A sphere of lead of radius 1.5 mm falls at a constant velocity vertically through water of a viscosity 1.0×10−3 Nsm−2 .
a. - a Draw a free-body force diagram of the sphere showing the forces acting on the sphere.
b. - b By equating the weight of the sphere with its buoyancy force and its drag force, show that the terminal velocity of the sphere is given by the expression:Vterminal=9η2r2g(ρlead−ρwater),where ρlead is the density of lead and ρwater is the density of the fluid through which it is falling.
c. - c Given that the density of lead is 1.14×104 kgm−3 , calculate the speed at which the sphere is falling. ( g=9.81 Nkg−1 )
d. - d In practice, such a sphere falling through water falls with a terminal velocity that is smaller than the value that Stokes' law predicts. Suggest a reason why this is.
e. - e If the same sphere were to fall through water of a higher temperature, state what would happen to the terminal velocity of the sphere and suggest a reason to support your statement.