Physics 9702 · AS & A Level · Stress and strain

Stress and strain — practice question

One end of the wire is fixed at a point. A force $F$ is applied so that the wire extends by $x$. Figure 5.1 shows how $x$ varies with $F$. The wire’s cross-sectional area is $4.1 \times 10^{-7}\,\text{m}^2$ and it is made from a metal with Young modulus $1.7 \times 10^{11}\,\text{Pa}$. Assume that the cross-sectional area stays constant while the wire is stretched.
(a)[1]

State the law that gives the relationship between $F$ and $x$ in Fig. 5.1.

(b)

The wire’s extension is $0.48\,\text{mm}$. Determine:

(b(i))[2]

the stress quantity.

(b(ii))[2]

the strain value.

(c)[3]

The resistivity of the wire’s metal is $3.7 \times 10^{-7}\,\Omega\,\text{m}$. Determine the change in resistance of the wire when the extension $x$ changes from $x = 0.48\,\text{mm}$ to $x = 0.60\,\text{mm}$.

(d)[1]

A force greater than $45\,\text{N}$ is now applied to the wire. Describe how it can be checked that the elastic limit of the wire has not been exceeded.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Hooke’s law identified

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