Dominoes-Effect of Spacing on Velocity
By Ben Augee
Introduction | Method
| Diagram | Results and Analysis | Conclusion | Bibliography | Links
| Return to Research
Introduction
Background Information
The earliest mention and use of Dominoes comes from the Song Dynasty in China around 1230-1300 C.E, it is unclear who exactly created these pieces for game and card (Wikipedia). However, while this is the earliest form of domino invented and known to man and also known as the Chinese Domino, it is different from the Modern Domino, which can be dated back to the 18th Century in Italy and France (Britannica). It was said that the domino was introduced to the Englishmen by a French war prisoner, which has now turned into the “Modern Domino”(Gamesver). Many different countries have different versions of the game, you might see Mexican Train Dominoes, Regular standard Dominoes, Chinese Dominoes, and so forth. A domino is a small and rectangular block often split into two square sides by a horizontal line with blanks or any numerical value of dots on each square; the dominoes usually have up to six dots, however there are different sets with values exceeding that. While different types of dominoes exist, the six spotted dominoes or the Standard Set are the most common form and most frequently used dominoes.
As a kid, I have many memories playing Mexican Train dominoes with my family during game nights and creating Rube Goldberg Machines with lines of Dominoes to topple over each other and start a chain reaction. Naturally, when I was presented with the opportunity to explore physics related topics at school, the incorporation of dominoes was the primary subject I wanted to use. When dominoes are pushed, potential energy from the first domino is turned into kinetic energy when it hits the neighboring domino. The domino accelerates, which then goes on to hit the neighboring domino at velocity. The farther the space between each domino, the harder it hits the neighboring domino. The following domino immediately gets pushed into motion at higher speed. The farther a domino is from its neighbor, the harder it hits, however the longer it takes to reach the next one.
While there are many variables such as the total length of the domino, the type of domino, and the arrangement, the variables decided to be used were the spacing of the dominoes, the velocity at which they fall, and the mass of the domino itself for the control variable. There are still some issues with only using these three as the main variables in the experiment, however that can be explored in another experiment testing different variables.
Statement of the Problem
The purpose of this investigation therefore, is to find the relationship, if any, between the spacing and velocity of the dominoes. Spacing, the independent variable, is defined as an amount of space between two things or dominoes. Velocity, the dependent variable, is defined as the rate at which the "fall line" or disturbance moves. The mass of the domino, the control variable, which will stay the same throughout the experiment (Geometry), is defined as any small oblong piece marked with 0–12 dots in each square of the domino.
Hypothesis
I believe that with the increase of space, there will be a direct correlation and increase in velocity because with more space, greater speeds can be reached before knocking over the next domino.
Method
Materials/Procedure
To collect my data, I first had to gather all materials necessary to start the experiment. I used my trusty tin of Dominoes from home, which consisted of about 91 Dominoes (as we have the four player version). I then got a meter stick for the measurement of distance, a stopwatch which measured in the thousands, and a Venire Caliper to correctly measure the distance each Domino should be placed. Oh, and the table which I most definitely picked up and carried to a flat surface. After measuring the small distance between each domino, the use of 3x5 cards came in handy as I could then use the selected distance from the Venire Caliper to then choose a fitting amount of cards to match the distance to easily mark the dominoes spots on the table. I obviously had to use safety glasses because the Dominoes seemed to jump around a lot and cause a loud mess. I ran a couple test-runs to see if the setup would work, and after that I began my trials.
Spacing, the independent variable, was changed
systematically after 3 trials for each distance. The Venire Caliper helped to
reduce error when trying to accurately measure the small distances to where the
dominoes were placed which took longer but definitely worth the time to set up.
When measuring the time of the trials, the stopwatch was used to obtain the
data which was then plugged into V=
to figure out the dependent variable, which was
velocity. So in the end, I ended up with 10 different averaged velocities.
Lastly, I kept the mass of the domino the same, the total distances the same,
and also the same distances of 20cm and 100cm (see diagram below). These were
kept at a constant because any change in these controlled variables could
potentially lead to faulty data and or clear outliers in the collected results.
I ran 3 trials each for 10 different distances from (0.40 Cm) to (4.00 Cm)
measured by the Venire Caliper. I decided to use ten different distances inside
four centimeters away from each other because I liked the idea of using smaller
distances that had a constant increase of the same distance every new run.
Ideally the more trials the more accurate the data is, so that's why I decided
to use three trials per distance rather than two or one with an increase in the
amount of distances.
The first domino to be knocked over would be the first
one about 20cm out. It would be knocked over from left to right, and once the
dominos broke into the 100cm stretch, the time between the first gate and the
end was measured by stopwatch This would be
repeated 3 times for 10 different distances.
(Materials)
-Dominoes
-Venire Caliper
-Stopwatch
-Meter stick
-3x5 Cards
-Chrome book (Record Data)
- Table (Inside of Tualatin High, specifically Mr. Murray’s room)
Results/Analysis
Distance vs Time RAW Data
|
Distances (Cm) |
Trial 1 (s) |
Trial 2 (s) |
Trial 3 (s) |
|
0.40 |
0.875 |
0.892 |
0.869 |
|
0.80 |
0.904 |
0.935 |
0.914 |
|
1.20 |
0.970 |
0.948 |
0.965 |
|
1.60 |
1.040 |
1.037 |
1.013 |
|
2.00 |
1.081 |
1.070 |
1.066 |
|
2.40 |
1.089 |
1.094 |
1.097 |
|
2.80 |
1.126 |
1.122 |
1.130 |
|
3.20 |
1.149 |
1.130 |
1.131 |
|
3.60 |
1.154 |
1.166 |
1.153 |
|
4.00 |
1.173 |
1.183 |
1.179 |
Graph of RAW Data
Calculations
Using
equation,
I calculated the velocity of each trial below and averaged them out by adding
all three numbers up and dividing by the given amount. Uncertainty was
calculated by taking one half the unit of the last decimal place of the number.
The data is as follows.
Distance vs Velocity Table
|
Distances (Cm) |
Velocity Trail 1 |
Velocity Trail 2 |
Velocity Trail 3 |
Average Velocities |
Uncertainty |
|
0.40 |
0.457 |
0.448 |
0.460 |
0.455 |
0.0025 |
|
0.80 |
0.885 |
0.856 |
0.875 |
0.872 |
0.0010 |
|
1.20 |
1.237 |
1.266 |
1.244 |
1.249 |
0.0045 |
|
1.60 |
1.538 |
1.543 |
1.579 |
1.554 |
0.0200 |
|
2.00 |
1.850 |
1.869 |
1.876 |
1.865 |
0.0025 |
|
2.40 |
2.204 |
2.194 |
2.188 |
2.195 |
0.0025 |
|
2.80 |
2.487 |
2.496 |
2.478 |
2.487 |
0.0035 |
|
3.20 |
2.785 |
2.832 |
2.829 |
2.815 |
0.0025 |
|
3.60 |
3.120 |
3.087 |
3.122 |
3.110 |
0.0005 |
|
4.00 |
3.410 |
3.381 |
3.393 |
3.395 |
0.0025 |
Average Velocities vs Distances Graph
Slope of line with uncertainty: 0.804+/-0.002
Drawing to a close, my initial hypothesis was deemed correct with this outcome and results as these data tables and graphs support and provide significant evidence that with the increase of space, there will be a direct correlation and increase in velocity. The average Velocity vs Distance graph has a strong linear correlation which provides clear evidence of an increase of velocity on the increase of spacing. I believe this is due to the fact that with more space, greater speeds were reached before knocking over the next domino. When dominoes are pushed into motion, potential energy from the first domino at the top is turned into kinetic energy when it hits the neighboring domino. The domino accelerates, which then goes on to hit the neighboring one at high velocity. The farther the space between each domino, the harder it hits the neighboring domino.
However, obtaining and calculating data is not as simple as it may seem, limiting factors like human error in stopping the time could have very likely warped the data. This limits the accuracy of the time collected, meaning that there is very much a high error in human reaction to stopping the timer. While error bars help us with this factor in validation of data by “give or take x amount” on the graph, they are still nowhere near perfect if trials are all off. Another limitation of the study is the sample size of the data. With more data and more trials, a better representation of the result could be obtained. Continuously, the specific sample size that was chosen could have limited the result of the data. A different sample size could produce different end results than that of what I had gotten. Furthermore, some improvements that could be used in further studies include a high speed camera with slow motion to decrease error in time. Another improvement would be using more trials and distances to increase the accuracy of data over more points. Lastly, selecting different distances not chosen in this IA could improve overall accuracy and be helpful in case both studies end up with varying results. I believe if I were to do this experiment again I would use these improvements to further research this attacking it from a new and improved angle. However, I am curious as to how the dominos would be affected by spacing on velocity when moving downwards on stairs; that would be an interesting follow up experiment which would include both intriguing subjects dominoes and physics. Conclusively, I'm really happy I decided to construct my IA around my favorite game, because although my grade might fall, at least I can calculate its velocity on the wall down.
https://www.youtube.com/watch?v=JZTHsWlkjQ0 – This Video helped me understand this experiment better, a helpful source indeed.
https://www.youtube.com/watch?v=rJNoiggryxo -This video helps break down the experiment in slow motion, similar to what I did.
https://sciencing.com/distance-dominoes-affect-rate-fall-8615178.html
- This helped me understand
the nature of dominoes and their movements.
https://www.degruyter.com/document/doi/10.1515/phys-2021-0049/html?lang=en
– Similar study with helpful in depth analysis.
https://ore.exeter.ac.uk/repository/bitstream/handle/10871/31015/DRAFT-JAM-17-1648-1.pdf;jsessionid=F549B0013F447F436A78DB1AEBEA216D?sequence=1
– A near perfect example from researchers at Exeter University.
Bibliography
The Editors of Encyclopedia Britannica. “Domino a Game piece” 1998 https://www.britannica.com/topic/domino-game-piece
Wikipedia. “Dominoes”
https://en.wikipedia.org/wiki/Dominoes
Gamesver Team. “History of Dominoes (Game): From China to Europe to Worldwide”
https://www.gamesver.com/the-history-of-dominoes-the-game/
Inside Science, “Dominoes: More Powerful
Than You Think”
https://www.insidescience.org/news/dominoes-more-powerful-you-think