Question

A Hydraulic system comprises two square water columns. One column has a surface area of 1 meter x 1 meter, and the other has a surface area of 10 meters x 10 meters. If a force of 10 Newtons is applied to the piston in the smaller water column, what is the force to load in the larger column?

1.1. How far would you need to depress the piston in the smaller column to raise the piston in the larger column 5 meters? What formula is used?

Answer 1

The force on the larger piston of a hydraulic system when a force of 10 N is applied to the smaller piston is 1000 N. To raise the larger piston by 5 meters, the smaller piston needs to be depressed by 500 meters, based on the principle of volume balance in hydraulic systems.

Step-by-step explanation:

Using Pascal's principle for hydraulic systems, we can determine the force on the larger piston given a force applied to the smaller piston. Pascal's law states that when pressure is applied to an enclosed fluid, it is transmitted undiminished to every portion of the fluid and the walls of its container.

If the smaller square column has a surface area of 1 m2, and a force of 10 N is applied, and the larger square column has a surface area of 100 m2 (10 m x 10 m), the force on the larger column can be calculated. The ratio of the piston areas is 100:1. Therefore, the force out would be 10 N multiplied by the ratio of the areas, which gives us a force of 1000 N on the larger piston.

When dealing with the distances the pistons move, remember that the volume displaced on one side must equal the volume displaced on the other, due to the incompressibility of liquids. This means that the small piston must travel 100 times the distance that the large piston moves to maintain the volume balance. So, to raise the larger piston by 5 meters, the smaller piston must be depressed 500 meters.