Answer to Question #49734 in Molecular Physics | Thermodynamics for Billy Joe

Question

A hydraulic jack system is created in the configuration below. A person pushes down with force F on one end of the lever arm of total length l= 1.2m. The lever arm is attached to a fixed pivot on the opposite end and in turn pushes straight down on the input piston, located halfway down the lever arm, with Fi. The ratio of the output pistons area to the input pistons area is Ao/Ai=55. You want the output force to sustain the weight of a W = 6000N object.
a) Algebraically find the input pistons force Fi in terms of the persons force F using a torque argument.
b) Find the required force the person must exert in order to support the object by relating the expression for Fi to Fo.