Answer:
The magnitude of the maximum load that can be applied to the wire is approximately 381703.51 N
The elongation to a 1.2 m length of the wire at the maximum load is approximately 8.696 mm
Explanation:
Result: 4
Calculate the magnitude of the maximum load
that can be applied to a
wire
made of tempered steel 1.8 cm in diameter
so as not to exceed its elastic limit;
also determine the elongation that will suffer
If the calculated maximum load is applied and
It has an initial length of 1.2m.
The given information are;
The diameter, D, of the tempered steel wire = 1.8 cm = 0.018 m
The initial length of the wire = 1.2 m
The cross-sectional area of the wire = π × D²/4 = π × (0.018)²/4 = 0.000254469 m²
When we take the yield strength for tempered steel as 1500 MPa, we have;
Therefore;
F = (Yield strength) × (Original cross-sectional area)
F = 1,500 MPa × 0.000254469 m² ≈ 381703.51 N.
The magnitude of the maximum load that can be applied to the wire = 381703.51 N
2. We have the modulus of elasticity, E = 207 GPa
∴ E = Yield strength/(Elastic strength)
Elastic strength = Yield strength/(E) = 1500 MPa/207 GPa ≈ 7.25×10⁻³
Elastic strength = Δl/l = (Change in length)/(Original length)
∴ 7.25×10⁻³ = Δl/1.2
Δl = 1.2 × 7.25×10⁻³ ≈ 8.696×10⁻³ m = 8.696 mm
The elongation to a 1.2 m length of the wire at the maximum load ≈ 8.696 mm.