modeling with first order equations
a body falling in a relatively dense fluid, oil for example, is acted on by three forces: a resistive force R, a buoyant force B, and its weight 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 a radius a, the resistive force is given by Stoke's law, R=6pi*μ*a*absolute value of v, where v is the velocity of the body, and μ is the coefficient of viscosity of the surrounding fluid.
1. Find the limiting velocity of a solid sphere of radius a and density p falling freely in a medium of density p' and coefficient of viscosity μ.
2. Millikan studied the motion of tiny droplets of oil falling in an electric field. A field of strength E exerts a force Ee on a droplet with charge e. Assume that E has been adjusted so the droplet is held stationary(v=0) and that w and B are as given above. Find and expression for e. Millikan repeated this experiment many times, and was able to deduce the charge of an electron.