Physics with Paper Mache

Classical Mechanics Level pending

A square paper thread is made from the remaining paper, after paper toys are made . After it is dipped in water due to presence of surface tension the sides of the square get stretched . If Young 's Modulus is Y , and surface tension of water is T . calculate Angle of deviation of the paper side . Note :- assume radius of paper to be "r" and length of total thread to be equal to "l"

\sqrt [ 2 ]{ \frac { Tl }{ 2\pi r^2 Y } }

\sqrt [ 3 ]{ \frac { Tl }{ 4\pi r^2 Y } }

\sqrt [ 3 ]{ \frac { Tl }{ 2\pi r^2 Y } }

\sqrt [ 3 ]{ \frac { Tl }{ 2\pi r Y } }

1 solution

Anish Kelkar
May 21, 2014

we know that calculated form of angle of deviation is $\theta =\sqrt [ 3 ]{ \frac { Force\quad }{ \quad Area.\quad *\quad Young's\quad Modulus\quad } }$ .
Also force due to surface tension "F" is $F=\quad 2T\frac { l }{ 4 } =\frac { Tl }{ 2\quad }$ . And $A=\pi { r^{ 2 } }$ . Hence simplifying we obtain the result . To obtain the formula for angle of deviation , one can prederive it , by considering a horizontal rod (beam ) of radius r and a mass of weight F being hung at the middle of the rod . Hence . assuming $\tan { x } \cong \quad x$ . we again obtain the result .

How do you deduce that formula of theta??...I want a proof of that!!

Anurag Ghosh - 6 years, 11 months ago

Physics with Paper Mache

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