In a car lift, compressed air exerts a force $F_1$ on a small piston of radius 5.0 cm. This pressure is transmitted to a second piston of radius 15 cm. If the mass of the car to be lifted is 1350 kg ($g = 9.8 \text{ m/s}^2$), what is the force $F_1$ required?
From Example 9.6: Force to be lifted ($F_2$) = mass $\times g = 1350 \text{ kg} \times 9.8 \text{ m/s}^2 = 13230 \text{ N}$. Radii are $r_1 = 5.0 \text{ cm}$ and $r_2 = 15 \text{ cm}$. We know $F_1/A_1 = F_2/A_2$, so $F_1 = F_2 (A_1/A_2) = F_2 (\pi r_1^2 / \pi r_2^2) = F_2 (r_1/r_2)^2$. $F_1 = 13230 \text{ N} \times (5/15)^2 = 13230 \text{ N} \times (1/3)^2 = 13230 \text{ N} \times (1/9) = 1470 \text{ N}$.