Final answer:
The pressure transmitted in the hydraulic system, given that a force of 480 N is applied to a pedal cylinder with a diameter of 0.475 cm, is calculated to be 0.2674 atmospheres using Pascal's Principle and the area formula for a circle.
Step-by-step explanation:
To find the pressure transmitted in the hydraulic system, we use Pascal's Principle, which states that pressure applied to a confined fluid is transmitted undiminished throughout the fluid. The formula used to calculate pressure is:
P = F / A, where P is the pressure, F is the force applied, and A is the area over which the force is applied.
The area A can be found using the formula for the area of a circle, A = πr^2, where r is the radius.
First, convert the diameter to meters (0.475 cm = 0.00475 m), then find the radius (r = 0.00475 m / 2 = 0.002375 m).
Now calculate area:
A = π(0.002375 m)^2 = π(5.640625 × 10^{-6} m^2)
= 1.772 × 10^{-5} m^2.
Next, calculate the pressure:
P = 480 N / 1.772 × 10^{-5} m^2
= 2.708 × 10^4 Pa.
To express this pressure in atmospheres, use the conversion factor where 1 atm = 101,325 Pa. Therefore:
P = 2.708 × 10^4 Pa / 101,325 Pa/atm
= 0.2674 atm.
Thus, the pressure transmitted in the hydraulic system is 0.2674 atmospheres.