The Lee-Tseung Lead Out Theory

[ltseung888]

I second that.

Dear Tinu,

Welcome back.  I took your suggestions and Slides 10-12 should be 100% correct now in terms of units of measurement.

Mr. T S Cheung is doing a complete set of experiments.  There will be a full set of results from 0-20 cm or more falling distances.  He is experimenting with different padding, different diameter tubes, different diameter wheels, different rim weights etc.  The necessary control experiments will be done and published when ready.  He is even considering a 16-foot double-sided wheel with closed (and thus heavy) rim.  That may be the modern Bessler Wheel.

Ms. Forever Yuen simply used the primitive set up in my dining room to shoot some videos.  The videos already showed padding one end makes a difference.

I would love to have your updated comments on Slides 10-12 again.

[ltseung888]

Reply to an email.

Dear Mr. Tseung,

I participated in the Shenzhen University Seminar and then read the posts in the overunity forum.  I do not intend to join the discussion forum because of the abuses and insults.

However, I would like to ask you the following question.  You used a simplified analysis that even a secondary school student can understand.  The more exact analysis should be the line integral.  Even in the first Lee-Tseung Pull, there are complexities.  The weight Mg is constant.  The Horizontal force F may be constant as that is supplied externally.  However, the tension of the String changes with the angle.  How would this changing tension affect your analysis?  Would the simple analysis and the line integral analysis produce similar results?

Regards,

XXX (Tseung changed all names to XXX)

Dear XXX,

This is an excellent Mathematics and Physics Question.  I should like to share it with the forum members.  Repeat:

However, the tension of the String changes with the angle.  How would this changing tension affect your analysis?  Would the simple analysis and the line integral analysis produce similar results?

[Top Gun]

However, I would like to ask you the following question.  You used a simplified analysis that even a secondary school student can understand.  The more exact analysis should be the line integral.  Even in the first Lee-Tseung Pull, there are complexities.  The weight Mg is constant.  The Horizontal force F may be constant as that is supplied externally.  However, the tension of the String changes with the angle.  How would this changing tension affect your analysis?  Would the simple analysis and the line integral analysis produce similar results?

Regards,

XXX (Tseung changed all names to XXX)

Dear XXX,

This is an excellent Mathematics and Physics Question.  I should like to share it with the forum members.  Repeat:

However, the tension of the String changes with the angle.  How would this changing tension affect your analysis?  Would the simple analysis and the line integral analysis produce similar results?

I love this type of constructive, stimulating analysis.  I would like to point out the following:

(1)   In the pulling of the pendulum bob by a constant horizontal force F, there will be acceleration of the bob initially.  The horizontal component of the tension in the string T1 is small at small angles.

(2)   The horizontal component of the tension of the string will increase with increasing angle.  I would expect even at the point when it is equal to F, the momentum acquired would swing a little more than the equilibrium angle a as in slide 11.

(3)   The analysis of the non-equilibrium motion is much more complex than the analysis at equilibrium.

I am sure Tseung and other top Physicists will lose more sleep thinking about the non-equilibrium analysis.  It is fun and educational.

[ltseung888]

Dear Top Gun,

Thank you for your post.  You will lose some sleep over non-equilibrium analysis too. 

I would like to comment on the line integral concept and calculus in general here.  The following is from http://en.wikipedia.org/wiki/Integral.

integration

Integration can be traced as far back as ancient Egypt, circa 1800 BC, with the Moscow Mathematical Papyrus demonstrating knowledge of a formula for the volume of a pyramidal frustum. The first documented systematic technique capable of determining integrals is the method of exhaustion of Eudoxus (circa 370 BC), which sought to find areas and volumes by breaking them up into an infinite number of shapes for which the area or volume was known. This method was further developed and employed by Archimedes and used to calculate areas for parabolas and an approximation to the area of a circle.

Similar methods were independently developed in China around the 3rd Century AD by Liu Hui, who used it to find the area of the circle. This method was later used by Zu Chongzhi to find the volume of a sphere. Some ideas of integral calculus are found in the Siddhanta Shiromani, a 12th century astronomy text by Indian mathematician BhÃ,,skara II.

Significant advances on techniques such as the method of exhaustion did not begin to appear until the 16th century AD. At this time the work of Cavalieri with his method of indivisibles, and work by Fermat, began to lay the foundations of modern calculus. Further steps were made in the early 17th century by Barrow and Torricelli, who provided the first hints of a connection between integration and differentiation.

Frankly, I doubt whether a forum member with no formal training in calculus would make any sense with our advanced discussion.  But since we want to benefit the World, a seed may fall on fertile soil and bear fruit. 

May be Top Gun, Forever and I are the only posting members who can understand the discussion.  Some will say that I am talking with myself and post more insults.  But there is the odd chance that a mathematician or Prof. Jian Lu and his students or some MIT professors may read it some time in the future.  They might be the ones to take charge to benefit the World.

@all forum members, if you do not understand the discussion and the mathematics, you are not alone.  Just be an observer.

[ltseung888]

Top Gun,

The line integral for work is the vector arithmetic of (force dot displacement).

In general, we can resolve the force into a vertical and a horizontal component.

We can also resolve the displacement into a vertical and a horizontal component.

The vector arithmetic of force x displacement can be broken down into
(1)  Vertical work = vertical component of force x vertical component of displacement (normal arithmetic)

(2)  Horizontal work = horizontal component of force x horizontal component of displacement (normal arithmetic)

(a)   Do you agree with the statements (1) and (2)?
(b)   Do you agree that the two statements (1) and (2) can be applied to the pendulum under the first Lee-Tseung Pull?