Question

An 8.0ft long Gorilla glass rod with a diameter of 0.25 mm has a Youngs Modulus of 71.3GPa. If the rod is pulled from the ends with a 175 N force: a. What would be the stress acting on the rod? b. What would be the strain felt by the rod? c. What would be the change in length of the rod?

Answer 1

a) The stress acting on the rod would be approximately 1.45 x 10^9 N/m^2.

b) The strain felt by the rod would be approximately 2.04 x 10^-4.

c) The change in length of the rod would be approximately 1.63 cm.

Step-by-step explanation:

a) Calculate the stress:

Convert the given values to SI units:

Length (L) = 8.0 ft = 2.44 m

Diameter (d) = 0.25 mm = 2.5 x 10^-4 m

Young's modulus (Y) = 71.3 GPa = 71.3 x 10^9 N/m^2

Force (F) = 175 N

Calculate the cross-sectional area (A):

A = π * (d/2)^2

A ≈ 4.91 x 10^-7 m^2

Calculate the stress (σ):

σ = F / A

σ ≈ 1.45 x 10^9 N/m^2

b) Calculate the strain:

Strain (ε) is the change in length (ΔL) divided by the original length (L):

ε = ΔL / L

We haven't calculated the change in length yet. However, we know the stress and Young's modulus:

σ = Y * ε

2.04 x 10^-4 = 71.3 x 10^9 N/m^2 * ε

ε ≈ 2.04 x 10^-4

c) Calculate the change in length:

Substitute the strain into the strain definition:

ΔL = ε * L

ΔL ≈ 2.04 x 10^-4 * 2.44 m

ΔL ≈ 0.00163 m = 1.63 cm

Therefore:

The stress acting on the rod is approximately 1.45 x 10^9 N/m^2.

The strain felt by the rod is approximately 2.04 x 10^-4.

The change in length of the rod is approximately 1.63 cm.