See attached image. The mass is being rotated on a lever where the pivot point (P) is a certain distance ($L_2$) from the right angle at the bottom. How do I calculate the force necessary to apply horizontally at point U to lift the mass in the worst case (i.e. where the rotation position requires the maximum force), ignoring for now the weight of the lever itself, friction, etc. The structure will never rotate counter-clockwise from its illustrated position, and will rotate up to $60^\circ$ clockwise. Also assume the mass will be distributed evenly across $L_1$, i.e. the center of the mass is in the center of $L_1$.
For those interested: this is part of a robotics project. A string attached to a motor/pulley system will be pulling at point U. I'm trying to determine if the motor has sufficient stall torque and if so, how much mass we can reasonably expect to be able to lift.