Final answer:
To determine the magnitude of the applied force on piston y, we use Pascal's law. We calculate the area of both pistons, the weight of the car, and then apply the formula derived from Pascal's law to find the force needed to lift the car.
Step-by-step explanation:
To calculate the magnitude of the applied force on piston y (Piston 2) in a hydraulic lift, we use the principle of hydraulic systems based on Pascal's law, which states that when pressure is applied to a confined fluid, it is transmitted undiminished throughout the fluid.
The formula derived from Pascal's law is:
F1/A1 = F2/A2
Where:
- F1 is the force applied on piston y,
- A1 is the cross-sectional area of piston y,
- F2 is the force exerted by the car's weight on piston x,
- A2 is the cross-sectional area of piston x.
First, we calculate the areas (A) of both pistons using the formula for the area of a circle (A = πr^2).
For piston y (radius = 0.11 m):
A1 = π * (0.11 m)^2
For piston x (radius = 0.33 m):
A2 = π * (0.33 m)^2
The weight (F2) of the car is the product of its mass (1300 kg) and the acceleration due to gravity (g = 9.8 m/s^2).
F2 = 1300 kg * 9.8 m/s^2
After calculating F2 and the areas A1 and A2, we can rearrange the formula to solve for F1:
F1 = (A1/A2) * F2
By substituting the computed values into the equation, we can determine the applied force F1 required to lift the car.
Remember, we have to ensure that the units are consistent; areas should be in square meters, force in Newtons, and so on.