As shown in the figure, a cube of edge length L = 0.640 m and mass 457 kg is sus

Question

As shown in the figure, a cube of edge length L = 0.640 m and mass 457 kg is suspended by a rope in an open tank of liquid of density 1030 kg/m3.

a) Find 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) Calculate the magnitude of the total upward force on the bottom of the cube.

c) Calculate the tension in the rope.

d) Calculate the magnitude of the buoyant force on the cube using Archimedes' principle.

Explanation / Answer

1.00 atm = 101325 Pa = 101325 N/m^2

I take it the top surface of the cube is L/2 below the surface
Area of a face = 0.64^2 = 0.4096 m^2
Force due to air pressure = pA = 0.4096*101325 = 41502.72 N
Force due to weight of liquid above cube = (density)*g*h*A = 1030*9.81*(1/2)(0.64^3) = 1324.4 N
(a) 40178.32 N
Force due to weight of liquid above bottom surface of the cube = (density)*g*h*A

= 1030*9.81*(3/2)(0.640^3) = 3973.2 N
(b) 45475.92 N
Weight of the cube = 457*9.81 = 4483.17 N
(c) T = 4483.17 + 40178.32 - 45475.92 = -814.43 N
(d) 1030*9.81*(0.640)^3 = 2648.78 N

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