Alice and Bob are re-enacting Cao Chong’s weighing experiment. They found two types of rocks, ~50...

Alice and Bob are re-enacting Cao Chong’s weighing experiment. They found two types of rocks, ~50 kg in weight and ~20 kg in weight, respectively. Now for an elephant that weighs ~1 ton, the measurement could be done with 20 of 50 kg rocks, or 50 of 20 kg rocks.

Alice argues that the first approach gives a more precise result as more rocks will introduce more error. Bob argues that the second approach is better as the error from different rocks tends to cancel out each other.

Calculate the uncertainty of the final result for the two approaches for the following two cases: (A) The absolute measurement uncertainty for each rock is fixed at 0.5 kg. (B) The relative measurement uncertainty for each rock is fixed at 2%. Which of the above two approaches win out for the two cases? (C) Is there a mathematical form of uncertainty-weight relationship for each rock that would lead to equal uncertainty of the final results for the two approaches?

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genius_generous answered 1 year ago

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