A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000kg. The area of the cross section of the piston carrying the load is 425 cm². What maximum pressure would the smaller piston have to bear?

To determine the maximum pressure that the smaller piston must withstand in a hydraulic lift, we can use the formula for pressure, which is defined as force per unit area.

Calculating the Force

The force exerted by the car can be calculated using the formula:

• Force (F) = Mass (m) × Gravitational Acceleration (g)

Here, the mass of the car is 3000 kg, and the gravitational acceleration is approximately 9.81 m/s². Thus:

F = 3000 kg × 9.81 m/s² = 29430 N

Finding the Pressure

Next, we can find the pressure using the formula:

• Pressure (P) = Force (F) / Area (A)

The area of the cross-section of the piston is given as 425 cm², which we need to convert to square meters:

425 cm² = 425 / 10000 = 0.0425 m²

Final Calculation

Now, substituting the values into the pressure formula:

P = 29430 N / 0.0425 m² ≈ 692,235.29 Pa

Conclusion

The maximum pressure that the smaller piston would have to bear is approximately 692,235 Pa or 692.24 kPa.