Question

The breaking load of a cotton yarn, with a twist multiplier of 4 tpi·Ne\(^ {-0.5} \), is 2.5 N. If the twist (number of turns per inch) of yarn is 20, then the tenacity (cN/tex) of the yarn (rounded off to 2 decimal places) is ______________.

Hint:

The tenacity of a yarn is a measure of its breaking load per unit of linear density (tex), which indicates its strength.

Answer 1

Correct Answer: 10.5

The formula for calculating the breaking load with twist multiplier is: \[ \text{Breaking load} = \text{Twist multiplier} \times \text{Tenacity} \] We are given:
- Twist multiplier = 4 tpi·Ne\(^ {-0.5} \),
- Breaking load = 2.5 N,
- Twist = 20 turns per inch.
First, we calculate the tenacity using the twist multiplier: \[ 2.5 = 4 \times \text{Tenacity} \] \[ \text{Tenacity} = \frac{2.5}{4} = 0.625 \, \text{N}. \] Next, convert the tenacity to cN/tex: 1 N = 100 cN, and 1 tex = 1 g/1000 m. So, tenacity in cN/tex is: \[ \text{Tenacity} = 0.625 \times 100 = 62.50 \, \text{cN/tex}. \] Thus, the tenacity of the yarn is 62.50 cN/tex.
Final Answer: 62.50