Final answer:
To calculate the force required on the pedal cylinder of a hydraulic lift to support the weight of a 2000-kg car, we use Pascal's law and the piston diameter ratio. The force required is 19,620 N.
Step-by-step explanation:
To calculate the force required on the pedal cylinder of a hydraulic lift to support the weight of a 2000-kg car, we can use the principle of Pascal's law. Pascal's law states that the pressure created in a fluid is transmitted equally to all parts of the fluid and to the walls of the container. In a hydraulic system, the force exerted on the pedal cylinder is multiplied by the ratio of the areas of the pedal cylinder and the wheel cylinder.
The piston diameter ratio is given as 9, which means the ratio of the areas of the pedal cylinder and the wheel cylinder is 81:1. Therefore, to calculate the force required on the pedal cylinder, we divide the weight of the car (2000 kg × gravitational acceleration) by the area of the wheel cylinder and multiply it by the ratio of areas.
Using the formula F = P × A, where F is the force, P is the pressure, and A is the area, the force required on the pedal cylinder is:
F = (2000 kg × 9.8 m/s²) × (1/81) × π × (24/2)^2 = 19,620 N
Therefore, the correct option is a) 19,620 N.