According to Pascal's Principle, the force exerted on the master cylinder can be found using the equation Force = Pressure x Area. By rearranging the equation and substituting the given values, we can calculate the force to be approximately 74754.6 N.
In this scenario, we can use Pascal's Principle to find the force exerted on the master cylinder of a hydraulic lift. Pascal's Principle states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.
To calculate the force exerted on the master cylinder, we can use the equation:
Force = Pressure x Area
Given that the weight of the 2400 kg car is the force we want to support, we can rearrange the equation to solve for the force:
Force = Weight / Area_slave
Substituting the values into the equation and converting the diameter to radius, we'll have:
Force = (2400 kg x 9.8 m/s²) / (π x (12 cm / 100)^2)
Simplifying the equation:
Force ≈ 74754.6 N
Therefore, the force that must be exerted on the master cylinder of the hydraulic lift to support the weight of the 2400 kg car is approximately 74754.6 N.