In a garage lift, two cylinders are connected by a rigid pipe completely filled with an incompressible liquid of density 850kgm−3. The smaller cylinder has an internal radius of 1.5cm and the larger cylinder has an internal radius of 15cm. The centre of the larger piston is 1.2m higher than the centre of the smaller piston. A car of mass 1500kg is to be raised slowly by applying a force on the smaller piston.
Solve the following.
(i) Obtain an expression for the least upward force Fs that must be applied on the smaller piston so that the car just begins to rise.
(ii) Evaluate Fs for the given numerical data.
(iii) Calculate the force that would have been needed if the two pistons had been at the same horizontal level.
(iv) Determine the percentage increase in the required force caused by the 1.2m height difference.