Question

In: Physics

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?

Solutions

Expert Solution


Related Solutions

Alice and Bob bet 50 dollars with each other in a game in which their friend...
Alice and Bob bet 50 dollars with each other in a game in which their friend Charlie tosses a two-sided coin 3 times in a remote location. If Alice correctly predicts the majority face (i.e. the face which occurred the most often in the three tosses), she gets to keep Bob's money as well. Charlie calls them and lets them know that at least 1 heads has occurred.a) Assuming that the coin was fair, what is the probability that the...
Bob has offered Alice the choice between the following two options:
Bob has offered Alice the choice between the following two options:Option A) Receive $10,000 in one year from today OptionB) Receive $500 every year starting one year from todayThe interest rate is fixed at 5%. Alice wants to choose the option with the higher present value. Calculate the present value for each option and determine which option should she choose?
Assume economy with two goods x and y and two people Alice and Bob. The MRSA...
Assume economy with two goods x and y and two people Alice and Bob. The MRSA of Alice is 15. The MRSB of the Bob is 10. (a) Is the current allocation of x and y is efficient? Why yes or why not? (b) Is there a trade that would be voluntary? Explain. Support your answer by graph. (c) Pareto Efficient Allocations, the Contract Curve and the Core. Define these three terms and explain the relationship between them. Use the...
Alice and Bob are portfolio managers from two fund houses. They are both using modern portfolio...
Alice and Bob are portfolio managers from two fund houses. They are both using modern portfolio theory, specifically mean-variance optimisation, to construct their portfolios. The following table shows the weightings of their portfolios: Manager     risk-free asset     Stock A     Stock B     Stock C     Stock D     Stock E     Alice 10% 20% 25% 30% 5% 10% Bob 15% 5% 20% 10% 30% 20% Give three possible reasons why Alice and Bob result in different portfolios.
Two rocks are found that have different ratios R' of 238U to 206Pb: R' = 0.87...
Two rocks are found that have different ratios R' of 238U to 206Pb: R' = 0.87 and 2.1. What are the ages of the two rocks? y (R' = 0.87) y (R' = 2.1)Did they likely have the same origin?
Alice and Bob Ray use cabbages, tomatoes and onions to make two kinds of relish: chow-chow...
Alice and Bob Ray use cabbages, tomatoes and onions to make two kinds of relish: chow-chow and tomato. A jar of Chow-chow contains 8 ounces of cabbage, 3 ounces of tomatoes, and 3 ounces of onions. A jar of tomato relish contains 6 ounces of tomatoes, 6 ounces of cabbage, and 2 ounces of onions. The Rays have 120 ounces of cabbages, 90 ounces of tomatoes and 45 ounces of onions each week. The profit for a jar of chow-chow...
Experiment #2: An experiment run found that the two enantiomers of Isoflurane do not act the...
Experiment #2: An experiment run found that the two enantiomers of Isoflurane do not act the same as anesthetics, in that it took a smaller amount of one to produce the same anesthetic effect as the other. What is a chiral receptor? What roles do chiral receptors play in biological systems? Does the fact that the two enantiomers of Isoflurane do not act the same support or disprove the hypothesis listed above? Explain your answer
In an experiment to measure the wavelength of light using two slits, it is found that...
In an experiment to measure the wavelength of light using two slits, it is found that the interference fringes are too close together to easily count them. To spread out the fringe pattern, one could… A. Increase the slit separation B. Decrease the slit separation C. Increase the distance from the slits to the viewing screen D. Decrease the distance from the slits to the viewing screen E. Both increasing the distance from the slits to the viewing screen and...
Two customers, Bob and Ed, with two types of services: premium (P) and simple (S). Bob’s...
Two customers, Bob and Ed, with two types of services: premium (P) and simple (S). Bob’s willingness to pay for the premium service is given by uB(P) and for the simple service is uB(S). Similarly, for Ed, these values are uE (P) and uE (S), respectively. Suppose these values are given as: uB(P) = 500, uB(S) = 200, uE(P) = 300, uE(S) = 100. The seller of these services is looking to maximize the total payment. 1. If the seller...
Differentiate between two types of nephrons found in kidneys
Differentiate between two types of nephrons found in kidneys
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT