Answer to Question #131808 in Physics for Kritagya Neupane

Question

A car’s brake system transfers pressure from the main cylinder to the brake shoes on all four wheels, as shown in the diagram. The surface area of the main cylinder piston is 7.20 × 10−4 m2 (7.20 cm2), and that of the piston in each individual brake cylinder is 1.80 × 10−4 m2 (1.80 cm2). The driver exerts a 5.00 N force on the pedal.
1. What is the pressure exerted on the main cylinder?
2. What is the pressure added to the liquid in this brake system?
3. What is the pressure added to each brake cylinder?
4. What is the force exerted on each brake shoe?
5. How much volume of brake fluid is pushed out of the main cylinder?

Answer 1

1)

$$P_{main}=\frac{5}{7.2\cdot10^{-4}}=6944\ Pa$$

2)

$$P_{system}=4\frac{5}{1.8\cdot10^{-4}}=111111\ Pa$$

3)

$$P_{cylinder}=\frac{5}{1.8\cdot10^{-4}}=27778\ Pa$$

4)

$$F=(27778)(1.8\cdot10^{-4})=5\ N$$

5)

$$V=(7.2)(2)=14.4\ cm^3$$