Problems for Intermediate Methods in Theoretical Physics Edward F. Redish

The floating ball

 In class on Monday we considered the following problem:A graduated cylinder is half-filled with water. A rubber ball is dropped into the water and it floats half-in and half-out of the water as shown. Some oil (shown on the right) is poured in on top of the ball. The oil floats on the water. After the oil is poured in, does the position of the ball get higher, lower, or stay the same? Various students gave a variety of arguments for what would happen. Three of the arguments presented included: It goes down because the oil added on top adds an additional downward force. It goes up because by Archimedes' principle it displaces more fluid. Assuming the ball would sink to the bottom in the oil, it will stay the same since the oil won't hold it up. Give the answer to the problem that you now believe and give a convincing argument in support. In addtion, give arguments that support or is in contradiction to the three arguments listed above, reconciling those arguments with your answer.

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