Drag on the Sphere

A sphere of radius \(r\) is abandoned in a chamber of height \(H\) (\(H\) much greater than \(r\)) filled with a fluid with viscosity \(\eta \) and density \(\rho \). According to the Stoke's Law, for small velocities and laminar flow, the frictional force exerted by the viscous fluid in the sphere is given by the expression \( \vec { { F }_{ d } } =-6\pi r\eta \vec { v } \). If \(W\) is the total work done by frictional force and buyoancy until the sphere reaches the height \(h\) in which the resultant force is zero, the correct expression for \(h\) is...

Details and Assumptions:

  • Use \(m\) for sphere's mass and \(g\) for the gravitational acceleration.

  • Assume also that the time elapsed is infinitely long, so that the sphere's velocity actually reaches the terminal velocity.

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