According to Archimedes' principle, the buoyancy force acting on an object that is partially immersed in a fluid is equal to the weight that is displaced by the portion of the object that is submerged. A spherical float with a mass of m_f=70 kg and a diameter of 90 cm is displaced in the ocean (density is 1030 kg/m3). The height, h, of the portion of the float that is above water can be determined by solving an equation that is displaced by the portion of the float that is submerged (Density)*(V_cap)3Dm_f where, for a sphere of Radius r, the volume of a cap (V_cap) of depth d is given by: V_cap3(1/3)*(pi) *(d*d)*(3*r- d) Write an equation for d and solve it for d using a Newton-Raphson Matlab script. Use relative error control (10A-5) percent.
According to Archimedes' principle, the buoyancy force acting on an object that is partially immersed in a fluid is equal to the weight that is displaced by the portion of the object that is submerged. A spherical float with a mass of m_f=70 kg and a diameter of 90 cm is displaced in the ocean (density is 1030 kg/m3). The height, h, of the portion of the float that is above water can be determined by solving an equation that is displaced by the portion of the float that is submerged (Density)*(V_cap)3Dm_f where, for a sphere of Radius r, the volume of a cap (V_cap) of depth d is given by: V_cap3(1/3)*(pi) *(d*d)*(3*r- d) Write an equation for d and solve it for d using a Newton-Raphson Matlab script. Use relative error control (10A-5) percent.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:According to Archimedes' principle, the buoyancy force acting on an object that is partially
immersed in a fluid is equal to the weight that is displaced by the portion of the object that is
submerged.
A spherical float with a mass of m_f=70 kg and a diameter of 90 cm is displaced in the ocean
(density is 1030 kg/m3). The height, h, of the portion of the float that is above water can be
determined by solving an equation that is displaced by the portion of the float that is submerged:
(Density)*(V_cap)3Dm_f
where, for a sphere of Radius r, the volume of a cap (V_cap) of depth d is given by:
V_cap3(1/3)*(pi)*(d*d)*(3*r - d)
Write an equation for d and solve it for d using a Newton-Raphson Matlab script. Use relative error
control (10A-5) percent.
d=
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