Physics
Physics
Problem
A mechanic operates a hydraulic jack with pistons of areas (small) and (large). The small piston is pushed down by . The jack is ideal (no losses). a. (i) Calculate the distance through which the large piston rises. b. (ii) If the weight supported by the large piston is , determine the minimum force that must be applied on the small piston.Intuitive explanation
Pascal's principle tells us that pressure is transmitted equally through an incompressible fluid, so the key is to use conservation of volume: the fluid pushed out by the small piston must equal the fluid that fills the large piston. Since pressure amplifies inversely with area, a small displacement on the input side produces a much larger force on the output side—that's the mechanical advantage of a hydraulic system. Set up the volume balance to find how far the large piston rises.
Intuitive explanation
Pascal's principle tells us that pressure is transmitted equally through an incompressible fluid, so the key is to use conservation of volume: the fluid pushed out by the small piston must equal the fluid that fills the large piston. Since pressure amplifies inversely with area, a small displacement on the input side produces a much larger force on the output side—that's the mechanical advantage of a hydraulic system. Set up the volume balance to find how far the large piston rises.