Question

Consider the hydraulic jack represented beside. It is filled with mineral oil (a lubricating liquid). Assume that a person is able to push the left piston (F1) with a maximum force of 343 N. The diameter of the piston on the left is only 2 cm and that of the piston on the right much larger at 40 cm.

• A) If the piston on the right is used to lift a car, what is the highest car weight (in N) that the person can lift using this device? What is the associated car mass (in kg)?

• B) What is the mineral oil pressure while lifting the car? Is it larger of smaller than the atmospheric pressure? If you were to generate such a pressure using a column of mercury (Hg) then how high it would need to be? Similarly if you were to generate such a pressure using a column of water (H2O) then how high it would need to be?

• Assume now that this hydraulic jack is indeed used by a shop to lift cars. A client arrives with a rather small automobile for which the technical manual claims it has a mass of 1385 kg when empty of passengers and luggage.

• C) What is the magnitude of the force that the mechanic has to apply on the left piston to lift this specific car?

• D) Assume that the mechanic pushes the left piston down over 1 meter. How much work has the mechanic done? How high has the small car been lifted by this action? How much has the potential energy of the car changed? Would you argue that energy conservation applies in this problem? How do you prove or justify your answer?

Answer 1

From Pascal law extra pressure supplied to liquid equally distributed in all directions.

D)from conservation of mass , volume of liquid compressed in left cylinder is equal to the volume of liquid raised in right cylinder.