Final answer:
The force that must be exerted on the pedal cylinder of a hydraulic lift to support the weight of a 2000-kg car is 3200 N.
Step-by-step explanation:
To calculate the force exerted on the pedal cylinder of a hydraulic lift, we can use Pascal's law, which states that pressure is transmitted equally in a fluid-filled system. We can use the formula:
F1/A1 = F2/A2
where F1 is the force on the pedal cylinder, A1 is the cross-sectional area of the pedal cylinder, F2 is the force on the wheel cylinder, and A2 is the cross-sectional area of the wheel cylinder.
From the given information, the diameter of the pedal cylinder is 2.00 cm, so the radius is 1.00 cm or 0.01 m.
The diameter of the wheel cylinder is 24.0 cm, so the radius is 12.0 cm or 0.12 m.
The weight of the car is 2000 kg, so the force on the wheel cylinder is the weight of the car, which is 2000 kg multiplied by the acceleration due to gravity (9.8 m/s^2). Plugging these values into the formula:
F1 / (pi * 0.01^2) = (2000 * 9.8) / (pi * 0.12^2)
Simplifying the equation, we find:
F1 = (pi * 0.01^2 * (2000 * 9.8)) / (pi * 0.12^2)
F1 = 3200 N
Therefore, the force that must be exerted on the pedal cylinder of the hydraulic lift to support the weight of the car is 3200 N.