University of Cape Town Department of Physics PHY1023H Principles of Physics June Class Test 4 June 2018 Section B: Question 1 The 'viscosity' of a liquid is a measure of how 'thick' or syrup-like the liquid is. If a small metal ball is dropped in a liquid, the ball will fall slower if the viscosity is high. If a ball of radius r and density p5 falls with speed v in a liquid of density p,, the coefcient of viscosity :7 is given by: 2 gr2 77 = 9,, (p, - 9;) (A) A student, Sisipho, does an experiment to nd the coefcient of viscosity for cooking oil. She drops different size steel balls into the oil, and takes measurements to nd the speed at which each ball falls in the oil. a) If a ball of radius R falls at speed V, what speed should Sisipho nd for a ball of radius 2R? (2) b) Sisipho plots a graph of v versus r. Sketch the shape of the graph which Sisipho obtains, if equation (A) above is valid in this experimental situation. (2) c) What would you advise Sisipho to plot in order to get a straight-line graph? (1) d) Suppose Sisipho follows your advice in (c) and obtains a straight-line graph. She nds that the gradient is m = 1.8 x 104 m'ls'l, using oil of density 969 kg m'3 and steel balls of density 7 950 kg m'3. Use this information to find 77 for the oil. (You are not required to calculate any uncertainties but you should work out the unit for 77.) (3) e) Name the controlled variable in Sisipho's experiment. (1)