Question

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) ______________.

Hint:

Higher wrap angle and friction always increase output tension in multiplicative tensioners.

Answer 1

Correct Answer: 13.5

The output yarn tension in a multiplicative type tensioner is given by:
\[ T_{\text{out}} = T_{\text{in}} \cdot e^{\mu \theta} \]
Here, \(T_{\text{in}} = 10 \, \text{cN}\), \(\mu = 0.2\), and \(\theta = 90^\circ = \frac{\pi}{2}\).
Substituting the values:
\[ T_{\text{out}} = 10 \cdot e^{0.2 \cdot \frac{\pi}{2}} \]
\[ = 10 \cdot e^{0.3142} \]
\[ = 10 \cdot 1.3695 \]
\[ = 13.695 \]
Rounded to one decimal place, the output tension is 13.7 cN.
Final Answer: 13.7