State what the term centre of gravity of a body means.
A uniform square sign with sides of length $0.68\,\text{m}$ is attached to a wall at its corner points A and B. The sign is also supported by a wire CD, as shown in Fig. 3.1. Its weight is $W$ and its centre of gravity is at point E. The sign is maintained in a vertical plane with side BC horizontal. The wire makes an angle of $35^{\circ}$ with side BC. The tension in the wire is $54\,\text{N}$. The force on the sign at B acts only vertically.
Calculate the vertical part of the tension in the wire.
Explain why the force acting on the sign at B produces no moment about point A.
By taking moments about point A, show that the sign's weight $W$ is $150\,\text{N}$.
Calculate the combined vertical force exerted by the wall on the sign at points A and B.
The sign in (b) is joined together by nuts and bolts. One nut drops vertically from rest through a distance of $4.8\,\text{m}$ to the pavement below. It reaches the pavement with a speed of $9.2\,\text{m s}^{-1}$. Determine, for the nut falling from the sign to the pavement, the ratio \(\frac{\text{change in gravitational potential energy}}{\text{final kinetic energy}}\).