The cargo ramp of a transport aircraft is hinged at its left end, which acts as a pivot. A heavy truck of weight 30 000 N30\,000\text{ N}30000 N is parked on the horizontal ramp. The ramp itself is uniform and has a weight of 10 000 N10\,000\text{ N}10000 N.
The line of action of the truck's weight is at a horizontal distance of 1.5 m from the pivot. The center of mass of the ramp is at a horizontal distance of 1.5 m further to the right. A hydraulic actuator exerts an upward vertical force of magnitude F F\,F at a horizontal distance of 2.0 m to the right of the ramp's center of mass.
Calculate the magnitude of the force F F\,F required to hold the ramp in this horizontal position.