Question

The Poisson's ratio for nylon 6,6 is 0.39. When a stress is applied longitudinally (i.e. along the length) on a rod of nylon, it experiences a strain of 1.8%. If the rod has an initial lengh of 100 mm and initial diameter of 10 mm, the diameter of the rod when the stress is applied is: (select the closest answer) Group of answer choices 10.702 mm 9.989 mm 10.07 mm 9.602 mm 2.98 mm 9.9636 mm 9.824 mm 7.02 mm 9.894 mm 9.7504 mm 9.9298 mm 9.783 mm

Answer 1

9.9298 mm

Step-by-step explanation:

When the force is applied to the nylon rod, it causes a a longitudinal strain of 1.8%.

Longitudinal strain is the ratio of change in length to the original length. i.e.

Longitudinal strain = ΔL / L

But Longitudinal strain = 1.8% = 0.018

The Poisson ratio (V) is the ratio of transverse strain to longitudinal strain.

V = transverse strain / longitudinal strain

0.39 = transverse strain / 0.018

transverse strain = 0.00702

Transverse strain is the ratio of change in diameter (ΔD) to the initial diameter (D).

Transverse strain = ΔD / D

Given that D = initial diameter = 10 mm

But an increase in length causes a decrease in diameter, hence:

Transverse strain = -ΔD / D

0.00702 = -ΔD / 10 mm

ΔD = -0.0702

ΔD = final diameter - initial diameter

final diameter - initial diameter = -0.0702

final diameter = initial diameter - 0.0702

final diameter = 10 - 0.0702

final diameter = 9.9298 mm