2. A monk uses a small brush to clean the stone floor of a monastery by pushing the brush with a force of \(P\) Newtons at an angle of \(60 ^ { \circ }\) to the vertical. He moves the brush at a constant speed. The mass of the brush is 0.5 kg and the coefficient of friction between the brush and the floor is \(\frac { 1 } { \sqrt { 3 } }\). The brush is modelled as a particle and air resistance is ignored.

1. Show that \(P = \frac { g } { 2 }\) Newtons.
2. Explain why it is reasonable to ignore air resistance in this situation.