Problem 11 {Centrifuge} Consider a cell with a mass of 5 x 10'\" kg which is in a test tube C-ntrm -'|'oo Vim filled with blood plasma rotating in a centrifuge as shown. The cell ll. v T \"T _ has a radius of 5 pm and a volume of 4 x 10\"? m3. The density of 5'1 1 *a the blood plasma is 1100 l-tgf'n'ia'3 its viscosity is 0.004 Pa - s, and Hi?\" _ ,. if the drag force on the blood cell as it drifts to the bottom is viscous. ,' \\ The centrifuge is rotating fast enough that the centripetal El {In acceleration is much greater than the acceleration due to gravity \\. I Com, DI lcl >> |g'|, so ignore the force of gravity in this problem. - WHO" A. If the test tube the cell is in has a length of 3 cm. what terminal speed does the blood cell need to drift to the bottom in a time interval of 15 3? Give your answer in refs. B. At this terminal speed, what is the magnitude of the drag forte an the blood cell? Give your answer in units of piconewtons {1 pN = 10-12 N}. D. Use the equation from the previous part to find the magnitude of the centripetal acceleration hi} |. Give your answer in 111152. Hint: The centripetal force has magnitude IF'CI = mlcl, and the buoyantforce has magnitude F3 = prVd Ificl in this situation. E. What frequency does the centrifuge need to rotate at in order to provide this centripetal acceleration to the blood cell, given that the blood cell is 12 cm from the center of the rotation of the centrifuge. Give your answer in rpm