A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area of cross-section of the piston carrying the load is 425 cm². What maximum pressure would the smaller piston have to bear?
The maximum pressure the smaller piston would have to bear is ⁵ Pa.
Explanation
This question tests the application of Pascal's law in hydraulic lifts. The key principle is that pressure is transmitted undiminished throughout the fluid. Therefore, the pressure on the smaller piston equals the pressure on the larger piston. The question asks for the maximum pressure, which corresponds to the maximum load of 3000 kg. We calculate the force on the larger piston using F = mg, then divide by its area to find the pressure, which is the same pressure the smaller piston must bear.
Solution Steps
Step 1: Identify the principle - According to Pascal's law, pressure is transmitted undiminished throughout the fluid. Hence, pressure on smaller piston = pressure on larger piston.
Step 2: Convert area to SI units - A₂ = 425 cm² = ⁻⁴ m² = ⁻² m²
Step 3: Calculate the maximum force on the larger piston - F₂ = mg = 3000 kg × 9.8 ms⁻² = 29400 N
Step 4: Calculate the pressure - P = F₂/A₂ = 29400 N / (⁻² m²) = ⁵ Pa