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May 20, 2011 IB Physics HL Year 1 Tomohiro UrakamiIntroduction During this investigation, an air rocket was launched vertically on launcherwith different amount of pressure inside. The motion of first few seconds of rocketlaunching was recorded by 600FPS high-speed camera. The purpose of this investigationwas to find the alteration of air rocket’s maximum forcein different values of pressure.The research question of this investigation is “How does the pressure inside air rocketaffect the maximum force of the rocket after launched.” In Pressure’s law, pressure is defined as the force applied per unit area. In theequation, this is defined as, P= (1.1)where F is force and A is the area.This equation could then reformed into the newequation, P= (1.2)where m is the mass and a is acceleration. From the logger pro, the acceleration of therocket could be calculated. By substituting value of acceleration and the mass of a rocket,a relationship between the force and the pressure of the rocket could beresearched.Therefore, confining that the area of the rocket is the same for all trials, itcould be stated that pressure of the rocket and the maximum force of the rocket are indirect linear proportional relationship.DesignR.Q: How does the pressure inside an air rocket affect the maximum force of the rocket?Independent Variables: the independent variable during this investigation was thepressure inside an air rocket, which was a 2L Coke water bottle. There were six differentvalues of pressure used and four trials were done for each pressure. The pressure wasinserted into the air rocket by the air pumper for bicycle wheels. Pressure weremeasuredand changed by the manometer that was attached to the pumper.Dependent Variable: The dependent variable was the acceleration of an air rocket. The
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May 20, 2011 IB Physics HL Year 1 Tomohiro Urakamimotion of air rocket launching was recorded by 600FPS high-speed camera. This videowas inserted into logger pro on computer and the acceleration was calculated by the slopeof v-t graph. According to this value, the maximum force of the air rocket was calculatedby substituting the number of acceleration and the mass of the rocket into the equation, “F=m*a”.Controlled Factors: The first controlled factor was the air rocket itself. This is because as shown inthe equation in introduction, the mass and the area of the air rocket affects the value ofacceleration of air rocket and thus these had to be controlled in order to find therelationship between pressure and the acceleration of air rocket. The second controlled factor was the launcher. Although there were some sametypes of launchers, the structures of those launchers are not exactly the same.Thediameter of pipe could be different and the friction of the pipe when rocket flies into aircould be different as well. Therefore, it was necessary to keep the shape of air rocket thesame in order to find accurate data. The third controlled factor was the angle of the launching. The launcher wasstabilized on the ground so that the rocket would launch vertically. This was controlledbecause angle would change the gravitational force applied to the rocket and thus thevalue of acceleration could be affected.Figure 1: Set Up
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May 20, 2011 IB Physics HL Year 1 Tomohiro Urakami Ruler As Scalar Water Bottle Air Rocket The Pipe Inserts Air Launching Lock Launch PadProcedure As shown in Figure 1, this investigation was done outside. Ruler was used asscalar so that during the process of analyzing video, acceleration of the rocket could befound. Rocket was connected to the pipe shown in the diagram. Before launching rocket,air was inserted inside rocket by the pumper of bicycle wheels so that the pressure insiderocket increases. The rocket was launched from the launch pad as the launching lock isunlocked. The rocket was flown into the air and the motion of rocket flying out of pipewas recorded by 600FPS high-speed camera. This experiment was done in 6 differentvalue of pressure in kPa and 4 trials were done for each pressure value.
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May 20, 2011 IB Physics HL Year 1 Tomohiro UrakamiData and ProcessingLength of the rocket: 0.3 mMass of the rocket: 55.38 gFigure 2: Data Table of Acceleration in Different Pressure Force (J) ±6 Pressure Trial 1 Trial 2 Trial 3 Trial 4 Average Uncertainty (kPa ) 68.9 36.44 34.81 36.21 38.03 36 4 137.9 49.09 48.08 47.64 49.06 48 4 206.8 90.60 90.38 87.83 90.38 90 6 275.8 95.25 95.14 93.20 95.25 95 4 344.7 126.04 120.89 125.21 126.21 125 5 413.7 146.81 146.98 145.59 144.98 146 4Figure 2 is the table of collected data during this investigation. As Figure 1 shows, thevalue of acceleration increases as the pressure inserted into rocket increases. The smallvalue of uncertainty shows that the data collected during this research were accurate.Thisdata table was used in order to find the maximum force or the rocket at each trial inFigutre 3.Figure 3: Data Table of Maximum Force in Different Pressure Acceleration (m/s/s)±50 Pressure Trial 1 Trial 2 Trial 3 Trial 4 Average Uncertainty (kPa) 68.9 658.0 628.5 653.8 686.8 660 26.00 137.9 886.5 868.2 860.2 885.8 880 13.00 206.8 1636.0 1632.0 1586.0 1632.0 1620 25.00 275.8 1720.0 1718.0 1683.0 1720.0 1710 19.00 344.7 2276.0 2183.0 2261.0 2279.0 2250 48.00 413.7 2651.0 2654.0 2629.0 2618.0 2640 18.00
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May 20, 2011 IB Physics HL Year 1 Tomohiro UrakamiFigure 3 is the data table with the value of maximum force in each trial in different valueof pressure. There is an increase in the value of force as the pressure increases. Accordingto this data table, a final graph of Maximum Force versus Pressure Graph was created.The uncertainty bar was set to be 50 for maximum force, which is about 2% off for therocket launch with 413.7kPa. This is a relatively small number, and it increases the levelof confidence.Figure 4: Final GraphFigure 4 is the final graph that gives the answer for the research question. The graphshows that the maximum force increases and the pressure inside the air rocket increases.The constant value of slope m is “0.326x”.
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May 20, 2011 IB Physics HL Year 1 Tomohiro UrakamiFigure 5: Final Graph with High and Low FitsFigure 5 is the final graph with high and low fits which indicates the level of confidenceof the data in this investigation. Although three dots are not in the range of high and lowfits, all dots are close to the fits and the uncertainty bars of those dots are reaching eitherhigh or low fits. This shows that data collected is accurate enough to answer the researchquestion.Sample CalculationFinding Uncertainty for Acceleration(Biggest acceleration-smallest acceleration)/2(686.8 m/s/s – 628.5m/s/s)/2 = 26Changing into kPa from PSI1Pa = 145.04×10−6Psi10PSI/ 145.04×10−6 = 68.9kPa
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May 20, 2011 IB Physics HL Year 1 Tomohiro UrakamiFinding Maximum Force for Each TrialF = (mass of the rocket) * (acceleration of a trial) = 0.05538kg * 658m/s/s = 36.44JFinding Uncertainty for Maximum Force{(Biggest a+50)*(0.05538+0.00003kg)-(Smallest a-50)*(0.05538-0.00003kg)}/2{(686.8+50)*(0.05541kg)-(628.5-50)*(0.05535kg)= 26Figure 6: Sample VideoFigure 6 is one of the scenes of the video, which was analyzed. In this figure, there aremany blue dots, which show the path of rocket as it left the launch pad. Those blue dotswere used in order to make graph.
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May 20, 2011 IB Physics HL Year 1 Tomohiro UrakamiFigure 7: Sample GraphThis is one of the graphs recorded by the high-speed camera during this investigation.The slope was found from a dot where exactly the rocket leaves the edge of the pipe. Theacceleration was found by finding the slope of this graph. The x-axis Time in this graphhad to be divided by 20 in order to find the time in 600FPS, which was used to record themotion of rocket in high-speed. This value of edited time was also applied to the y-axis,the velocity of the rocket. The value of acceleration is negative because as Figure 6 shows,the rocket moves to left in the video. Going direction of left is considered negative andthis is why the value of acceleration is negative in the graph. However, the actual value issupposed to be in positive and thus when data was transferred into data table, thosenegative turned into positive.
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May 20, 2011 IB Physics HL Year 1 Tomohiro UrakamiConclusion According to the data collected and calculated in data and processing column,the final equation given was, F = (0.326 0.03 J/kPa)P+(11.4 J) (4.1)where F is the force and P is pressure in kPa. The equation above shows the linear directproportional relationship between the maximum force and the pressure. As more pressureis inserted into a rocket, a rocket will have faster acceleration, which eventually increasesthe maximum force of the rocket. It was calculated that the constant increase of force per1kPa is 0.326X. This equation supports the hypothesis stated in introduction. Figure 2 is the collection of original data collected during this investigation.The uncertainties for each pressure show that the difference among 4 trials of launchingwas small enough to be stated that the data was recorded accurately. Furthermore, theuncertainty of the slope of final graph Figure 4 is 0.03K/kPa, which is about 9% off. Sincethis uncertainty value is relatively small, it increases the level of confidence in terms ofthe data collection. The y-intercept of this graph is supposed to show the value ofmaximum force when the rocket is at rest, which is supposed to be 0. The y intercept is11.4, which is relatively a small off. As a result, the relatively small value of uncertaintyand the accuracy of the slope of the final graph indicate the high level of confidence of theresult in this research. This research could be repeated in different circumstances. Different type ofwater bottle could be used as rocket in this research. In this case, same as thisinvestigation, only one rocket should be used in order to keep the mass and the shape ofthe rocket same. Also, water could be inserted inside the rocket and use water rocket inorder to record data of acceleration of the rocket. In this case, the amount of the waterinside rocket needs to be controlled so that the mass of the rocket stays the same in eachtrial. Also, different angle could be used for this investigation. However, since thegravitational force that applies to the rocket would change in different angle, the angleneeds to be controlled in order to find the relationship between the maximum force of therocket and the pressure inside it.Evaluation
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May 20, 2011 IB Physics HL Year 1 Tomohiro Urakami Although the hypothesis was supported, there are some possible errors madeduring this research. Those errors need to be improved in next research. The first possible error was that the rocket launcher was not stabilized on theground. Thus, when the rocket was launched, the rocket did not launch in the samedirection in all trials. This could cause some error in the value of acceleration because ofthe lost in the momentum due to the non-stabilized launcher base. Therefore, the rocketlauncher needs to be stabilized in order to launch the rocket in the same direction. The second possible error was the pressure inside the rocket. Although thepressure put inside the rocket was measured by the manometer attached to the pump,some pressure could have gone out of the rocket when the needle was unplugged.However, this is inevitable since when the needle is unplugged, space is createdwhere theair inside the rocket could escape. Thus, in order to avoid a big amount of pressure goingout of the rocket, the needle must be unplugged as fast as possible. The third possible error made during this investigation was the shape of thewater bottle used. During this investigation, only one water bottle was used to keep themass the same. The water bottle was added pressure in each trial and hit hard on theground after it flew into air. This could cause the damage to the bottle and could havechanged its shape, which could affect the value recorded during the investigation.Therefore, experimenters must make sure that they catch the rocket after each launch sothat big damage will not apply to the rocket. Consequently, if this investigation was to be repeated in the same circumstance,those three errors need to be improved in order to eliminate possible errors and collect asaccurate data as possible.
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