1) [Sedimentation Rate and Centrifuge] Proteins and other macromolecules can be separated by size using centrifugation. The idea is to spin a sample of proteins to produce a centripetal acceleration go

that is much higher than gravitational acceleration g. We assume that a protein in the sample can be approximated as a ball of radius R. (a) Start from Newton 2nd law, prove that the terminal speed of the protein follows Vt 2(Pprotein - Psolvent)9cR² 9η where pprotein and psolvent are the densities of the protein and the solvent, n is the solvent viscosity. (b) We would like to separate two similar proteins, having the same density of 1.35g/cm³ but different diameters of 4nm and 5nm, respectively. The two protein species start out mixed together in a thin layer at the top of a 1cm long centrifuge tube. How large should the centripetal acceleration be so that the two proteins are separated before they drift to the end of the tube within about 20s? Assume the solvent as water where density is 1000kgm³ and viscosity is 10-³Nsm-². (Hint: Initially, the proteins are all on the same height, with both centers on the surface level, separation is achieved when their radii no longer overlaps)