Challenges in Statics

Classical Mechanics Level 5

Imagine a rope, attached to two points and whirling about the line joining those points at a constant angular velocity \(\omega\).

Now you start to view the rope in a rotating frame as well so that it appears something as in the figure, and you wish to calculate the area under the curve that describes the rope in your frame.

All you have is a protractor and hence you know the angle the rope makes at the two points (A and B) with the axis.

You also know the minimum value of tension in the rope (don't ask me how), and the mass per unit length of the rope is \(\lambda\).

So if the area can be expressed as:

\(ln(\frac { Asec\theta +Btan\theta }{ Asec\theta -Btan\theta } )\frac { C(T) }{ D(\lambda { \omega }^{ 2 }) } \)

and \(\lambda\) is the linear density, \(T\) is the minimum tension in the rope and \(\omega\) is the angular velocity of rotation,

then find A+B+C+D.

Details and Assumptions

1) There is no gravity.

2) Assume ideal conditions;

3) It might help to think about why the rope possesses a different shape in the first place;

In the spirit of JEE, I am making it an integer type question;
As usual, this is original.

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