State what the centre of gravity of an object means.
A uniform beam $AB$ is joined to a vertical wall by a frictionless hinge at end $A$. As shown in Fig. 3.1, a metal wire $CD$ keeps the beam horizontal. The beam has length $0.96\,\text{m}$ and weight $23\,\text{N}$. A block of weight $W$ sits on the beam $0.20\,\text{m}$ from $B$. The wire is fixed to the beam at point $D$, which is $0.40\,\text{m}$ from $B$. The wire exerts a force of $45\,\text{N}$ on the beam at an angle of $37^\circ$ to the horizontal. The beam is in equilibrium.
Calculate the vertical component of the force exerted by the wire on the beam.
Using moments about A, determine the block's weight W.
The hinge applies a force on the beam at end $A$. Calculate this force's horizontal component.
The block is now moved nearer to point $D$ on the beam. State whether the tension in the wire increases, decreases or stays unchanged.
The stress in the wire is $5.3 \times 10^7\,\text{Pa}$. It is replaced by another wire whose radius is three times the original radius. The tension stays the same. Calculate the stress in the second wire.
The hinge applies a force on the beam at end A. Calculate the horizontal part of this force.
The block is now moved nearer to point D on the beam. State whether the tension in the wire increases, decreases or has no effect.
The stress in the wire is $5.3 \times 10^7\,\text{Pa}$. It is replaced by another wire whose radius is three times the original radius. The tension stays the same. Calculate the stress in the second wire.