5. If someone (perhaps an economist?) were to say to you, cost is not always proportional...

 

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5. If someone (perhaps an economist?) were to say to you, cost is not always proportional to quality, but very high quality is non-linearly proportional to cost, what would or could s/he mean? 6. You meet a cook who is known for his maxims. One day you hear him or her say, the speed with which a pot cooks is inversely proportional to the excellence that comes out. What does that mean? Sketch the idea as a graph. 7. The car manufacturer Hyundai says its 130 consumes 8.0 l/100 km within city driving. Convert this value to mi/gal. Show your work. 8. Define measurement fiducial. Explain how the idea of the fiducial gives rise to a measurement unit. Give an example in real life. 9. Prof. Walter Lewin of MIT is famous for the maxim measurement without uncertainty is meaningless. (A) Explain its meaning and what is so important about the phrase. (B) What, then, makes a measurement meaningful? 10. What is the relationship between Precision, Trueness and Accuracy? 11. Modern digital measurement would have us believe that, in the absence of an explicit statement of error, the uncertainty is ± the last digit. So, if we write a value in scientific notation, in the form a.bcdx10m, that is with four significant digits, the uncertainty would be ± 1x10m-³ (the digit in the "d" position). Only, that is more than a little artificial. Who said errors should be constrained to powers of ten? The short and definitive answer is: it does not need to be. You need to look no farther than the kitchen, in fact! The Nature of Error can have other plans. I personally can reliably measure a length to within ± 1/3 mm, as long as the ruler I use is at least as accurate as all of the millimeter marks (and if my eyes will cooperate). (1) Why would I specify or require that the ruler is accurate to each of its millimeter marks so that I can measure by eye to within ± 1/3 mm? RPM X 1000 6 9 8 5. If someone (perhaps an economist?) were to say to you, cost is not always proportional to quality, but very high quality is non-linearly proportional to cost, what would or could s/he mean? 6. You meet a cook who is known for his maxims. One day you hear him or her say, the speed with which a pot cooks is inversely proportional to the excellence that comes out. What does that mean? Sketch the idea as a graph. 7. The car manufacturer Hyundai says its 130 consumes 8.0 l/100 km within city driving. Convert this value to mi/gal. Show your work. 8. Define measurement fiducial. Explain how the idea of the fiducial gives rise to a measurement unit. Give an example in real life. 9. Prof. Walter Lewin of MIT is famous for the maxim measurement without uncertainty is meaningless. (A) Explain its meaning and what is so important about the phrase. (B) What, then, makes a measurement meaningful? 10. What is the relationship between Precision, Trueness and Accuracy? 11. Modern digital measurement would have us believe that, in the absence of an explicit statement of error, the uncertainty is ± the last digit. So, if we write a value in scientific notation, in the form a.bcdx10m, that is with four significant digits, the uncertainty would be ± 1x10m-³ (the digit in the "d" position). Only, that is more than a little artificial. Who said errors should be constrained to powers of ten? The short and definitive answer is: it does not need to be. You need to look no farther than the kitchen, in fact! The Nature of Error can have other plans. I personally can reliably measure a length to within ± 1/3 mm, as long as the ruler I use is at least as accurate as all of the millimeter marks (and if my eyes will cooperate). (1) Why would I specify or require that the ruler is accurate to each of its millimeter marks so that I can measure by eye to within ± 1/3 mm? RPM X 1000 6 9 8

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