Chapter 14, Problem 032 In the figure, a cube of edge length L = 0.486 m and mas
ID: 1564897 • Letter: C
Question
Chapter 14, Problem 032 In the figure, a cube of edge length L = 0.486 m and mass 868 kg is suspended by a rope in an open tank of liquid of density 1.02E+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 Archimede's principle.
Chapter 14, Problem 032 In the figure, a cube of edge length L 0.486 m and mass 868 kg is suspended by a rope in an open tank of liquid of density 1.02E +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 Archimede's principle. (a) Number Units (b) Number Units (c) Number Units (d) Number Units click if you would like to show Work for this question Open Show WorkExplanation / Answer
1.0atm = 101 325 pascals = 101 325 N/m^2
I take it the top surface of the cube is L/2 below the surface (or is it above?)
Area of a face = 0.468^2 = 0.219024 m^2
Force due to air pressure = pA = 0.219024*101 325 = 22192.6068 N
Force due to weight of liquid above cube = (density)*g*h*A = 1020*9.81*(1/2)(0.468^3) = 512.833
(a) 22701 N (22705.43)
Force due to weight of liquid above bottom surface of the cube = (density)*g*h*A = 1020*9.81*(3/2)(0.468^3) = 1538.5017
(b) 23734 N (23731.1085)
Weight of the cube = 868*9.81 = 8515.08 N
(c) T = 8515.08+ 22705.43 – 23731.1085 = 7489.4015 N
(d) 1020*9.81*(0.468)^3 = 1025.66 N
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