If a trash compactor pushes down with a force of 500 N on a 3 cmsquare input piston causing a force of 30000 N to crush the trash. What is the area of the output piston that crushes the trash?

To find the area of the output piston, we can use Pascal's principle, which states that the pressure applied to a confined fluid is transmitted undiminished throughout the fluid. The pressure on the input piston is ( P = \frac{F}{A} = \frac{500 , \text{N}}{3 , \text{cm}^2} ). The pressure on the output piston is the same, so ( P = \frac{30000 , \text{N}}{A_{\text{output}}} ). Setting the pressures equal gives us ( \frac{500 , \text{N}}{3 , \text{cm}^2} = \frac{30000 , \text{N}}{A_{\text{output}}} ). Solving for ( A_{\text{output}} ) results in ( A_{\text{output}} = 180 , \text{cm}^2 ).