Answer: a) Strain on Steel rod = 0.0001078
b) elongation on the steel rod = 0.00008085m = 0.008085cm = 0.0081mm.
c) strain on Copper Rod = 0.000189
Explanation: a) To obtain the strain of the steel rod, we invoke Hooke's law which states that, provided the elastic limit of A material isn't exceeded, the stress it undergoes is directly proportional to its strain.
(Stress, σ) ∝ (Strain, ε)
The constant of proportionality is called Young's modulus, E.
σ = Eε
For steel, Younger Modulus as obtained from literature = 210GPa.
Strain = Stress/Young's Modulus
Stress = (Force or Load applied)/ Cross sectional Area.
Force applied For the steel = 4000N
Cross sectional Area = (π(D^2))/4
D = 1.50cm = 0.015m
A = 0.0001767 m2
σ = 4000/0.0001767 = 22637238.257 N/m2
ε = σ/E = 22637238.257/(210 × (10^9)) = 0.0001078.
b) To solve for elongation.
Strain, ε = (elongation, dl)/(original length, lo)
Elongation, dl = strain × original length
dl = 0.0001078 × 0.75 = 0.00008085m = 0.008085cm = 0.0081mm.
c) strain in Copper
ε = σ/E; σ = 22637238.257 N/m2
Young's modulus of Copper, from literature, = 120GPa
ε = 22637238.257/(120 × (10^9)) = 0.000189
