Exploring the Relationship Between the Distance a Rubber Band is Stretched and its Launch Velocity
Kelly Nguyen
Introduction || Method || Results || Evaluation || Bibliography || Return to Research
Introduction: Top
Rubber bands have always been integrated into my life. Ever since I was little, rubber bands have been scattered all over my room. I use them for everything. I use them to tie my hair up for work and when I’m working out, I use them to shoot at my brother, I use them to close chip bags, and more. Besides the versatility of them, I was always picky about what rubber bands I used and have always wondered what made a rubber band good versus bad. Rubber bands are either made from natural (normally from a tree) or synthetic rubber (polymers) which could be a factor in how good the quality is. But, no matter how it’s made, I figured out that the elasticity of rubber bands is what makes them good. The more elastic, stronger, and stretchier they are, the better they are in my opinion. In my head, the elasticity of a rubber band directly correlates to the launch velocity of it. The physics behind a rubber band seem so simple but complicated at the same time.
When an object such as a rubber band is launched, the launch velocity of it can be found using the final velocity, displacement, acceleration, and time. The acceleration is given because of gravity (gravitational acceleration) and so is the final velocity because it will always land at a rest. By using one of the equations below, we can determine how fast a rubber band is launched and examine the relationship between the amount a rubber band is stretched and its launch velocity.
With more potential energy being stored in the rubber band the further it is stretched, we can assume that it will shoot at a higher velocity the more it is stretched because more potential energy can be converted into kinetic energy allowing the rubber band to launch quicker.
Statement of the problem:
The purpose of this investigation is to find the relationship, if any, between the velocity of a rubber band and the amount it is stretched.
Experimental hypothesis:
If a rubber band is increasingly stretched by a centimeter for each trial, then the rubber band’s launch velocity will also increase with a linear trend. This might occur because when a rubber band is stretched there is more potential energy which therefore means there will be more kinetic energy. With more kinetic energy, the launch velocity will increase.
Variables:
The independent variable in this experiment is the length the rubber band is stretched in centimeters (cm). This is defined by how far the rubber band is pulled back in order for it to be launched. This will be measured with a ruler and will increase in increments of 1 cm. In total, there will be 12 trials and it will go from 0 to 12 centimeters. The lengths were chosen out of practicality because a rubber band can’t be stretched to enormous lengths but going from 0 to 12 centimeters will show a drastic change in launch velocity. I chose 1 cm increments in hopes that it will give me more accurate data because the lengths are close together.
The dependent variable is the velocity of the rubber band once it’s launched dependent on the amount it’s stretched (also known as the launch velocity). This will be calculated using SUVAT to determine the initial velocity, or the launch velocity, of the rubber band. By using the distance it went, the time it took to land, and the acceleration, I will be able to calculate the initial velocity.
By using the same rubber band, I am controlling the length, mass, and elasticity of the rubber band. The place in which the rubber band is launched from will also be constant. Additionally, gravity will be constant and the acceleration will also be constant (9.81 ms-1). Furthermore, multiple trials (3 trials) will be recorded for each increment in order to ensure that the data is as accurate as possible. This will include rejecting trials that don’t meet up to certain criteria such as shooting off diagonally instead of straight, hitting a wall, not launching correctly, etc.
Method: Top
Materials:
- Thumb tacks
- 2 Tape Measures (with centimeter units)
- Rubber Band
- Phone (for recording)
- Stopwatch
Diagrams and Pictures of Set Up:
Procedure:
Because a rubber band is unpredictable in where it goes and how it’s launched, for each distance, 3 trials were conducted to cover any uncertainties. Twelve distances were used in 1 centimeter (cm) increments (0-12 cm). For the further distances, an open area is needed to make sure the path of the rubber band isn’t obstructed. More trials weren’t conducted because it took multiple tries to get the rubber band to go straight instead of stray diagonally for accurate data.
To conduct this experiment, I pinned a tape measure to
the ground to ensure the length the rubber band was stretched was not heavily
altered. The same rubber band was also used for the entire experiment. The
independent variable of the experiment is the length the rubber band is
stretched. I pulled the rubber band back to the desired length using the tape
measure pinned to the ground, and a thumb tack was used to mark where the
distance the rubber band was stretched was zero centimeters. This ensured that
the starting distance I used was consistent with every trial. Once I shot the
rubber band from the starting point, a different tape measure was used to
measure how far the rubber band went. I placed the tape measure at the starting
point and measured it to the first edge of the rubber band. I recorded each
trial so that the time could be recorded using a stopwatch after. I played the
video and used the stopwatch to record the time it went. The dependent variable
of this experiment is the launch velocity of the rubber band. By using the time
recorded using the stopwatch and the distance the rubber band went, the launch
(initial) velocity can be calculated. This is calculated using the SUVAT
equation, 
, in which displacement (s) is the distance the rubber
band went, the final velocity (v) is zero, and time (t) is the time it took for
the rubber band to land after it’s launched.
Safety Concerns:
Some safety concerns include making sure you don’t hurt yourself when launching the rubber band. The trajectory of a rubber band is very unpredictable and can possibly injure you or others. For instance, I almost hit my dog with the rubber band because I wasn’t aware of the dangers of launching rubber bands. However, if the experiment is conducted safely and responsibly, the safety of yourself and others is guaranteed.
Results: Top
Data Table 1: Raw Data of Stretch Distance (+/- 0.25 cm) on the Distance the Rubber Band went (cm) and the Time the Rubber Band Took to Land (s)
|
Stretch Distance |
Distance the rubber band went |
Time rubber band took to land |
||||
|
+/- 0.25 |
Centimeters (cm) |
Seconds (s) |
||||
|
cm |
Trial 1 |
Trial 2 |
Trial 3 |
Trial 1 |
Trial 2 |
Trial 3 |
|
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
|
1.00 |
33.27 |
36.78 |
31.78 |
0.70 |
0.82 |
0.63 |
|
2.00 |
79.12 |
83.49 |
81.53 |
0.89 |
0.56 |
0.76 |
|
3.00 |
107.92 |
117.86 |
121.95 |
0.78 |
0.64 |
0.67 |
|
4.00 |
155.70 |
179.83 |
182.40 |
0.81 |
0.77 |
0.85 |
|
5.00 |
195.33 |
205.51 |
209.07 |
0.40 |
0.74 |
0.55 |
|
6.00 |
233.43 |
264.67 |
269.49 |
0.38 |
0.38 |
0.52 |
|
7.00 |
353.59 |
372.87 |
360.60 |
0.60 |
0.54 |
0.57 |
|
8.00 |
379.22 |
392.43 |
404.39 |
0.70 |
0.62 |
0.72 |
|
9.00 |
458.22 |
437.13 |
463.04 |
0.60 |
0.71 |
0.69 |
|
10.00 |
536.70 |
488.70 |
512.06 |
0.68 |
0.80 |
0.72 |
|
11.00 |
629.92 |
593.62 |
602.74 |
0.69 |
0.58 |
0.70 |
|
12.00 |
672.59 |
658.11 |
698.50 |
0.74 |
0.76 |
0.69 |
Data Table 2: Average Distance (cm) and Time (s) of each Stretch Distance (+/- 0.25 cm) and the Calculation of the Uncertainty of Distance (cm) and Velocity (cm/s)
|
Stretch Distance |
|
|
|
|
|
+/- 0.25 |
cm |
s |
cm |
cm/s |
|
cm |
Average Distance |
Average Time |
Uncty of Dist. |
Velocity |
|
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
|
1.00 |
33.94 |
0.72 |
2.50 |
94.28 |
|
2.00 |
81.38 |
0.74 |
2.19 |
219.95 |
|
3.00 |
115.91 |
0.70 |
7.02 |
331.17 |
|
4.00 |
172.64 |
0.81 |
13.35 |
426.27 |
|
5.00 |
203.30 |
0.56 |
6.87 |
726.07 |
|
6.00 |
255.86 |
0.43 |
18.03 |
1190.05 |
|
7.00 |
362.36 |
0.57 |
9.64 |
1271.44 |
|
8.00 |
392.02 |
0.68 |
12.59 |
1153.00 |
|
9.00 |
452.80 |
0.67 |
12.96 |
1351.64 |
|
10.00 |
512.49 |
0.73 |
24.00 |
1404.08 |
|
11.00 |
608.76 |
0.66 |
18.15 |
1844.73 |
|
12.00 |
676.40 |
0.73 |
20.20 |
1853.15 |
Sample calculations for average distance, average time, and velocity are located below.
Sample Calculations:
Average Distance
for stretch distance of 1 cm:
= 33.94 cm
Average Time for
stretch distance of 1 cm:
0.72 seconds
Velocity for
stretch distance of 1 cm:
→ 
→ u = 94.28 cm/s
Chart 1:
The stretch distance (cm) and the distance the rubber band went (cm) were plotted on the graph because they were the most accurate data from the data I gathered and directly reflect the launch velocity of the rubber band. The time I gathered with the stopwatch had a large uncertainty because of how quickly the rubber band landed.
Although a trendline is present, it does not hit all error bars which prevents me from calculating the max/min slopes. Instead, the LINEST function on google sheets was used to calculate the slope and the standard error of the slope which then indicated that the uncertainty of the slope was approximately 2.09 cm.
Data Table 3: LINEST Google Sheets Function Data Processing Results
|
Slope |
56.40328791 |
|
Standard Error of the Slope |
2.093292088 |
Evaluation and Conclusion: Top
The results of the experiment imply that there is a connection between the stretch distance of a rubber band and its launch velocity. Specifically, the data shows a linear trend in the stretch distance (cm) and the distance the rubber band went (cm). Therefore, my hypothesis, that a rubber band’s launch velocity will increase in a linear trend when it is increasingly stretched by a centimeter for each trial, was accepted.
The results found in this experiment can be supported by the knowledge that
with a larger stretch distance, there’s more elastic potential energy (EPE).
Elastic potential energy is when energy is stored from applying a force that
deforms an elastic object. This means when more force is applied, when the
rubber band is stretched further, it will hold more EPE. The equation for
elastic potential energy is 
with x representing distance. This emphasizes the idea
that with a larger distance, there is more potential energy which in turn means
there is greater kinetic energy (KE). Kinetic energy is directly related to
launch velocity because kinetic energy is the energy an object has relative to
its motion. Furthermore, kinetic energy also depends on the velocity of an
object squared (
). This shows the direct relation velocity has with
kinetic energy. This leads to the conclusion that when a rubber band is
stretched at a larger distance, the launch velocity will be greater because of
its kinetic and potential energy. The data is linear because the stretch
distance is proportional to the distance the rubber band went and follows the
equation for EPE and KE.
Some limitations of this experiment include the fact that there was a large uncertainty in the distance the rubber band went because it didn’t go in a completely straight line. Also, the way a rubber band launches is inconsistent and can cause huge discrepancies in the data. Another limitation of the experiment was the time. Because of how fast the rubber band landed, it was difficult to record the exact time from the launch to its landing which may have affected the data gathered. By using a human with a stopwatch, reaction time can also affect the outcome. I attempted to minimize these errors by carrying out multiple trials and throwing out trials that would cause huge uncertainties in the data. By doing this, I was able to create a graph that showed a linear relationship and provide accurate results. Some improvements that could be made are using machinery that would allow the rubber band to consistently shoot straight and with a precise stretch distance. Machinery could also be used to time the trials instead of using a stopwatch to minimize errors with reaction times.
Further research could be done in the future on how temperature affects the launch velocity of a rubber band because temperature affects elasticity. Another experiment that could be done in the future could be different types of rubber bands and their effect on launch velocity. Both of these would contribute to the understanding of the physics involved with elasticity and rubber bands and the overall question of what makes a rubber band good or bad.
Related websites: Top
, https://www.khanacademy.org/science/physics/work-and-energy/hookes-law/a/what-is-elastic-potential-energy. - This website refreshed my memory on what elastic potential energy is and how energy transfers which connects to the results of my experiment.
https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-kinetic-energy. - This website also talked about the transfer of energy, but specifically how the velocity is connected to kinetic energy.
https://www.wired.com/story/how-much-energy-can-you-store-in-a-rubber-band/#:~:text=The%20rubber%20band%20has%20a,6605%20J%2Fkg%20for%20twisting. – This website directly refers to what my experiment was on and how the force a band pulls back is proportional to the stretch distance (spring constant).
http://scienceline.ucsb.edu/getkey.php?key=1353 – This is another study on a similar experiment to mine that found the same results as mine.
https://www.youtube.com/watch?v=NPtNE4SRq_Y – This is a visual representation about the work done in a rubber band when it is stretched which directly relates to its launch velocity.
Khan, Sal. “What Is Elastic Potential Energy? (Article).” Khan Academy, Khan Academy, https://www.khanacademy.org/science/physics/work-and-energy/hookes-law/a/what-is-elastic-potential-energy.
Khan, Sal. “What Is Kinetic Energy? (Article).” Khan Academy, Khan Academy, https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-kinetic-energy.