Answer to Question #161001 in Classical Mechanics for Ermus Ken

Question

An engineering student wants to build a hydraulic pump to lift a 1,815 N crate. The pump will have two pistons connected via a fluid chamber. The student calculates that a force of 442 N will be exerted on the small piston, which will have an area of 50.2 cm². What must be the area of the large piston be to exert the desired force?

Answer 1

$\dfrac{F_1}{A_1}=\dfrac{F_2}{A_2},$ $A_2=\dfrac{A_1F_2}{F_1}=\dfrac{50.2\ cm^2\cdot(\dfrac{1\ m}{100\ cm})^2\cdot1815\ N}{442\ N}=0.0206\ m^2=206\ cm^2.$