State the principle of moments in words.
A solid plastic cylinder floats in water and is used to support one end of a horizontal uniform beam AB, as shown in Fig. 2.1. The beam is $6.0\,\text{m}$ long and has weight $1700\,\text{N}$. It is hinged to the solid ground at A. The cylinder floats upright in the water, and its top is fixed at its centre to the beam $5.0\,\text{m}$ from A. The cylinder exerts a vertical force of $1300\,\text{N}$ on the beam. A person with weight $660\,\text{N}$ stands on the beam at point P. Beam AB is in equilibrium.
Use moments about end A to find the distance $x$ from A to P.
Show that the cylinder experiences an upthrust of $1400\,\text{N}$.
Water density is $990\,\text{kg m}^{-3}$. Calculate the depth $y$.
On Fig. 2.3, sketch how the depth of the bottom of the cylinder varies with the person’s distance from A, for distances from $0$ to $6.0\,\text{m}$. You do not need to include numerical values.