In one form of plethysmograph (a device for measuring

Chapter 17, Problem 17.29

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In one form of plethysmograph (a device for measuring volume), a rubber capillary tube with an inside diameter of 1.00mm is lled with mercury at 20C. The resistance of the mercury is measured with the aid of electrodes sealed into the ends of the tube. If 100.00cm of the tube is wound in a spiral around a patients upper arm, the blood ow during a heartbeat causes the arm to expand, stretching the tube to a length of 100.04cm. From this observation, and assuming cylindrical symmetry, you can nd the change in volume of the arm, which gives an indication of blood ow. (a) Calculate the resistance of the mercury. (b) Calculate the fractional change in resistance during the heartbeat. [Hint: The fraction by which the cross-sectional area of the mercury thread decreases is the fraction by which the length increases, since the volume of mercury is constant.] Take