#11 | Formulating the Moment of Motion! Modeling Practices for Maximum Static Friction

This article is part of the series below👇.

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.

Last time, we incorporated kinetic friction to reproduce the frictional resistance when the 10-yen coin is in motion.

So, this time, we will incorporate the static friction that acts at the moment it starts to move.

Let's take a look together at what kind of difference this creates!

The Excel model created in the steps of this article is available to the public.
You can get it from the download area below👇.

✔︎ How to incorporate maximum static friction

The Excel model we have created so far is designed so that the frictional force is reflected in the calculations once the 'friction coefficient' is entered.

For this friction coefficient, last time we only entered the kinetic friction coefficient, but this time we will enter both the static friction coefficient and the kinetic friction coefficient.

Specifically, we will formulate and enter the following curve as the friction coefficient. ($${\mu_s: 静止摩擦係数、\mu_k: 動摩擦係数、v_s: 遷移速度}$$)

✔︎ I made it into a video

I formulated the curve mentioned above as the friction coefficient and incorporated it into the Excel model to perform calculations.

The main calculation conditions are below👇.

And so, I made it into a video.

Since static friction only acts at the exact moment the 10-yen coin starts to move, the irregular movements characteristic of Kokkuri-san didn't change enough to be visually noticeable...

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

I hope you all enjoy simulating with various conditions, such as changing the friction coefficient! 😊

✔ Conclusion

This time, I incorporated static friction, which is the resistance at the moment the 10-yen coin starts to move, into the Excel model.

With this, the model is complete, incorporating friction forces for both 'when it is stationary' and 'when it is moving'.

Under the conditions I calculated, there was no major change in the movement of the 10-yen coin, as seen earlier.

This means that,
under these conditions, the main cause of Kokkuri-san's unnatural movements is likely the trembling of the fingertips, not friction.

However,
if you change the conditions, could friction become the main factor?

I hope you all try changing the settings and playing around with it!

Next time, I will quickly expand this movement to a 2D plane and make it into a video.

Please look forward to it!

🔗 Continues to the next article (in progress)

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 write the next article!

• Subject: #Kokkuri-san

• Theme: #StaticFriction #StribeckCurve

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

• Topic: #ILovePhysics #MadeIt