A piece of copper having a rectangular cross-section of $15.2\ ext{mm} imes 19.1\ ext{mm}$ is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain.

Question

A piece of copper having a rectangular cross-section of $15.2\ 	ext{mm} 	imes 19.1\ 	ext{mm}$ is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain.

Accepted Answer

> [!TLDR]
> Using Young's modulus for copper ($Y = 1.1 	imes 10^{11}\ 	ext{Pa}$, Table 8.1) and the relation $\sigma = Y \cdot \varepsilon$, dividing the tensile stress by $Y$ gives the strain. The printed answer for this question is $\boxed{0.127}$.

Young's modulus is the material's stiffness -- it tells you how much strain (fractional change in length) a given stress produces, as long as the deformation stays elastic. For copper, Table 8.1 gives $Y = 1.1 	imes 10^{11}\ 	ext{Pa}$. The key relation is:

> [!FORMULA]
> $$ \sigma = Y \cdot \varepsilon \quad 	ext{or} \quad \varepsilon = \frac{\sigma}{Y} $$

where $\sigma$ is tensile stress (force per unit area) and $\varepsilon$ is the strain (dimensionless). So the plan is: compute the cross-sectional area, find the stress, then divide by $Y$.

1. **Convert dimensions to metres.**
   The cross-section is $15.2\ 	ext{mm} 	imes 19.1\ 	ext{mm}$.
   $$ 15.2\ 	ext{mm} = 0.0152\ 	ext{m}, \qquad 19.1\ 	ext{mm} = 0.0191\ 	ext{m} $$

2. **Calculate the area.**
   $$ A = 0.0152 	imes 0.0191 = 2.9032 	imes 10^{-4}\ 	ext{m}^2 $$

3. **Find the tensile stress.**
   Force $F = 44{,}500\ 	ext{N}$.
   $$ \sigma = \frac{F}{A} = \frac{44{,}500}{2.9032 	imes 10^{-4}} \approx 1.53 	imes 10^{8}\ 	ext{Pa} $$

4. **Apply Young's modulus.** …

Q.A piece of copper having a rectangular cross-section of $15.2\ \text{mm} \times 19.1\ \text{mm}$ is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain.

Concept understanding — Youngs Modulus

Young’s Modulus: The Stretchiness of a Solid

The Intuition: Stiffness per Unit Size

The Precise Definition

What the Number Tells You

A Worked Example

Q.A piece of copper having a rectangular cross-section of 15.2 mm×19.1 mm15.2\ \text{mm} \times 19.1\ \text{mm}15.2 mm×19.1 mm is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain.

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Q.A piece of copper having a rectangular cross-section of $15.2\ \text{mm} \times 19.1\ \text{mm}$ is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain.

Unlock everything free for 14 days