In the figure, a cube of edge length L = 0.826 m and mass 944 kg is suspended by

Question

In the figure, a cube of edge length L = 0.826 m and mass 944 kg is suspended by a rope in an open tank of liquid of density 1.03E+3 kg/m3. 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 Archimedes' principle. (a) Number Units (b) Number Units (c) Number Units (d) Number Units

Explanation / Answer

a)F(top) = P A

F(top) = 1.013 x 10^5 x (0.826)^2 = 6.9 x 10^4 N

Hence, F(top) = 6.9 x 10^5 N

b)F(bot) = P x A

P = Patm + h rho g

P = 1.013 x 10^5 + 0.826 x 1030 x 9.8 = 1.1 x 10^5 Pa

F = 1.1 x 10^5 x 0.826^2 = 7.5 x 10^4 N

Hence, F(botm) = 7.5 x 10^4 N

c)T = Mg - (F(bot) - F(top))

T = 944 x 9.8 - 7.5 x 10^4 + 6.9 x 10^4 = 3251.2 N

Hence, T = 3251.2 N

d)Fb = rho g V

Fb = 1030 x 9.8 x 0.826^3 = 5688 N

Hence, F = 5688 N

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