Question

A hydraulic lift has pistons with diameters 8.00 cm and 36.0 cm, respectively. If a force of 825 N is exerted at the input piston, what maximum mass can be lifted by the output piston

Answer 1

Given:

$d_1=8.00\rm\: cm$

$d_2=36.0\rm\: cm$

$F_1=825\:\rm N$

The hydraulic press equation says

$$\frac{F_1}{A_1}=\frac{F_2}{A_2}$$

Hence, the output force

$$F_2=F_1\frac{A_2}{A_1}=F_1\frac{d_2^2}{d_1^2}$$

The maximum mass can be lifted by the output piston

$$m=\frac{F_2}{g}=\frac{F_1}{g}\frac{d_2^2}{d_1^2}$$

$$m=\frac{825}{9.81}\frac{36.0^2}{8.00^2}=1700\:\rm kg$$