#12 | Move Freely! Extending the Excel Model of a 10-Yen Coin as a Point Mass to a 2D Plane

This article is part of the series found here 👇.

The goal of this series is to theoretically animate the unnatural movement of a 10-yen coin in Kokkuri-san using high school-level mathematics and physics.

Up until the last installment, we built an Excel model that incorporates factors like "fingertip tremors" and the "frictional force between the 10-yen coin and the paper."

However, up to this point, it was a model that only moved horizontally.

So, this time, we will quickly add the vertical direction and turn the movement of the 10-yen coin into a video!
Then, I will conclude by touching on the potential applications of this Excel model.

✔︎ How to add the vertical direction (overview)

For those of you who have carefully modeled the horizontal movement so far, adding the vertical direction can be done quickly by applying what you have already learned!

Since the calculation formulas look a bit more complex with the additions, I will briefly introduce only the key points of "how it was extended to two dimensions" here.

If you are interested in the specific mathematical formulas, please take a look at the contents of the distributed Excel model.

I have made the Excel model created in the steps of this article available to the public.
You can obtain it from the download area below 👇.

▶ Key points for adding the vertical direction to the calculation section

1. Copy and paste the horizontal section of the calculation area to create the vertical section

2. Add columns to input the force of the fingertip in the plane (magnitude of force and direction of force)

   • Magnitude of force: Input using "normally distributed random numbers" just like the fingertip force (horizontal direction)

   • Direction of force: Input using "uniformly distributed random numbers" in the range of 0 to 360°

3. From the fingertip force in the plane, use trigonometric functions (sin, cos) familiar from high school mathematics to find the component forces in the horizontal and vertical directions, and incorporate them into their respective calculation formulas

*The vertical force (normal force) that the 10-yen coin receives from the fingertip uses the same value for both the horizontal and vertical sections.

✔︎ I turned it into a video

I have turned the results calculated by adding the vertical direction as shown here into a video.
I think it successfully reproduces the irregular movements characteristic of Kokkuri-san, as if it were searching for letters.

✔ Conclusion

This time, I quickly added the vertical calculations and made a video showing the 10-yen coin moving freely on the Kokkuri-san paper.

Based on the tremors of the fingertip force, I believe I was able to reproduce the irregular movements typical of Kokkuri-san.

With this, if a child is scared of Kokkuri-san, you should be able to confidently explain the trick behind it.

And with this addition of the vertical direction...
the 'Kokkuri-san Excel Model' is finally complete!

Regarding this Kokkuri-san model,
it can actually be applied to various situations.

For example, a basketball shot👇

You can calculate the 'angle' and 'strength' required to make a successful shot, even taking air resistance into account.

Next, the SASUKE tackle👇

You can determine the minimum force required to clear the target time...

I would like to talk about specific application methods in more detail (if there is a request) at some point, but once you can handle a physical model like this, the fun of capturing all sorts of everyday questions with numbers will expand😊

If you found this even a little helpful
or are curious about what comes next,
please give it a like or follow me,
as it encourages me to create the next article!

• Subject: #Kokkuri-san

• Theme: #2D #2DConversion #PointMassModel

• Usage scenario: #IndependentResearch #Relearning #Relearning #ClassroomIdeas #Physics

• Topic: #ILovePhysics #MadeIt