Rubber has a Poisson's ratio close to 0.5…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Rubber has a Poisson's ratio close to $0.5$ . A round rubber cord is stretched by $3.0\%$ of its length.

Use Poisson's ratio to find the percentage change of its radius.
Find it exactly, assuming the volume does not change at all. Compare.

Need a reminder? The key ideaShow

Poisson's ratio: $\sigma = \dfrac{\Delta d/d}{\Delta L/L}$ , between $0$ and $0.5$ . A stretched rod's volume changes by $\dfrac{\Delta V}{V} = \varepsilon(1 - 2\sigma)$ . The moduli are linked: $Y = 2G(1 + \sigma)$ and $Y = 3B(1 - 2\sigma)$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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← A metal has Y = 1.2 × 10¹¹ Pa and G = 4.5 × 10¹⁰ Pa. Find its Poisson's ratio and its bulk modulus.A wire of volume 4.0 × 10⁻⁶ m³ is stretched to a longitudinal strain of 2.5 × 10⁻³… →

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