An aluminium sphere has a radius of r = 0.2 cm, is dropped in a glass cylinder filled with glycerine. The velocity of the sphere as a function of time, v(t) can be modelled by the following equation: v(t) = V(Pal-Pgl) tanh k V(Pal-Pgi)gk VPal where V, is the volume of the sphere, g = 9.81 m/s² is the gravitational acceleration, k = 0.0018 is a constant, Pal = 2700 kg/m³ is the density of aluminium and Pgl = 1260 kg/m³ is the density of and glycerine respectively. Determine the velocity of the sphere for time, t = 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, and 0.35 s. Solve the above problem through the following steps (1) Figure: Aluminium sphere, dropped into a cylinder filled with glycerine. a) the program first determines the volume of the aluminium sphere, V which is calculated through the following equation: 4 V = πr by using the information of the radius (r = 0.2 cm). Note: be VERY CAREFUL of SI units, the radius r, is in centimetre, cm whereas the other constants contain a standard SI unit of meter, m. You will have to convert the radius from cm to m when calculating the volume of the sphere. c) next, the velocity of the aluminium sphere is calculated by the equation 1:
An aluminium sphere has a radius of r = 0.2 cm, is dropped in a glass cylinder filled with glycerine. The velocity of the sphere as a function of time, v(t) can be modelled by the following equation: v(t) = V(Pal-Pgl) tanh k V(Pal-Pgi)gk VPal where V, is the volume of the sphere, g = 9.81 m/s² is the gravitational acceleration, k = 0.0018 is a constant, Pal = 2700 kg/m³ is the density of aluminium and Pgl = 1260 kg/m³ is the density of and glycerine respectively. Determine the velocity of the sphere for time, t = 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, and 0.35 s. Solve the above problem through the following steps (1) Figure: Aluminium sphere, dropped into a cylinder filled with glycerine. a) the program first determines the volume of the aluminium sphere, V which is calculated through the following equation: 4 V = πr by using the information of the radius (r = 0.2 cm). Note: be VERY CAREFUL of SI units, the radius r, is in centimetre, cm whereas the other constants contain a standard SI unit of meter, m. You will have to convert the radius from cm to m when calculating the volume of the sphere. c) next, the velocity of the aluminium sphere is calculated by the equation 1:
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:An aluminium sphere has a radius of r = 0.2 cm, is dropped in a glass cylinder filled with glycerine. The velocity
of the sphere as a function of time, v(t) can be modelled by the following equation:
v(t) =
V(Pal-Pgl) tanh
k
V(Pal-Pat)gk
VPal
where V, is the volume of the sphere, g = 9.81 m/s² is the gravitational acceleration, k = 0.0018 is a constant,
Pal = 2700 kg/m³ is the density of aluminium and Pgl = 1260 kg/m³ is the density of and glycerine
respectively. Determine the velocity of the sphere for time, t = 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, and 0.35 s.
Solve the above problem through the following steps
(1)
Figure: Aluminium sphere, dropped into a cylinder filled with glycerine.
4
V ==
a) the program first determines the volume of the aluminium sphere, V which is calculated through the
following equation:
by using the information of the radius (r = 0.2 cm). Note: be VERY CAREFUL of SI units, the radius r, is in
centimetre, cm whereas the other constants contain a standard SI unit of meter, m. You will have to
convert the radius from cm to m when calculating the volume of the sphere.
c) next, the velocity of the aluminium sphere is calculated by the equation 1:
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