Final answer:
Pascal's law is applied to calculate the force created at each wheel cylinder in a hydraulic brake system, using the areas of the pedal and wheel cylinders to find the force exerted on each wheel cylinder.
Step-by-step explanation:
The subject question pertains to calculating the force created at each wheel cylinder in a hydraulic brake system. To find the force F2 created at the wheel cylinders, we use the principle of Pascal's law, which states that pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and to the walls of its container.
Since pressure is equal to force divided by area (P = F/A), and the pressure in the pedal cylinder must equal the pressure in the wheel cylinders, we can set up a ratio of the forces to the areas of the two cylinders.
First, we calculate the area of the pedal cylinder (Ap) and the wheel cylinder (Aw):
- Ap = (pi)(d/2)^2 = (pi)(0.005/2)^2 m^2
- Aw = (pi)(d/2)^2 = (pi)(0.025/2)^2 m^2
With the areas calculated, we use the proportion F1/Ap = F2/Aw to find the force at the wheels:
- F2 = F1 * (Aw / Ap) = 500 N * (Aw / Ap)
Plugging in the numbers, we solve for F2, which represents the force exerted on each of the four wheel cylinders.