Question

A body falling in a relatively dense fluid, oil for example, is acted on by three forces (see Figure 2.3.5): a resistive force R, a buoyant force B, and its weight w due to gravity. The buoyant force is equal to the weight of the fluid displaced by the object. For a slowly moving spherical body of radius a, the resistive force is given by Stokes's law, R = 6*pi*u*a*|v|, where v is the velocity of the body, and u is the coefficient of viscosity of the surrounding fluid.

Show that the equation for the sphere center position on instant t is given by x, knowing that at t=0, the sphere is on x=0 and is at rest.

Mg M T = -(1-){t - (1 - ere')}, t>0, 6 лва 6 тра

Answer 1

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Page- intral anditius apply ग co = (t ca a and 2) in -R Ce ēkt + R - Ret2 to R R2 C = - = R2 o becomes - RG all - kr nilt) = t- k kellel rate of a 4 k Subshhte the na g GAMA Sv m. 7 4) nit) = bota fua hance prooved.