Question

The figure shows the arrangement of master cylinder and slave cylinder of a part of braking system. The master cylinder piston, of surface area 8 cm2 exerts a force of 28 N on the brake fluid when the driver presses the brake pedal Calculate the pressure on the brake fluid produced by the master piston This pressure is transmitted to the slave piston that has surface area of 40 cm2. Calculate the force exerted on this piston State two methods of increasing the force produced by the slave cylinder piston.

Answer 1

Answer:

a) 35 kPa

d) 140 N

c) 1) Increasing the brake fluid  pressure

2)  Increasing the slave piston surface area.

Explanation:

The parameters given are;

a) Force applied to the master cylinder piston = 28 N

Cross sectional area of the master cylinder piston = 8 cm² = 8 × 10⁻⁴ m²

The pressure P on the brake fluid is given by the formula for pressure as follows;

$P= \dfrac{Applied \ force}{Area \over \ which \ force \ is \ applied} = \dfrac{28 \, N}{8 \times 10^{-4} \, m^2} = 35,000 \, N/m^2 = 35,000 \, Pa$

The pressure on the brake fluid, P, produced by the master cylinder piston = 35,000 Pa = 35 kPa

b) Given that the area of the slave piston = 40 cm² = 0.004 m², we have from the formula for pressure, P;

$P= \dfrac{Applied \ force}{Area \over \ which \ force \ is \ applied} = \dfrac{Applied \ force}{4 \times 10^{-3} \, m^2} = 35,000 \, N/m^2$

Therefore;

Applied force on the slave piston = 4 × 10⁻³ m² × 35,000 N/m² = 140 N

c) The force, F produced by the slave cylinder piston is given by the relation;

F = Pressure × Area

Therefore, the two ways of increasing the force produced by the slave cylinder piston is as follows;

1) Increasing the pressure in the brake fluid by increasing the force exerted by the master cylinder piston

2) Increasing the surface area of the slave piston.