8 Three forces act in a vertical plane on an object of mass 250 kg , as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{7ac7dfd0-4c3e-4eb7-920f-ce5b24ad1281-5_481_1139_408_447} The two forces \(P\) newtons and \(Q\) newtons each act at \(80 ^ { \circ }\) to the horizontal. The object accelerates horizontally at \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\) under the action of these forces.

1. Show that $$P = 125 \left( \frac { a } { \cos 80 ^ { \circ } } + \frac { g } { \sin 80 ^ { \circ } } \right)$$
2. Find the value of \(a\) for which \(Q\) is zero.