A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with incompressible oil with a density of 800 kg/m³ and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the force that must be applied to the smaller piston in order to lift the car after it has been raised 1.20 m? (For purposes of this problem, you can neglect the weight of the pistons.)

Question

Quizplus · Accepted Answer

The force needed is determined by the principle of hydraulic lift, which states that the force applied is proportional to the area of the pistons. The force on the smaller piston is calculated using the formula: F1/A1 = F2/A2, where F1 is the force on the smaller piston, A1 is the area of the smaller piston, F2 is the weight of the car, and A2 is the area of the larger piston. After calculating the areas and solving for F1, the force required is approximately 1.96 kN.

A 12,000-N Car Is Raised Using a Hydraulic Lift, Which