Question

A structural steel rod- has a radius of 10mm and a lenght of 1.0 m. A 100kN stretches it along its length. Calculate (a) stress , (b) elongation, and (c) strain on the rod. Young's modulus, of the structural steels is$2.0 \times {10}^{11} N {m}^{ - 2}$
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Answer 1

✨$\huge\mathcal\color{maroon} AnSwEr:$

•We assume that the rod is held by a clamp at one end, and the force "F" is applied at the other end, parallel to the lenght of the rod. Then the stress on the rod is given by

$Stress = \frac{F}{A} = \frac{F}{ {\pi}r^{2} }$

$= \frac{100 \times {10}^{3}N }{3.14 \times ( {10}^{ - 2}m) {} ^{2} }$

$\bold{ = 3.18 \times {10}^{8} N {m}^{ - 2}}$

• The elongation::

$\triangle \:L = \frac{(F / \: A)L}{Y}$

$= \frac{(3.18 \times {10}^{8}N \: {m}^{ - 2} )(1m) }{2 \times {10}^{11 \: }N \: {m}^{ - 2} }$

$= 1.59 \times {10}^{ - 3} \: m$

$\bold{= 1.59 \: mm}$

• Tʜᴇ Sᴛʀᴀɪɴ ɪs ɢɪᴠᴇɴ ʙʏ:-

Strain ::-

$= \triangle \: L / \: L$

$= (1.59 \times {10}^{ - 3}m) \setminus (1m)$

$= 1.59 \times {10}^{ - 3}$

$\bold{= 0.16\%}$

${\boxed{\huge{\green{\mathcal{BeBrainly...!}}}}}$

Answer 2

Answer:

We assume that the rod is held by a clamp at one end, and the force "F" is applied at the other end, parallel to the lenght of the rod. Then the stress on the rod is given by