The brake in most cars makes use of a hydraulic system. This system consists of a fluid filled tube connected at each end to a piston. Assume that the piston attached to the brake pedal has a cross sectional area of 3 cm2 and the piston attached to the brake pad has a 2 cross section area of 15 cm . When you apply a force of 50 Newton to the piston attached to the brake pedal, how much will be the force at the brake pad

The force at the brake pad = 250 N

Explanation:

The hydraulic brake system works on the Pascal's Principle for pressure transmission in fluids; the pressure applied to a fluid is transmitted undiminished in all directions.

For hydraulic systems, the pressure applied to the brake pedal is transmitted undiminished through the fluid filled tube, connected at each end to a piston, to the brake pad.

Hence, mathematically,

P(brake pedal) = P(break pad)

Pressure is given as the force applied divided by the cross sectional Area perpendicular to the direction of applied force.

P(brake pedal) = (Force applied on the brake pedal) ÷ (Cross Sectional Area of the brake pedal)

Force applied on the brake pedal = 50 N

Cross Sectional Area of the brake pedal = 3 cm²

P(brake pedal) = (50/3) = 16.67 N/cm²

P(brake pad) = P(brake pedal) = 16.67 N/cm²

P(brake pad) = (Force applied on the brake pad) ÷ (Cross Sectional Area of the brake pad)

Force applied on the brake pad = F = ?

Cross Sectional Area of the brake pad = 15 cm²

16.67 = (F/15)

F = 16.67 × 15 = 250 N

Hence, the force at the brake pad = 250 N

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