A uniform wire has length $L$ and a constant cross-sectional area $A$. The material of the wire has Young modulus $E$ and resistivity $\rho$. A tension $F$ in the wire causes its length to increase by $\Delta L$. For this wire, state expressions, in terms of $L$, $A$, $F$, $\Delta L$ and $\rho$ for:
Stress, $\sigma$.
Strain, $\varepsilon$.
Young modulus, $E$.
Resistance, $R$.
A metal wire of length $2.6\,\text{m}$ and constant cross-sectional area $3.8\times10^{-7}\,\text{m}^2$ has one end fixed to a point, as shown in Fig. 4.1.
A metal wire of length $2.6\,\text{m}$ and constant cross-sectional area $3.8 \times 10^{-7}\,\text{m}^2$ is fixed at one end, as shown in Fig. 4.1. The Young modulus of the material of the wire is $7.0 \times 10^{10}\,\text{Pa}$ and its resistivity is $2.6 \times 10^{-8}\,\Omega\,\text{m}$. A load of $30\,\text{N}$ is hung from the lower end of the wire. Assume that the cross-sectional area of the wire does not change. For this load of $30\,\text{N}$, show that the extension of the wire is $2.9\,\text{mm}$.
Calculate the change in resistance for the wire.
The resistance of the wire changes with the applied load. Comment on the suggestion that this change in resistance could be used to measure the size of the load on the wire.