Terminal Velocity Lab Report
Lab_Terminal Velocity- Amrit, MD, Asma, Anika
Terminal Velocity of a Balloon
By Amrit, Md, Asma, Anika, & Yifang
March 12, 2018
The City College of New York
Writing for Engineering ENGL 21007-E
Professor Maryam Alikhani
Table of Contents
Data 6-7
References 10
Abstract
The purpose of the experiment was to measure the terminal velocity of a weighted balloon. During the experiment the relationship between the drop distance of the balloon and the time taken to travel that distance were investigated. Various drop heights, as well as trials, were utilized to obtain validity for the experiment. After every trial, the data was recorded and calculated multiple times to remove unprecedented sources of error. After obtaining all the necessary data, the average time for the balloon to fall from the various heights assigned was calculated. This information was then used to calculate the average and final speed. It was hypothesized that the higher the drop point of the balloon, the longer it will take to fall, causing an increase in its terminal velocity. This is clearly seen when observing the formula for terminal velocity since it is dependent on the average speed. The results of the experiment concluded that an increase of terminal velocity is directly reliant on the average speed, as well as the height of the drop. Factors such as the mass of the balloon can also be tested in further research, allowing us to see the correlation between mass and terminal velocity.
Introduction
Terminal Velocity is the constant speed that an object falling freely obtains when it reaches a certain point, this causes a cease in further acceleration (Encyclopedia Britannica). As the object falls through air it experiences drag force or air resistance that acts upwards and opposes gravity (Encyclopedia Britannica). When an object reaches terminal velocity, “Air resistance equals in magnitude the weight of the falling object. Because the two are oppositely directed forces, the total force on the object is zero, and the speed of the object has become constant” (Encyclopedia Britannica). An example of this would be tying an oxygen inflated balloon and attaching four coins to the bottom of the balloon (opposite side of the knot). The coins will create additional mass dragging the balloon downwards, from here on you will record the time it takes for the balloon to travel various distances and create a distance vs time graph to represent this data. The Average Speed of the balloon will be measured using the formula,
Average Speed = Distance Traveled
Time of Travel
and calculate the final speed using the formula,
Final Velocity = Average Velocity * 2
Materials
Figure 1: Materials used for the experiment
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1 balloon
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4 coins (Quarters)
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1 stopwatch
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1-meter tape
- Masking tape
Procedure
- Blow up a large balloon to full capacity and tie a knot on the top. Tape four quarters to the opposite side of the balloon knot (As shown in figure 3).
- Put temporary marks on a wall or door frame using the masking tape at the designated marks, 50cm, 75cm, 100cm, 125 cm, 150 cm, 175 cm, and 200 cm.
- Have a partner help you drop the balloon starting from the lowest height. Perform the drop at each specific height three times and record your timed results in a data table (As shown in figure 4)
- After obtaining all the results, calculate the average time for the different heights and record it in your data table.
- Using the average time for each specific height, look back at the formula for average velocity which is given in the introduction. Using the formula, calculate the average velocity for each of the drop heights tested. After getting the average velocity, multiply it by two to get the final speed. Record your results.
- Create a line graph with the average time on the horizontal axis and the final speed on the vertical axis. This will allow for a more visual way to comprehend the relationship between the two.
Figure 2: Diagram replicating the actual experiment (shown above)
Figure 3: Experiment set-up, balloon used during drop
Data
Average Time vs. Final Speed
| Distance (cm) | Time 1 (sec) | Time 2 (sec) | Time 3 (sec) | Average Time (sec) | Average Speed (m/s) | Final Speed (m/s) |
| 50 | .37 | .38 | .37 | .37 | 1.35 | 2.70 |
| 75 | .41 | .43 | .40 | .41 | 1.83 | 3.66 |
| 100 | .46 | .46 | .47 | .46 | 2.17 | 4.34 |
| 125 | .60 | .59 | .61 | .60 | 2.08 | 4.16 |
| 150 | .67 | .68 | .66 | .67 | 2.24 | 4.48 |
| 175 | .86 | .86 | .88 | .87 | 2.01 | 4.02 |
| 200 | .91 | .92 | .89 | .91 | 2.20 | 4.40 |
Figure 4: Chart showing data collected from dropping the balloon at different heights.
Figure 5: Line graph showing a relationship between average time and final speed.
Calculations
- Converting (cm) to (m)- Same calculations used for the rest of the distances
Conversion (cm) to (m) = cm/100
(Cm) to (m) = [50cm/100]
(Cm) to (m) = .5(m)
- Average Time (for 50m)- Same calculation method used for rest of the distances
Average Time = Total Time/3
Average Time = [.38(sec) + .37(sec) + .37(sec)]/3
Average Time = .37(sec)
- Average Speed (for 50m)- Same calculation method used for rest of the distances
Average Speed = Total Distance/Time of Travel
Average Speed = [ 50(cm)/.37(sec)]
Average Speed = 1.35(m/s)
- Final Speed (for 50m)- Same calculation method used for rest of the distances
Final Velocity = Average Velocity * 2
Final Velocity = 1.35(m/s) * (2)
Final Speed = 2.70(m/s)
Results and Conclusion
The purpose of this lab was to calculate the terminal velocity of a balloon that had four quarters attached to it. During the experiment we had to calculate the average time and final speed to obtain the terminal velocity of the balloon. After completing a sufficient number of trails, we created a graph to represent the data received, making it easier to depict the relationship between the final and average velocity. We used a basic physics, being distance and time to calculate the average time which was to calculate the average and final speed. The observable trends that were seen throughout the results were, while average speed increased so did the final, portraying a direct correlation between the two. In most cases time had a direct relationship with average speed, being that it increased it. After observing the graph, it was concluded that, as the average time increased so did the final speed. The independent variable here would be average time and the dependent would be being the final speed, this is because as the time increased so did the final speed, thus showing a direct correlation. Sources of error in the experiment would have been the time calculated for each trial. The time could have been off by +/- .05s, this is because of the delay between the balloon drop and the person timing it with the stopwatch. An example of this would be seen when the balloon was dropped from each height either before after the timer has started. The dropper could have dropped the balloon a second or two late having a +/- .01s delay. Sources of error could have also been seen within the measurements, which could have been off by +/- 1 cm. Multiple sources of errors are observed in scientific experiments, being one of the reasons multiple trials are conducted, and the person conducting each stage of the experiment is considered a constant. These sources of errors tend to have a minor impact on the results, still allowing to see the basic correlation between all the variables.
References
- Britannica, Encyclopaedia. “Terminal Velocity.” Encyclopaedia Britannica, Encyclopaedia Britannica, Inc., 24 Oct. 2016, www.britannica.com/science/terminal-velocity.
- [SciShow]. (2012, July 19). Terminal Velocity [Video File]. Retrieved from https://www.youtube.com/watch?v=p0IZsfzDS4s
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