Question

A structural steel rod has a
radius of 10 mm and a length of 1.0 m. A
100 kN force stretches it along its length.
Calculate (a) stress, (b) elongation, and (c)
strain on the rod. Young's modulus, of
structural steel is 2.0 x 10^11 N m^2.​

Answer 1

Answer:

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Answer 2

Answer :

Given -

• F = 100 kN = 100 × 10³ N
• Radius = 10 mm = 10^{-2} m
• Length = 1.0 m
• Young's modulus = 2.0 × 10¹¹ Nm^-2

To Find -

• Stress
• Elongation
• Strain

Solution -

We know that, Stress = F/A.

Stress = F/πr².

⇒ (100 × 10³ N)/[3.14 × (10^-2 m)²]

⇒ 3.18 × 10⁸ Nm^-2

Elongation, ∆L = (F/A)L/Y

⇒ (3.18 × 10⁸ Nm^-2)(1 m)/(2 × 10¹¹ Nm^-2)

⇒ 1.59 × 10^-3 m

⇒ 1.59 mm

We know that, Strain = ∆L/L.

⇒ 1.59 × 10^-3 m/1 m

⇒ 1.59 × 10^-3

⇒ 0.16 %

Conclusion -

• Stress = 3.18 × 10⁸ Nm^-2
• Elongation = 1.59 mm
• Strain = 0.16%