Question

(a) A 2000-kg car is lifted to a height h by a hydraulic lift containing an incompressible fluid. A force of F1 applied on a piston of area A1 results in a larger force of F2 on the plunger of larger area A2 . Suppose the piston has a radius of 0.0120 m and the plunger’s radius is 0.750 m.

Calculate the height to which the car is lifted if the work done by the plunger is 200 J. (Assume that the weight of the plunger and fluid are negligible).

(b) Calculate the distance the piston moves to lift the car to a height h.

(c) A surgeon inserted a needle in the patient’s vein. The needle was connected to a top-open plastic bag filled with therapeutic fluid and lifted to a height h. Find h , which is just sufficient for the fluid to enter the vein, if the pressure gauge inside the vein was 5980 Pa. The therapeutic fluid density was adjusted to be the same as that of blood (see the lecture notes or textbook for the value).

(d) At the next stage of the treatment procedure, the surgeon used a syringe to administer a drug fluid into the same vein as in part (c). The syringe was positioned at the same level as the vein. A force of 1.20 N was applied to the plunger of the cross-sectional area 0.81 cm² connected to the needle of the inner radius 0.6 mm. What was pressure difference between the proximal and distal parts of the needle given that the proximal end opened into the vein? Use the same drug fluid density as in (c).

(e) What volume of the drug fluid was injected into the vein in 2.5 s by the pressure difference calculated in (d)? [Hint: neglect the fluid speed in the syringe].

Answer 1