The tensile strain is applied on a specimen of length of 2m and cross-sectional area is 1cm². When it to the…

Question

The tensile strain is applied on a specimen of length of 2m and cross-sectional area is 1cm². When it to the thin wire, determine the tensile stress.

ScanSolve AI Tutor · Accepted Answer

The image quality is low, so I've interpreted the problem as follows: A force of $300 \text{ N}$ is applied to a material with an original length of $2 \text{ m}$ , causing an extension of $1 \text{ mm}$ . The material has a cross-sectional area of $1.5 \text{ cm}^2$ . I will calculate the tensile strain and tensile stress.

Identify the given values and convert units to SI.
- Original length ( $L_0$ ) = $2 \text{ m}$
- Extension ( $\Delta L$ ) = $1 \text{ mm} = 1 \times 10^{-3} \text{ m}$
- Cross-sectional area ( $A$ ) = $1.5 \text{ cm}^2 = 1.5 \times (10^{-2} \text{ m})^2 = 1.5 \times 10^{-4} \text{ m}^2$
- Applied Force ( $F$ ) = $300 \text{ N}$
Calculate the tensile strain.
Tensile strain ( $\epsilon$ ) is defined as the ratio of the extension to the original length.
$\epsilon = \frac{\Delta L}{L_0}$
Substitute the values:
$\epsilon = \frac{1 \times 10^{-3} \text{ m}}{2 \text{ m}}$ $\epsilon = 0.0005$
The tensile strain is dimensionless.
$\boxed{\text{Tensile strain} = \textbf{0.0005}}$
Calculate the tensile stress.
Tensile stress ( $\sigma$ ) is defined as the ratio of the applied force to the cross-sectional area.
$\sigma = \frac{F}{A}$
Substitute the values:
$\sigma = \frac{300 \text{ N}}{1.5 \times 10^{-4} \text{ m}^2}$ $\sigma = 2,000,000 \text{ N/m}^2$ $\sigma = 2 \times 10^6 \text{ Pa}$ $\boxed{\text{Tensile stress} = \textbf{2} \times \textbf{10}^{\textbf{6}} \textbf{ Pa}}$

The tensile strain is applied on a specimen of length of 2m and cross-sectional area is 1cm². When it to the thin wire, determine the tensile stress.

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Step-by-step solution

Identify the given values and convert units to SI.

Calculate the tensile strain.

Calculate the tensile stress.

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