Question

In a hydraulic brake, a force of 700 N is applied to a piston of area 10 cm2.

What is the pressure transmitted throughout the liquid in N/cm2 and N/m2?       (4 marks)

  If the other piston has an area of 25 cm2, what is the force exerted on it in N/cm2? 

Answer 1

(a) By the definition of the pressure, we have:

$$P=\dfrac{F}{A}=\dfrac{700\ N}{10\ cm^2}=70\ \dfrac{N}{cm^2},$$ $$P=70\ \dfrac{N}{cm^2}\cdot(\dfrac{100\ cm}{1\ m})^2=7.0\cdot10^5\ \dfrac{N}{m^2}.$$

(b) By the hydraulic lift equation, we have:

$$\dfrac{F_1}{A_1}=\dfrac{F_2}{A_2},$$ $$F_2=\dfrac{F_1A_2}{A_1}=\dfrac{700\ N\cdot25\ cm^2}{10\ cm^2}=1750\ N,$$ $$P_2=\dfrac{F_2}{A_2}=\dfrac{1750\ N}{25\ cm^2}=70\ \dfrac{N}{cm^2}.$$