Research question: How does the velocity of the balloon depend on how much air is pumped into the balloon?

Transcription

1 Katie Chang 3A For this balloon rocket experiment, we learned how to plan a controlled experiment that also deepened our understanding of the concepts of acceleration and force on an object. My partner and I decided on seeing if the amount of air pumped into the balloon would affect the velocity of the balloon. Thus, how many pumps of air was our independent variable and its velocity was our dependent variable. In order to carry out this experiment, we taped a string from one wall to the other with our blown up balloon, which was attached to it by a straw (the string went through the straw that was taped onto the balloon), and let it go without any force. We let the air inside of it carry it as far as it would go. After doing this several times, each time lowering the amount of air pumped into the balloon, we reached the conclusion that the less air there is inside of the balloon the faster it would go and therefore the greater velocity it would have. However, this does not necessarily mean that it travelled farther. Even though more pumps of air slowed down the balloon, it went farther than when there was less air in the balloon, going at a faster speed. Therefore, the amount of air in the balloon and the velocity of the balloon are inversely proportional. Research question: How does the velocity of the balloon depend on how much air is pumped into the balloon?

2 Expectations: Figure 1 I expected the position of the balloon to move forward suddenly (steeper slope), and then slow down more gradually. For the position of the balloon, I predicted that balloon would go forward at a fast rate, shown by the steep slope at the beginning, and then slow down very gradually. When I first thought about it, I imagined that the air would be let out slowly through the back, which would explain the smaller slope of the line in the second part. However, as this was compared with my results, I quickly realized that this was not true. First of all, when the balloon started to run out of air towards the end of the run, it did not gradually slow down. Instead, it did not slow down at all until all the air was gone, where it then abruptly stopped. I was accurate on the first half of the graph where the forward movement would cause the positive slope (Figure 6); they were consistent with each other on that. However, even though having the gentler slope at the end was consistent with what I expected the position graph to look like, it ended up not being correct. The balloon s position carried a steady, increasing slope and therefore had a constant increase in velocity.

3 Figure 2 I expect the velocity of the balloon to be as shown: to speed up suddenly until it reaches its fastest point, where it then slows down at a lesser rate than it sped up in. The line ends at 0 because it eventually has to stop. For my predictions of the balloon s velocity, I drew it so that the velocity would increase at a very high rate and once reaching the peak of its speed, it would slow down at a lesser rate than it sped up in. At the end of the graph, the velocity is constant and 0, meaning that the balloon has come to a stop. Overall, my velocity expectations were pretty consistent with my results, but just drawn a little exaggerated and extreme. The velocity did increase and change constantly, as I drew it at the beginning of Figure 2, but it was not as steep and it did not start at 0. However, if I had filmed the balloon going from the very start, it would have started at 0, but I only captured the middle part of the run. This also explains why the velocities of the 6, 5, 4, and 3 Pump trials end in the middle of the graph and not at 0 like they should (Figure 7).

4 Figure 3 I expect the balloon to accelerate a lot towards the beginning until it reaches its fastest point, where it will then start to decelerate until it stops completely. I expected my bullet to have constant acceleration, and then slowly decelerate back down to 0, which is what I meant by this drawing. I drew an upward slope to represent the constant acceleration, and the decreasing slope to represent the deceleration. These predictions were consistent with my results, but I drew it completely off. Even though I do not have a separate acceleration graph, I do know what it would look like. Since I did not start recording from the very beginning, the line would start at somewhere greater than 0. From there, it would move horizontally to show the constant acceleration and then it would drop dramatically to 0 once the balloon stopped moving.

5 Figure 4 This free body diagram represents the balloon when it has more air in it. It has less net force acting upon it. Also, because pumping more air inside the balloon would make the overall surface area larger, it would have a greater air resistance. Though the interaction between the string and the straw would bring some friction, it wouldn t bring a lot due to the material it is made out of. Figure 5 This free body diagram represents the rocket balloon with less air in it. Because it now has a smaller surface area, the entire balloon would have less air resistance, though friction would remain more or less the same. The net force is larger than when the balloon has less air in it, as shown in Figure 8. Gravity would remain the same.

6 List of controlled variables: Air per pump Pushed and pulled the pump to the very end to make sure the same amount of air was put in with each pump. Type of string Used the same string for all trials. Straw Instead of attaching and detaching the straw from the string and using different sized straws, we left the straw on the string and just moved the balloon on and off with tape. Same balloon If the balloon had a different shape, for example, there might have been more or less air drag which would affect the velocity Position of Camera The position of the camera needed to stay the same since it would affect the marking of the videos.

7 Qualitative Observations: Position of 5 Balloon Trials(m) Position(m) 4.50E E E E E E E E E E E Time(sec) 6 Pumps 5 Pumps 4 Pumps 3 Pumps 2 Pumps Figure 6 Combined position of all 5 balloon run trials. In the position graphs, I noticed that all the trials graphs were curving a little bit upwards, more or less (except for the 2 Pump trial, which had a significant downward curve). This means that the balloon had constant acceleration, even if it was only accelerating a small amount. If the position lines were completely straight, however, it would mean that the balloons had a constant velocity, which results in the acceleration being 0, but this was not the case. The lines are curving up positively meaning a constant change in velocity and therefore a constant acceleration. It can also be seen that the slope increases, or gets steeper, with each trial. From this piece of data, we can tell that the balloon moves at a faster rate, or has a greater velocity, with less air than when it has more air. This results in a faster acceleration. In addition, from my analysis of these graphs, stating that there is a point at which the velocity stops increasing with each lesser number of pumps is reasonable. If the 2 pumps trial is closely looked at, the slope decreases so that the beginning of it is almost the same as the 6 Pump trial. While it is likely that I may have been a little inaccurate in marking the videos, the slope would not have changed so dramatically. In addition, also in the 2 pumps trial, the trend of the graph tapers out until it is almost horizontal. This type of curving means that there is a negative change in velocity, which means that the balloon was decelerating until it eventually stopped.

8 Velocity of 5 Balloon Trials(m/s/s) Velocity (m/s/s) Pumps 5 Pumps 4 Pumps 3 Pumps 2 Pumps Time(sec) Figure 7 A combined velocity graph of all 5 trials. I noticed that the velocity points are not exactly in line with each other. In fact, even though they do show a trend, some points are significantly higher or lower than the rest of the data in that trial. When marking the video, it is difficult to mark the same exact point for each frame. Therefore, it is extremely likely that I was off while doing so. In addition, while the balloon was moving, it kept on wobbling which could explain the unevenness of the trends of the graph. I also noticed that the data points for the 2 Pumps trial was the exact opposite of the previous trials; instead of going at an upward slope, it starts from the same place and has a negative steep slope until it finally reaches 0 where it evens out. This is saying that the velocity decreases at a fairly constant rate until it almost comes to a complete stop. Because the slope of velocity decreases, you can safely say that the balloon decelerates at a constant rate. However, after I watched the video of the 2 Pumps trial again, I noticed that suddenly jerked to a stop, something that did not happen with the other trials. The reason for this could be that the straw and the string got stuck in the tape on the straw, which happened before, and therefore caused it to suddenly stop. Though I believe that the 2 Pump trial would have decelerated without this issue, I do not think that the slope would have been so dramatic. Also, the second part of the 2 Pump trial (and the entire 6 Pump trial) has a constant velocity due to the basically horizontal (zero) slope which therefore results in again, 0 acceleration and 0 net force. In this case, this is when the balloon stopped. The bumpiness at the end is because the balloon bounced up and down for a period of time before it completely stopped. If you refer to Figure 9, you can see this happening with the marked dots.

9 In the 4, 5, and 6 Pump trials, slope is relatively increasing constantly, which means that the balloons also accelerated constantly. All of the trials also started at a number greater than 0 in this graph. I would have thought, as shown in Figure 2, that they would have steadily increased from the origin, or 0. However, what I forgot to take into account was that the balloon was not filmed from the very beginning; only the middle part of the trial was filmed which means that the balloon was already moving when I started to mark it. Calculating Forces: To calculate the total net force on the balloon, I used the formula Fnet=ma, or net force= mass x acceleration. I obtained the mass by weighing the balloon on a scale and then converting it to kilograms. Finding out the acceleration was simple: I used the Linear Fit tool on LoggerPro with the velocity graphs after marking each video, which would find the approximate slope (acceleration). All I had to do now was multiply everything together. OOPS!!! MISTAKE! I miscalculated the mass of the object! OH NOES D: Instead of kg, it should be kg. The original mass was 2.43g, which means that the decimal has to be moved to the left 3 places. Correct NET FORCES: 6 Pumps: Fnet= 0.011N 5 Pumps: Fnet= 0.013N 4 Pumps: Fnet= 0.018N 3 Pumps: Fnet= 0.020N For example: in the 6 Pumps calculations, the represents the acceleration of the balloon (obtained from its velocity graph) and the kg, or the CORRECT kg, represents the mass of the object. Figure 8 Notice that as the number of air pumps goes down, the faster it accelerates. This corresponds with the velocity and position graphs. Also, because the net forces are greater than the force of gravity on the balloon, N, it could theoretically lift and push the balloon straight into the air.

10 Figure 9 Marked videos of the 2 Pumps trial (left) and the 3 Pump trial (right). Figure 10 Marked videos of the 4 Pump trial(left) and the 5 Pump trial(right). Figure 11 Marked video of the 6 Pump trial.

11 Figure 12 I obtained all of my graphs from excel by using this table format. Originally using LoggerPro to get those numbers, I copied and pasted the Time and X (position) column into Excel, leaving a column in between for the Actual Time. In order to get the actual time, I used the formula that subtracted from each of the cells in the Time(sec) column. Figure 13 The formula in Excel I used to obtain my velocity data. To get the velocity, I subtracted the second cell in the Position column from the third cell in the position column to get the distance travelled by the balloon. I then divided that by the time it took to travel that distance, which was found by subtracting the same cells from each other in the Actual Time column. This would then result in velocity because you would have the distance, meters, over time, seconds or m/s. To find the acceleration, the same thing would be done, except using the velocity and time columns instead of the time and position columns.

12 Conclusion: In conclusion, my initial question of How does the velocity of the balloon depend on how much air is pumped into the balloon? ended having a clear answer. Looking back at the velocity graph of Figure 7, it can immediately be seen that the velocity increases as the number of pumps decreases; they have an inverse relationship. Starting from the trial where the balloon had 6 pumps of air, the velocity was almost if not, constant. From then on, with each fewer number of pumps of air, the velocity increased or had a steeper line; the velocity also changed at a constant rate within that line. Because of this, the balloon was also accelerating at a constant rate. However, there is a point at which the velocity stops increasing with each lesser number of pumps of air. For the 2 Pumps trial, instead of its velocity changing at a constant rate upwards, the velocity changed its rate at a velocity downwards. This can mean many things. First, the velocity had a negative slope, and since the slope of the velocity equals acceleration, this also means that the balloon was decelerating while, during all the other trials, they were accelerating. Therefore, this must mean that the balloon s velocity goes up as the number of air pumps goes down until a certain point (number of pumps), where the velocity no longer increases. As a result, this Balloon Rocket experiment proved that the velocity of the balloon increases as the number of pumps of air in the balloon decreases. Our method of finding these results was simple. We taped a long piece of a thin, nylon material string from one wall to another, making it as level as possible. Before securing down both ends, however, we first slipped the string through the straw that would be attached to the balloon and allow it to glide along. Before taping the straw to the balloon, we would first blow the balloon up, and tie a loose knot while taping it to the straw. One person would stay with the balloon, and one person would start the camera, which was tilted at an angle against books so it would be the same each time. The person with the balloon would then untie the knot and let go of the balloon. We repeated this for each change in the independent variable. If I were to do this experiment again, I would try to get thicker rope, since this one allowed the balloon wobble up and down too much. This affected my overall results in velocity and acceleration. Also, I would film the trials from a camera tripod because although the books made a somewhat sturdy base, it was tilted at an angle; I would much rather have it at the same level at which the balloon was traveling in.