Consider a child sitting in a park swing with a total mass of 30 kg, suspended by chains of length 2.5 meters. To start the swing, a horizontal force $\vec{F}$ is gently applied to the swing, moving it so slowly that the acceleration of the child is negligible. Compute the work done by this force to move the swing from its stationary position ($\theta=0\degree$) to an angle $\theta=15\degree$with the vertical.