Answer:
(a) 3.23×10⁸ N/m²
(b) 1.46×10⁻³
(c) 2.21×10¹¹ N/m²
Explanation:
(a) Stress = Force/Area.
Stress = F/A................ Equation 1
But,
F = mg................. Equation 2
Where m = mass, and g = acceleration due to gravity
A = πd²/4................. Equation 3
d = diameter of the circular cross section.
Substitute equation 2 and equation 3 into equation 1
Stress = 4mg/πd²............. Equation 4
Given: m = 25.4 kg, d = 0.555 mm = 0.000555 m
Constant: g = 9.8 m/s², π = 3.142
Substitute these values into equation 4
Stress = 4(25.4)(9.8)/(3.142×0.00555²)
Stress = 995.68/(3.08×10⁻⁶)
Stress = 3.23×10⁸ N/m²
(b)
Strain = ΔL/L.............. Equation 5
Where ΔL = extension, L = Length.
Given: ΔL = 1.1 mm = 0.0011 m, L = 75.1 cm = 0.751 m
Substitute into equation 5
Strain = 0.0011/0.751
Strain = 1.46×10⁻³.
(c)
Young modulus = Stress/Strain
Young modulus = 3.23×10⁸/ 1.46×10⁻³
Young modulus = 2.21×10¹¹ N/m²
