The foot pedal on hydraulic brake system exerts a force of 45 lb on a piston with a diameter of 1.00 cm. The brake fluid in the brake system exerts the pressure from the foot pedal on a brake pad piston with a diameter of 2.50 cm. The force on the brake pad is

Question

Quizplus · Accepted Answer

Using the formula for pressure:
$P = F/A$
Where $P$ is the pressure, $F$ is the force exerted, and $A$ is the area upon which the force is exerted.

We can use this formula twice to solve the problem.

First, we can find the pressure at the foot pedal piston:
$P_1 = F_1/A_1 = 45	ext{ lb}/(0.01	ext{ m})^2 = 450000	ext{ Pa}$

Note that we converted the diameter from centimeters to meters.

Next, we can find the force at the brake pad piston:
$P_1 = P_2$ (pressure is the same throughout the system)
$F_2/A_2 = F_1/A_1$
$F_2 = F_1	imes A_2/A_1 = 45	ext{ lb}	imes (0.025	ext{ m}/0.01	ext{ m})^2 = 281.25	ext{ lb}$

Therefore, the force on the brake pad is 281.25 pounds, which is answer choice C.

The Foot Pedal on Hydraulic Brake System Exerts a Force