Define the moment of a force about a point by describing its turning effect.
A tree of mass $270\,\text{kg}$ is growing from sloping ground and is held up by a post, as shown in Fig. 2.1. The ground exerts a resultant force $R$ on the tree at point $Q$. The centre of gravity of the tree is $1.2\,\text{m}$ horizontally from $Q$. The post exerts a force $F$ of $1800\,\text{N}$ perpendicular to line PQ. The line of action of $F$ passes through point $P$ and makes an angle $\theta$ with the vertical. $P$ is $1.6\,\text{m}$ horizontally from $Q$. The tree is in equilibrium and every force acts in the same plane. By taking moments about point $Q$, show that $\theta = 25^\circ$.
On Fig. 2.2, produce a labelled scale vector triangle to show the forces acting on the tree. The weight of the tree has already been drawn to scale.
The pressure exerted by the tree on the top of the post is $150\,\text{kPa}$. Find the surface area of the tree that is in contact with the post.
On Fig. 2.2, construct a labelled scale vector triangle to represent the forces acting on the tree. The tree’s weight has already been drawn to scale.
The pressure from the tree on the top of the post is $150\ \text{kPa}$. Find the area of the tree that touches the post.