In a hydraulic garage lift, the small piston has a radius of 4.0 cm and the larg

Question

In a hydraulic garage lift, the small piston has a radius of 4.0 cm and the large piston has a radius of 20 cm. What force must be applied on the small piston in order to lift a car weighing 20,000 N on the large piston? Assume the pistons each have negligible weight.

An object of a material A of density 10.6 g/cm3 is placed in a tub of mercury (density 13.6 g/cm3). Which answer best describes the result?

-The object A will float with about 78% of its volume above the surface of the mercury

-The object will float with its top exactly even with the surface of the mercury.

-The object will float with about 22% of its volume above the surface of the mercury.

-The object will sink to the bottom of the mercury

Explanation / Answer

Part-A

Given that,

radius of the small piston, rs = 4.0 cm

radius of the large piston, rl = 20 cm

force applied on the small piston, Fs = ?

force applied on the large piston, Fl = 20,000 N

Fs / As = Fl / Al

Fs = Fl*As / Al = 20000*42 / 202

force applied on the small piston, Fs = 800 N

Part-B

V1*rho1*g = V2*rho2*g

V1 / V2 = rho2 / rho1

V1 / V2 = 10.6 / 13.6 = 0.78

Therefore, the object A will float with about 78% of its volume above the surface of the mercury

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.