#9 | Make the 10-yen coin dance with the power of the unconscious! Simple modeling of fingertip tremors
This article is part of the series here👇.
If you prefer to listen, please play the audio commentary here👇😊
The goal of this series is to theoretically animate the unnatural movement of the 10-yen coin in Kokkuri-san using high school level mathematics and physics.
Last time, after verifying (debugging) the Excel model, I enabled the calculation results to be output as a video using Python.
However, there are still physical elements that are only using tentative values.
They are the following two:
The force with which the 10-yen coin is pushed by the fingertips
Frictional force (coefficient of friction)
This time, I will think about one of them: 'The force with which the 10-yen coin is pushed by the fingertips'!
The Excel model created in the process of this article is available to the public.
You can get it from the download area below👇.
Kokkuri-san participants think, 'I am not moving it.'
They believe their conscious force is zero.
But in reality, their fingertips are trembling slightly, albeit unconsciously.
The force pushing the 10-yen coin is the combined force of the 'unconscious tremors' transmitted from the fingertips of all participants, in other words, the resultant force.
Participants feel that resultant force through the 10-yen coin. Then, they feel, 'I'm not applying any force, but it's moving on its own!' This is one of the true natures of Kokkuri-san.
✔ How can this resultant force be expressed in a mathematical formula?
If you are looking for precision, the ideal approach is to measure the force of your fingertips while actually performing Kokkuri-san using a measuring instrument.
However, for this time, we will roughly model it by assuming that the resultant force follows a normal distribution.
A normal distribution is a distribution often seen in nature and human behavioral data; it is a symmetrical bell-shaped curve where data clusters near the mean and becomes less frequent as you move away from it. It might be easier to visualize by thinking about the distribution of test scores or heights.
The shape of this distribution is determined by the following two indicators:
[Mean]The center of the data, the most likely value
[Standard Deviation]A value representing how much the data is scattered from the mean
An important characteristic of a normal distribution is the rule that approximately 68% of all data falls within the range of "mean ± one standard deviation" (roughly two out of three times).
Assuming that unconscious tremors also fluctuate finely around an average force, we will use the following values this time.
Median (Mean) = 0 [N]
*Because the conscious force to move it is zeroStandard Deviation = 0.01 [N]
*Assuming that the magnitude of the tremor falls within a slight range of about one 1-yen coin (approx. 1g) with a probability of about two out of three times (68%)
To create random numbers that follow this normal distribution of "median = 0, standard deviation = 0.01" in Excel, we use the following function.
=NORM.INV(RAND(), 0, 0.01)We will enter this formula only into the "Force pushed from the fingertip (horizontal direction)" (column H) of the Excel model.
The "Force pushed from the fingertip (downward direction)" (column I) will remain at 0 (zero) as before.
⚠️ The friction coefficient will also remain at 0 (zero) as before.
[Improvements for ease of use]
To make the simulation more comfortable, I have added the following two improvements to the Excel model I created.
Parameterized so that the strength of the fingertip force can be easily changed
Installed an [Update Switch] to prevent random numbers from updating automatically
If you are interested, please download it and take a look inside 😊
You can get it from the download area below 👇.
I have turned the results calculated by inputting these 'unconscious fingertip tremors' into a video using the Python script from last time.
Kokkuri-san, Kokkuri-san...
Will my paid note be sold by tomorrow?🤑
When you play the video...
😱😱😱
What do you think?
The 10-yen coin wobbles and slides smoothly and irregularly across the board, successfully reproducing a movement like Kokkuri-san, right!
Sometimes the 10-yen coin even flies off the Kokkuri-san board.
✔ Conclusion
This time, I modeled the fingertip tremors using 'random numbers based on a normal distribution'.
As a result, I was able to reproduce the movement of the 10-yen coin like Kokkuri-san.
But!
There are still physical elements remaining that only use tentative values.
That's right.
Frictional force (coefficient of friction).
The current model still has the frictional force set to zero.
Therefore, even with such a small force as this, the 10-yen coin was able to move as easily as an air hockey puck.
So, next time, I will incorporate kinetic friction. Let's see together what kind of difference that makes.
Let's see together what kind of difference that makes.
Stay tuned!
🔗 Continue to the next article
If you found this even a little helpful
or are curious about what comes next,
please give it a like or follow,
as it encourages me to create the next article!
Series: #EquationOfMotion #SurprisinglyUseful
Subject: #KokkuriSan
Theme: #InputModel
Use Case: #IndependentResearch #Relearning #Relearning #ClassroomMaterial #Physics
Topic: #ILovePhysics #MadeIt
いいなと思ったら応援しよう！
もし具体的に何かのお役に立てたなら、チップで応援していただけると励みになります！
いただいたチップは、今後の活動に使わせていただきます😊