Question

A 30 tex cotton yarn is made into a lea of 120 yards for determining CSP. If the lea strength is 500 N, then the CSP of the yarn (rounded off to the nearest integer) is ____

Hint:

CSP in the English system uses \(\mathrm{Ne}\) and lea strength in lbf. Convert tex to \(\mathrm{Ne}\) via \( \mathrm{Ne}=590.5/\text{tex} \) and newtons to lbf before multiplying.

Answer 1

Correct Answer: 2190

Step 1: Convert tex to English count (Ne)
For cotton, \( \mathrm{Ne} = \dfrac{590.5}{\text{tex}} \Rightarrow \mathrm{Ne} = \dfrac{590.5}{30} = 19.6833\ldots \)
Step 2: Convert lea strength to pound-force
\(1~\mathrm{lbf} \approx 4.44822~\mathrm{N} \Rightarrow \) lea strength \(= \dfrac{500}{4.44822} = 112.4045~\mathrm{lbf}\).
Step 3: Compute CSP
By definition, \( \mathrm{CSP} = \mathrm{Ne} \times \text{Lea Strength (lbf)} \).
\( \Rightarrow \mathrm{CSP} = 19.6833 \times 112.4045 = 2212.495\ldots \)
Rounded to the nearest integer \( \Rightarrow 2212 \).
\[ \boxed{\mathrm{CSP} = 2212} \]