Consider two concentric cylinders with a newtonian liquid of constant density, r, and constant dynamic viscosity, µ, contained between them. the outer pipe, with radius, ro, is fixed while the inner pipe, with radius, ri, and mass per unit length, m, falls under the action of gravity at a constant speed. there is no pressure gradient within flow and no swirl velocity (i. e., tangential velocity) component. determine the vertical speed, v, of the inner cylinder as a function of the following (subset of) parameters: g, ro, ri, m, r, and µ.

An electron and a proton have the same kinetic energy upon entering a region of constant magnetic field and their velocity vectors are perpendicular to the magnetic field. suppose the magnetic field is strong enough to allow the particles to circle in the field. note: you'll need to look up the masses for an electron and proton. 1) what is the ratio of the radii of their circular paths rp/re?

When does your body conduct current more readily?

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)