In a hydraulic press, the piston in the small cylinder has a diameter of d 1 cm, while the larger piston has a diameter of d 2 cm. If a force F 1 is applied to the small piston, then the force F

Question

In a hydraulic press, the piston in the small cylinder has a diameter of d 1 ​ cm, while the larger piston has a diameter of d 2 ​ cm. If a force F 1 ​ is applied to the small piston, then the force F 2 ​ on the large piston is given by

TestHub · Accepted Answer

According to Pascal's law, the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.

Pressure on the small piston is $P_{1} = \frac{F _{1}}{A _{1}} = \frac{F _{1}}{\frac{π d _{1}^{2}}{4}}$

Pressure on the large piston is $P_{2} = \frac{F _{2}}{A _{2}} = \frac{F _{2}}{\frac{π d _{2}^{2}}{4}}$

Equating the pressures, $P_{1} = P_{2}$

$\frac{F _{1}}{d _{1}^{2}} = \frac{F _{2}}{d _{2}^{2}}$

$F_{2} = \frac{d _{2}^{2}}{d _{1}^{2}} F_{1}$

Answer: $F_{2} = \frac{d _{2}^{2}}{d _{1}^{2}} F_{1}$

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