GATE (TF) Textile 2022 Question Paper Solution | GATE/2022/TF/48

Question 48 (Textile Technology & Fibre Science)

In a multiplicative type tensioner, the angle of wrap is 90° and the coefficient of friction between the yarn and the guide is 0.2. If the input yarn tension is 10 cN, then the output yarn tension (cN) is (rounded off to 1 decimal place) _.

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Given in the question-

Multiplicative type tensioner

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

Coefficient of friction between yarn and guide( $\mu$ )=0.2

Input yarn tension( $\ T_1$ )=10 cN

The output yarn tension(cN)=?

By formula:

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

$T_2=10\times e^(0.2\times\frac{\pi}{2})$

$T_2=10\times e^(0.2\times\frac{3.14}{2})$

$T_2=10\times e^(0.1\times3.14)$

$T_2=10\times e^(0.314)$

$T_2=10\times 1.37$

$T_2=13.7$ (Ans)

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Frequently Asked Questions | FAQs

What is coefficient of friction ?

The coefficient of friction (COF) is a dimensionless number that describes the resistance to sliding between two surfaces in contact. It represents the ratio of the force required to keep two surfaces sliding against each other to the normal force pressing the two surfaces together. The COF is a material property that depends on the nature of the two surfaces in contact, as well as any intermediate layers, such as lubricants, that may be present. The COF is used in a variety of fields, including engineering, physics, and materials science, to describe the behavior of sliding systems and to design systems that require controlled frictional behavior. A low COF means that the surfaces slide easily against each other, while a high COF means that they resist sliding and grip each other more tightly.

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