State the two requirements for an object to be in equilibrium.
A uniform beam AC is fixed to a vertical wall at A. As shown in Fig. 3.1, the beam is kept horizontal by a rigid bar BD. The beam has length $0.40\,\text{m}$ and weight $W$. A bucket with weight $12\,\text{N}$ and no contents hangs from C on a light metal wire. The bar applies a force of $33\,\text{N}$ to the beam at $52^\circ$ to the horizontal. The beam is in equilibrium. Calculate the vertical component of the force applied by the bar to the beam.
By taking moments about A, calculate the weight $W$ of the beam.
The metal used for the wire in (b) has a Young modulus of $2.0 \times 10^{11}\,\text{Pa}$. At first, the bucket is empty. When paint of weight $78\,\text{N}$ is added to the bucket, the strain in the wire rises by $7.5 \times 10^{-4}$. The wire follows Hooke’s law. Calculate the increase in stress in the wire caused by the paint.
Calculate its diameter.