In a car lift, compressed air exerts a force on a piston with a diameter of 5.00 cm. This pressure is transmitted to a second piston with a diameter of 15.0 cm. How large a force must the compressed air exert to lift a 1.33 x 10^3 kg car? Show work please
using pascal's law,we know that Pressure 1 pressure 2, P1 P2. pressure force(N)/area(m^2) in this case,P1 F1/A1 P2 F2/A2 so,this gives us, F1/A1 F2/A2 where F1 is the force of the compressed air ,A1 is the area of the first piston,F2 is the weight of the car A2 is the area of the second piston. Our mission here is to find F1 since its the unknown here. F2 weight of the car mass x gravitational acceleration (1.33x10^3 kg) x 9.81 m/s^2 13407 N 13.407 kN A1 is the area of the first piston,which is a circle so A1 pi R^2 since radius,R 1/2 Diameter R (1/2)(0.05m) 0.025 m so area of A1 pi (0.025^2) 1.96 x 10^-3 m^2 for A2 ; R (1/2)(0.15m) 0.075 m so area of A2 pi (0.075^2) 0.0177 m^2 Plugging in the values into the formula F1/A1 F2/A2 F1 / (1.96 x 10^-3 m^2) 13407 N/ 0.0177 m^2 F1 757457 x (1.96 x 10^-3) 1485 N Thus,the compressed air must exert a force of 1485 N to lift the car ) hope i helped.Take care.
