In order to lift the 15,000-N car on a hydraulic lift using compressed air pressure, a force must be applied to the smaller piston of radius 0.040m by driving it with compressed air. To calculate this required force, Bernoulli’s equation is used which states that the sum of all pressures within a system remain constant when flow remains steady. This means that for any two points in a system with different pressure levels, the difference between their values can be calculated using P1 + (density x velocity^2)/2 = P2 where ‘P’ represents pressure and ‘Density’ stands for density of fluid .

Applying this equation to the situation at hand allows us to determine two equations – one representing pressure at larger piston and other at small one since they are dealing with same liquid – thus enabling us calculate total force needed by smaller piston lift car by taking into account cross sectional area both pistons as well as density water or oil being used.. With this information we can create an expression stating: F = (P1 – P2) x A2/A1 where ‘F’ represents Force ,’A1′ stands Area large piston while ‘A2’ refers small one.

To find value ‘P1’, simply multiple weight car (15000 N ) by area large piston(0.20 m) resulting 300 kPa .For value ‘P2’, assume atmospheric pressure 101 kPa meaning ratio between larger and smaller pistons will equal 7.5: 1 meaning value Density should multiplied 7 times before determining value ‘F’. After substituting calculation appropriate variables into above formula ,we arrive final result ,which is 9800 N rounded up slightly due decimal points..

Therefore ,in order lift 15 000-N car on hydraulic liftt via compressed air driven cylinder with 0.040-m radius requires applying force roughly 9800 Newtons onto small piston .

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