Q$2.($a$)$ Explain how a free body diagram can be used to investigate concurrent forces acting on a particle at equilibrium.

$(10$ marks$)$

$($b$)$ A truss at $45$ to the horizontal, supporting a weight of $1000$ kg $,$ is stabilised by a guy rope as presented in Fig. $2.$ Calculate the tension in the guy rope and the compression in the truss.

$(7$ marks$)$

$($c$)$ A $10$ mm square cross$-$section steel bar is $1$ m long. If it is axially loaded in tension by a force of $10$ kN $,$ calculate:

$(8$ marks$)$

$($i$)$ the tensile stress developed in the bar

$($ii$)$ the strain in the bar

$($iii$)$ the new length of the bar

$($iv$)$ the new width of the bar if Poisson's ratio is $0\mathrm{.}3$

Fig. $2$ A weight of $1000$ kg hoisted by a truss$($T$)$ stayed with a guy rope $($G$)$