A uniform steel gantry AB AB\,AB has a length of 9 m and a mass of 2.4 kg. A heavy equipment crate of weight 4W newtons4W\text{ newtons}4W newtons is attached to the gantry at end AAA, and a secondary load of weight W newtonsW\text{ newtons}W newtons is attached at end BBB.
The gantry is held in horizontal equilibrium by a single vertical support cable attached at a point z metresz\text{ metres}z metres from end AAA.
Show that
z=9W+10.8g5W+2.4g z = \frac{9W + 10.8g}{5W + 2.4g} z=5W+2.4g9W+10.8g