In the figure below, a cube of edge length L = 0.700 m and mass 510 kg is suspen
ID: 1906967 • Letter: I
Question
In the figure below, a cube of edge length L = 0.700 m and mass 510 kg is suspended by a rope in an open tank of liquid of density 1030 kg/m3. (a) Find Ftop, 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. N (b) Find Fbottom, the magnitude of the total upward force on the bottom of the cube. N (c) Find T, the tension in the rope. N (d) Calculate Fbu, the magnitude of the buoyant force on the cube using Archimedes' principle. N What relation exists among all these quantities? (Select all that apply.) Fbu = Ftop - Fbottom Fbu = Fbottom - Ftop Fbu = T - m Fbu = m - T Fbu = Fbottom + T
Explanation / Answer
1 atm = 101325 Pa
a) Pressure on top surface = P_top = P_atm + gh = 101325 + 1030*9.81*(0.7/2) = 104861 Pa
Force on top = P_top*area = 104861 *(0.7*0.7) = 51382 N
b) Pressure on bottom surface = P_bottom = P_atm + gh = 101325 + 1030*9.81*(0.7/2 + 0.7) = 111934 Pa
Force on bottom = P_bottom*area = 111934 *(0.7*0.7) = 54847.8 N
c) T = mg - (F_bottom - F_top) = 510*9.81 - (54847.8 - 51382) = 1537.4 N
d) Fbu = Vg = 1030*(0.7*0.7*0.7)*9.81 = 3465.8 N
e) We can verify that,
Fbu = Fbottom - Ftop
Fbu = m - T