.49 to 3.43 Newtons. This was sufficient enough for the lab because the amount of data collected from the independent variables was more than enough to increase the accuracy of the result. The values found for each trial were not consistent; instead they changed in similar but not accurate intervals either increasing or decreasing. Reproducing the data will be difficult because replicating inconsistent data is near to impossible and the rubber bands always end up stretching out after being tested on. The graph of the data recorded represents the relationship between the amount of force applied to the rubber bands used and distance it stretched. The rubber band stretches about meters per Newton applied. The numerical equation is Distance (m) = [Force (N)] The correlation between the amount of force applied to the rubber bands used and

12 Cyriax, Pereira, Ritota 12 distance it stretched is that every time the amount of force applied to the rubber bands is multiplied by and is added to , it equals the distance the rubber band will stretch. This data was then used to find the spring constant of the rubber bands which is 10000/691. This was found by using the reciprocal of the slope from the graph. After finishing the rest of the calculations, we found out the number of rubber bands needed was 25 rubber bands. Next, we tested our results from our two methods. On our first trial and method of dropping the Barbie from the balcony was with eighteen rubber bands. After dropping her, we found that we did not have a sufficient number of rubber bands, as Barbie had still been elevated too high off the ground. In our second trial and method we attached twenty-five rubber bands to Barbie, but we had found that it was too long as she had hit the ground. Then we tested to see what would be the perfect amount of rubber bands to use for the bungee jump. In a third trial using twenty-four rubber bands, we found that there were still too many rubber bands as it had been slightly too long. In our final trial we attached twenty-three rubber bands to Barbie and had found that it was the sufficient amount which enabled her to be dropped from the top of the balcony and still remain about ten centimeters off the ground. Our first hypothesis didn t work out very well because the number of rubber bands was way less than actually needed. Because of this, the percent of error was about 21.74%. In our second hypothesis, it was shown that it more accurate. We were only off by two rubber bands, which made the percent of error about 8.7%. Overall, the second method of using conservation of energy principles was the best method of all. Reflection: From this experiment we had a taste of the hard work and diligence that must be put in by engineers to find accurate measurements for making safe and effective amusement park bungee

13 Cyriax, Pereira, Ritota 13 jumps. We also applied what we learned about conservation of energy principles to almost-reallife situations. In the future we may be able to more accurately measure the distance she reached by making sections on the meter sticks with tape that can more precisely direct us to the region in which Barbie s head reaches with each set of rubber bands, as well as using a camera to record her drop. If we had more precise ways of gathering that data, we might have been able to prevent much of the inaccuracy in our data. Inputting more research about how amusement park bungee jumps are created could have helped as well.

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