A bar made of uniform metal, and initially unstretched, has side lengths $w$, $x$ and $y$, as shown in Fig. 3.1. It is then pulled by a tensile force $F$ applied to the shaded ends. Any changes in the lengths $x$ and $y$ are negligible. The bar then has side lengths $x$, $y$ and $z$, as shown in Fig. 3.2. Determine expressions, in terms of some or all of $F$, $w$, $x$, $y$ and $z$, for:
(a(i))[1]
the stress $\sigma$ produced in the bar by the tensile force.
(a(ii))[1]
the strain $\epsilon$ in the bar due to the tensile force.
(a(iii))[2]
the Young modulus $E$ for the metal from which the bar is made.
(b(i))[1]
State the greatest extension of the wire for which it obeys Hooke’s law.
(b(ii))[3]
Use Fig. 3.3 to work out the strain energy in the wire when the tensile force is $120\,\text{N}$.
(b(iii))[2]
Explain why the work done in stretching the wire to an extension of $12\,\text{mm}$ is not equal to the energy recovered when the tensile force is removed.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “stress written as $\sigma = \frac{F}{xy}$” …