An interesting yet serious question hidden in Newton's bucket experiment

--Does a soft hanging rope possess the torque necessary to make the bucket rotate noticeably?

Author: Guan Keying

(Beijing Jiaotong University , retired )

Email: keying.guan@gmail.com

While co-authoring the paper " From Newton's Bucket " with ChatGPT , I discovered that although it is a common phenomenon for a heavy bucket to rotate when suspended by a rope, it implies a serious academic problem.

To exaggerate the idea that the water surface in a rapidly spinning bucket would form a concave curve after reaching equilibrium, Newton assumed the rope was initially tightened. However, in everyday life, people don't intentionally tighten the rope; it's usually left slack. There's generally no reason to tighten the rope when lifting a bucket. Nevertheless, when the bucket is lifted, it usually exhibits a noticeable rotation. What is the reason for this?

To illustrate the prevalence of this phenomenon, the author conducted multiple experiments (a video of one of these experiments is attached to the previous blog post, but due to file format issues, it may be difficult for general readers to download and watch). This article includes photos and a video of another similar experiment to further confirm the prevalence of this phenomenon and the problems it causes.

The rope used in this experiment is a very ordinary, soft cotton rope that retains the texture formed during the twisting process; its diameter is approximately 1.5 mm (see Photo 1).

Photo 1.

 At the start of the experiment, the rope was attached to the handle of a large padlock placed on a table (the handle extended off the table so the rope could hang naturally). A loop was attached to the lower end of the rope to suspend a weight. At this point, the rope was relaxed and stationary, showing no apparent torsional force. (Photo 2 ) 

Photo 2.

 Then, a larger but lighter combination lock was gently hung in the loop below the suspension rope without twisting the rope's twist, allowing the lock to suspend and move naturally. The experiment showed that the lock began to rotate naturally after suspension, with the rotation speed increasing until it reached a certain maximum value, after which it began to decrease in speed, and after coming to a stop, it began to rotate in the opposite direction. In reality, this repeated rotation is similar to periodic rotation; due to various resistances and corresponding energy consumption, the rotation will naturally slow down and eventually stop after a period of time. Because this process takes too long, the following 1 minute and 13 second video only shows a portion of the experimental phenomena, retaining a short segment of the repeated rotation.

0630.mp4

Experimental video

As stated in the note at the end of the previous blog post:

•       Where does the rotational energy of a suspended combination lock actually come from?

•       Can it be entirely attributed to the torsional elastic potential energy stored in the thin cotton rope?

•       Or is this rotational energy a result of a combination of factors such as gravitational potential energy, tension redistribution, torsional deformation, structural reorganization of the suspension system, and energy dissipation?

These present us with interesting yet serious challenges in mathematics, mechanics, and materials science.

If readers have difficulty downloading or watching the videos, they can notify me by emailing my email address, and I will distribute the video files directly to the reader's email address.

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