Final answer:
The maximum pressure the smaller piston in a hydraulic lift must bear to lift a car with a mass of 3000 kg, considering a larger piston area of 425 cm², is approximately 692.47 kPa, calculated using the force due to the weight of the car and Pascal's principle.
Step-by-step explanation:
The question concerns the maximum pressure that a hydraulic lift's smaller piston must withstand to lift a maximum mass of 3000 kg, considering the larger piston's area is 425 cm². To find this, we use the formula derived from Pascal's principle, which relates force, area, and pressure in a hydraulic system. By knowing the weight of the car (mass times acceleration due to gravity), we can calculate the force exerted on the larger piston and then apply Pascal's principle to find the required pressure on the smaller piston.
First, calculate the force exerted by the car on the larger piston (F2): F2 = mass × gravity = 3000 kg × 9.81 m/s² = 29430 N. Then, we convert the area of the larger piston from cm² to m² by dividing by 100² to obtain the area in m² (A2 = 425 cm² / 100² = 0.0425 m²). Now, we can calculate the pressure exerted by the car on the larger piston (P = F2 / A2), and since this is a hydraulic system and Pascal's principle applies, this is also the maximum pressure the smaller piston would have to bear.
Therefore, P = 29430 N / 0.0425 m² = 692470.59 Pa or approximately 692.47 kPa. This is the maximum pressure the smaller piston must be able to bear to lift a 3000-kg car.