PhysicsLAB AP Free Response Question
2010 B2

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A large pan is filled to the top with oil of density ro . A plastic cup of mass mc, containing a sample of known mass ms, is placed in the oil so that the cup and sample float, as shown above. The oil that overflows from the pan is collected, and its volume is measured. The procedure is repeated with a variety of samples of different mass, and the pan is refilled each time.
(a) On the dot below that represents the cup-sample system, draw and label the forces (not components) that act on the system when it is floating on the surface of the oil.

 (b) Derive an expression for the overflow volume Vo (the volume of oil that overflows due to the floating system) in terms of r o, ms, mc, and fundamental constants. If you need to draw anything other than what you have shown in part (a) to assist in your solution, use the space below. Do NOT add anything to the figure in part (a).

Assume that the following data are obtained for the overflow volume Vo for several sample masses ms.
(c) Graph the data on the axes below, plotting the overflow volume as a function of sample mass. Place numbers and units on both axes. Draw a straight line that best represents the data.

 (d) Use the slope of the best-fit line to calculate the density of the oil.

 (e) What is the physical significance of the intercept of your line with the vertical axis?

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