Question

In a tensile test, a 50 tex yarn specimen of 500 cm length extends by 10% at 600 cN. The length of the yarn after the removal of the load is 525 cm. The elastic recovery (%) of the yarn is:

Hint:

Elastic recovery is a measure of how much of the initial extension returns after the load is removed. It can be calculated as the percentage of recovery of the extension after the load is released.

Answer 1

Step 1: Understanding the given data.
Initial length of the yarn: \( L_0 = 500 \, {cm} \).
The yarn extends by 10% under the applied load.
Final length after the removal of the load: \( L_f = 525 \, {cm} \).
Step 2: Calculating the extension during loading.
The yarn extends by 10%, so the extension during the load is: \[ {Extension during loading} = 500 \times 0.10 = 50 \, {cm}. \] Therefore, the length during loading is: \[ L_{{loaded}} = 500 + 50 = 550 \, {cm}. \] Step 3: Calculating the elastic recovery.
The elastic recovery is the difference between the extension under load and the extension after the load is removed. This can be calculated as: \[ {Elastic recovery} = \frac{L_{{loaded}} - L_f}{{Extension during loading}} \times 100. \] Substituting the values: \[ {Elastic recovery} = \frac{550 - 525}{50} \times 100 = \frac{25}{50} \times 100 = 50%. \]