Define what is meant by the moment of a force about a pivot.
Objects A, B and C are arranged on a horizontal beam. The beam is in equilibrium, as illustrated in Fig. 2.1. The beam is uniform and has a length of $9.0\,\text{m}$. A pivot is positioned at the midpoint of the beam. Object A has mass $90\,\text{kg}$ and is placed at one end of the beam. Object B has mass $m$ and is $3.0\,\text{m}$ from the pivot. Object C has mass $150\,\text{kg}$ and is located at the other end of the beam. Calculate $m$.
Object A is taken away and replaced by a wire attached to the end of the beam and to the ground, as shown in Fig. 2.2. After this change, the beam is horizontal once more and in equilibrium. The positions of B and C remain unchanged. The wire has a diameter of $1.8 \times 10^{-3}\,\text{m}$ and a strain of $1.2 \times 10^{-3}$. The wire is not stretched beyond its limit of proportionality. Calculate the Young modulus of the wire.
Object B is now shifted to a new spot nearer to the pivot without crossing it. The beam is again horizontal and in equilibrium. State and explain the effect, if any, that this has on the strain in the wire.
Calculate the Young modulus for the wire.
Object B is now moved to a new place nearer to the pivot, but not beyond it. The beam is once more horizontal and in equilibrium. State and explain the effect, if any, that this has on the strain in the wire.