Final answer:
The force exerted on the master cylinder of the hydraulic lift to support the weight of the car is 2.08 × 10^5 N.
Step-by-step explanation:
To calculate the force exerted on the master cylinder, we can use Pascal's law, which states that pressure in a fluid is equal in all directions. The formula to calculate force is:
Force = Pressure x Area
First, we need to calculate the pressure in the system. Pressure is equal to force divided by area:
Pressure = Force / Area
The area of the master cylinder can be calculated using the formula for the area of a circle:
Area = π x radius²
The force exerted on the master cylinder can then be calculated by rearranging the formula for force:
Force = Pressure x Area
Substituting the values given:
Master Cylinder Area = π x (0.02/2)² meters²
Second Cylinder Area = π x (0.24/2)² meters²
Weight of the car = mass x acceleration due to gravity = 2000 kg x 9.8 m/s²
Using these values, we can calculate:
- Calculate the pressure in the system by dividing the weight of the car by the area of the second cylinder.
- Calculate the force exerted on the master cylinder by multiplying the pressure by the area of the master cylinder.
Plugging the values into the formulas, we find that the force exerted on the master cylinder of the hydraulic lift to support the weight of the car is approximately 2.08 × 105 N.