Depressing the brake pedal in a car pushes on a piston with cross-sectional area

Question

Depressing the brake pedal in a car pushes on a piston with cross-sectional area 2.1 cm2. The piston applies pressure to the brake fluid, which is connected to two pistons, each with area 12.1 cm2. Each of these pistons presses a brake pad against one side of a rotor attached to one of the rotating wheels. See the figure for this problem. (a) When the force applied by the brake pedal to the small piston is 7.7 N, what is the normal force applied to each side of the rotor? N (b) If the coefficient of kinetic friction between a brake pad and the rotor is 0.80 and each pad is (on average) 12 cm from the rotation axis of the rotor, what is the torque on the rotor due to the two pads? N

Explanation / Answer

Force expansion ratio = 12.1/2.1 = 5.76
Force at each larger piston = 5.76 x 7.7 = 44.367 N ANS (a)

kinetic friction force = 44.367(0.80) = 35.493 N
Torque of 1 pad against rotor = 35.493 x 0.12 = 4.2592 m-N
Torque of both pads against rotor = 2 x 4.2592 = 8.5184 m-N ANS (b)

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