In the figure, a cube of edge length L = 0.478 m and mass 1080 kg is suspended b

Question

In the figure, a cube of edge length L = 0.478 m and mass 1080 kg is suspended by a rope in an open tank of liquid of density 1.01E+3 kg/m^3. Find (a) the magnitude of the total downward force on the top of the cube from the liquid and the atmosphere, assuming atmospheric pressure is 1.00 atm, (b) the magnitude of the total upward force on the bottom of the cube, and (c) the tension in the rope. (d) Calculate the magnitude of the buoyant force on the cube using Archimede's principle. (a) Number Units (b) Number Units (c) Number Units (d) Number Units

Explanation / Answer

Area of a face = 0.478^2 = 0.228484 m^2
Force due to air pressure = pA = 0.228484*101325 = 23151.14 N
Force due to weight of liquid above cube = (density)*g*h*A = 1010*9.81*(1/2)(0.478^3) = 541.06

(a) 23151.14 + 541.06 = 23692.2 N
Force due to weight of liquid above bottom surface of the cube = (density)*g*h*A = 1010*9.81*(3/2)(0.478^3) = 1623.2 N
(b) 23692.2 +1623.2 = 25315 N
Weight of the cube = 1080*9.81 = 10594.8 N
(c) T = 10594.8 + 23692.2 - 25315 = 8972 N
(d) 1010*9.81*(0.478)^3 = 1082.12 N

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