Physics Help. You hang a 5kg mass from the end of a rod that is 1.7 m by 2 mm by 2 mm. you observe that the rod's length increases to 1.74 m.

Question

What is the stress? What is the strain? What is Young's modulus for this material?

Answer 1

Stress:

 

σ = mg / A = (5 kg)(9.8 m/s²) / (2 x 10^-3 m)² = 1.225 x 10⁷ Pa

 

Strain:

 

ε = ΔL / L₀ = (1.74 m - 1.7 m) / (1.7 m) ≅ 2.353 x 10^-2

 

Young's modulus:

 

E = σ/ε = (1.225 x 10⁷ Pa) / (2.353 x 10^-2) ≅ 5.206 x 10⁸ Pa

 

 

Answer 2

Stress = Force/cross sectional area

 

Stress = 5 * 9.81/2*2 = 12.265 N/mm²  = 12.265 MN/m² (note that the weight = mass * acceleration due to gravity (9.81 m/s²))

 

Strain = change in length/original length = 0.04m/1.7m = 0.0235

 

Youngs Modulus = stress/strain = 12.265/0.0235 = 522 N/mm²  = 522 MN/m²