GATE (TF) Textile 2014 Question Paper Solution | GATE/2014/TF/43

Question 43 (Textile Engineering & Fibre Science)

A yarn is passing over a multiplicative tensioner with an angle of wrap of 90^o. If the input yarn tension is 100 cN and coefficient of friction between yarn and tensioner is 0.2, then the output yarn tension in N, accurate to two decimal place, would be …………………

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Given in the question–

Multiplicative type tensioner

Angle of wrap( $\theta$ )=90^o
or
$Angle of wrap(\theta)=\frac{\pi}{2}$

Input yarn tension(T₁)=100 cN

Coefficient of friction( $\mu$ )=0.2

The output tension(T₂)=?

Formula:
$T_2=T_1\times e^(\mu\theta)$

$T_2=100\times e^(0.2\times \frac{\pi}{2})$

$T_2=100\times e^(0.1\times\pi)$

$T_2=100\times e^(0.1\times 3.14)$

$T_2=100\times e^(0.314)$

$T_2=100\times 1.37$

$T_2=137 cN$

$T_2=1.37 N$ (Answer)

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