A hydraulic car lift consists of two vertically oriented cylindrical pistons…
PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids
Problem
A hydraulic car lift consists of two vertically oriented cylindrical pistons connected by a completely filled line of hydraulic fluid. The small piston, of cross-sectional area As, is pushed downward by a mechanic with a force Fs. The large piston, of cross-sectional area AL, supports a car of weight W. The fluid is assumed to be incompressible, and fluid levels in both cylinders remain at the same elevation.
Address the following tasks related to the operation of the lift.
(a) Derive an expression relating Fs and W in terms of the piston areas.
(b) If the mechanic pushes the small piston downward a distance ds, show that the car rises a distance dL=ALAsds, and explain the physical principle underlying this relationship.
(c) Using energy considerations, verify that the work done by the mechanic on the small piston equals the increase in gravitational potential energy of the car, neglecting any losses due to friction or turbulence in the fluid.