Answer to Question #276175 in Physics for Amber

Question

In the hydraulic press used in a trash compactor, the radii of the input piston and the output plunger are 6.0 ✕ 10-3 m and 4.5 ✕ 10-2 m, respectively. If the height difference between the input piston and the output plunger can be neglected, what force is applied to the trash when the input force is 330 N.

Answer 1

$$\dfrac{F_{input}}{A_{input}}=\dfrac{F_{output}}{A_{output}},$$ $$F_{output}=\dfrac{F_{input}A_{output}}{A_{input}}=\dfrac{F_{input}\pi r_{output}^2}{\pi r_{input}^2},$$ $$F_{output}=\dfrac{330\ N\times(4.5\times10^{-2}\ m)^2}{(6.0\times10^{-3}\ m)^2}=18562.5\ N.$$