Physics 9702 · Paper 2

Reading E off a Graph

A stress-strain graph plots stress up the vertical axis against strain along the horizontal axis. On it, $E$ is the gradient of the straight part, and this lesson is about reading that gradient off.
Pick one clear point on the line and divide its stress by its strain.
Use only the first straight section, where Hooke's law holds. Past it the line curves and the gradient no longer gives $E$ .

Reading E off the straight line

A metal in its linear region: pick one clear point on the line, far from the origin. Here strain 2.0 × 10⁻³ gives stress 140 MPa, so E = 140 × 10⁶ / 2.0 × 10⁻³ = 70 GPa.

Worked example

Young modulus from a graph reading

The straight line passes through the origin and reaches a stress of 140 MPa at a strain of $2.0\times10^{-3}$ .

Take the gradient using that point: $E=\sigma/\varepsilon$ .
$E=\dfrac{140\times10^{6}}{2.0\times10^{-3}}=7.0\times10^{10}\text{ Pa}=70\text{ GPa}$ .

Answer

E=7.0\times10^{10}\text{ Pa}\ (70\text{ GPa})

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