as... WorldEnergyZ ll. 3 c at: Em i e i D =3 - i 2 g E LL} 0 Stiffness 5 Food scientists have created a new oil. At room temperature, the oil is a liquid. As the oil gets colder, however, it stil'l'ens (thickens) into a sticky gel. To explore the puoperties ol' the oil, the scientists ll a container with the oil to a height D, as shown in the gure above on the left. They drop a small steel ball of mass M from rest at the top of the oil. Using video to capttu'e the hall's motion, the scientists calculate Em , the mechanical energy lost by the ball-Earth system from the time the ball enters the oil to the time just before the hall strikes the bottom of the container. The scientists also dene the \"stiffness\" S ofthe oil as a quantity proportional to the force required to move a rod through the oil at a standard constant speed. The scientists calculate E1051 and S at several different temperatures. ranging from room temperature to the lamest temperature at which the ball still falls through the oil. The graph abmre on the right shows El\". as a function ol'S for the calculated data points and a best-t curve. a. Give a physical reason why the curve in the graph would not reach the vertical (Elm) axis even if the scientists had taken data over a broader range of temperatures. b. As 3 increases. Em, approaches a maximum value labeled Em on the graph above. Write an equation for Em in terms of M. D. and physical constants. as appropriate. Justify your answer. c. One of the scientists, in trying to represent the relationship between the oil stiffness and the mechanical energy lost. writes down the equation 2 Elm = ('53. where t'.' is a constant with appropriate units. Another scientist points out that this equation cannot be correct. Give two reasons why the equation cannot be correct. d. Further attempting to model the ball's motion, the scientists write the following equation for the time t the ball takes to fall through the oil: r= Z25 , where}. is a constant with appropriate units. Is this equation plausiblein other words, does it make physical sense? Plausible Not plausible Briefly explain your reasoning. e. ink is the change in kinetic energy of the ball between the time it is released from rest and the time just before the ball strikes the bottom ol'the container. On the axes below. sketch AK as a function of S, the oil stifiess. AP Physics I Page 9 of 13