Problem

Figure 4

A beam $AB$ has mass $30\text{ kg}$ and length $3\text{ m}$.

The beam rests on supports at $C$ and $D$ where $AC = 0.4\text{ m}$ and $DB = 0.4\text{ m}$, as shown in Figure 4.

A person of mass $55\text{ kg}$ stands on the beam between $C$ and $D$.

The person is modelled as a particle at the point $P$, where $CP = x$ metres and $0 < x < 2.2$

The beam is modelled as a uniform rod resting in equilibrium in a horizontal position.

Using the model,

(a) show that the magnitude of the reaction at $C$ is $(686 - 245x)\text{ N}$.

The magnitude of the reaction at $C$ is four times the magnitude of the reaction at $D$.

Using the model,

(b) find the value of $x$

The person steps off the beam and places a package of mass $M\text{ kg}$ at $A$.

The package is modelled as a particle at the point $A$.

The beam is now on the point of tilting about $C$.

Using the model,

(c) find the value of $M$