The larger piston has four times as much horizontal area as the smaller piston. If the small piston is compressed 8 inches, how far will the larger piston move?

To understand the relationship between the movement of the two pistons, we can apply Pascal's principle, which states that when pressure is applied to a confined fluid, that pressure is transmitted undiminished throughout the fluid.

In this scenario, since the larger piston has four times the horizontal area of the smaller piston, we can deduce that there is an inverse relationship between the areas of the pistons and the distances they move. Specifically, if the smaller piston is compressed by a certain distance, the larger piston will move a lesser distance because the larger piston has greater area to accommodate the same pressure.

When the smaller piston is compressed by 8 inches, the pressure generated is uniform across the fluid. Because the larger piston has four times the area, it will compress a quarter of the distance of the smaller piston to maintain the same pressure.

Thus, we can calculate the movement of the larger piston by taking the distance the smaller piston is compressed (8 inches) and dividing it by the ratio of the areas (4), leading to the movement of the larger piston being 8 inches divided by 4, which equals 2 inches.

This relationship between area and movement in hydraulic systems helps us ascertain that when one piston moves a significant distance due to its