Question

A force of 100 N is applied to the brake pedal, which acts on the cylinder called the master through a lever. A force of 500 N is exerted on the master cylinder. Pressure created in the master cylinder is transmitted to four so-called slave cylinders. The master cylinder has a diameter of 0.55 cm, and each slave cylinder has a diameter of 2.50 cm. How much pressure is transmitted in the hydraulic system? Express your answer in pascals and in atmospheres.

Answer 1

The pressure transmitted in the hydraulic system is 10794.74 Pa or 0.1079 atm.

Step-by-step explanation:

First, we need to calculate the pressure created in the master cylinder, which is the force divided by the area. The diameter of the master cylinder is 0.55 cm, so the radius is 0.275 cm.

The area is then calculated using the formula for the area of a circle (A = πr^2).

In this case, the area is equal to 0.2375 cm^2.

The pressure is then calculated by dividing the force (500 N) by the area (0.2375 cm^2), which gives us a pressure of 2105.26 Pa or 0.0211 atm.

To find the pressure transmitted to each of the slave cylinders, we can use the same formula.

The diameter of each slave cylinder is 2.50 cm, so the radius is 1.25 cm.

The area is then calculated as 12.25 cm^2 (A = πr^2).

The pressure transmitted to each slave cylinder is equal to the pressure in the master cylinder (2105.26 Pa) multiplied by the ratio of the areas (12.25 cm^2 / 0.2375 cm^2), which gives us a pressure of 10794.74 Pa or 0.1079 atm.

Therefore, the pressure transmitted in the hydraulic system is 10794.74 Pa or 0.1079 atm.