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Unformatted text preview: Solution to Experimental Question 1 Preliminary: Calculation of Terminal Velocity When the cylinder is moving at its terminal velocity, the resultant of the three forces acting on the cylinder, gravity, viscous drag and buoyant force, is zero. V g- 6 r m v T- V g = 0 where V = 2 r 3 is the volume of a cylinder (whose height is 2 r ). This gives v r = Cr 3- m ( - ) where C = g 3 Experiment Determination of the exponent m Aluminium cylinders of different diameters are dropped into the glycerine. Fall times between specified marks on the measuring cylinder containing the glycerine are recorded for each cylinder. A preliminary experiment should establish that the cylinders have reached their terminal velocity before detailed results are obtained. The measurements are repeated several times for each cylinder and an average fall time is calculated. Table 1 shows a typical set of data. To find the value of m a graph of log(fall time) as a function of log(diameter) is plotted as in figure 1. The slope of the resulting straight line graph is 3function of log(diameter) is plotted as in figure 1....
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