sol1 - Massachusetts Institute of Technology - Physics...

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Massachusetts Institute of Technology - Physics Department Physics - 8.01 Assignment #1 Fall 1999 SOLUTIONS by David Pooley — dave@mit.edu Problem 1.1 ( Estimates and Uncertainties – Ohanian Question 1.1 ) For the frst two objects, I estimated the error by using hal± the smallest division on my wooden ruler, 0.5 mm. For the last two objects, I used a metal tape measure which can expand and contract with changing temperature, just as the wooden ruler can with changing humidity. For large distances, such as a desk, it can produce a noticeable error, which I estimated at ± 2 mm. Object Estimate by Eye Measured Value Comments Mug (height) 22 cm 15.75 ± 0.05 cm I didn’t start o² too hot CD Case 15 cm 14.20 ± 0.05 cm a bit better Desk 1.6 m 1.524 ± 0.002 m not bad ±or something so big Ruler 30.5 cm 30.48 ± 0.05 cm I am the greatest! Problem 1.2 ( Fundamental Units – Ohanian Question 1.14 ) As Ohanian says, “position, time, and mass give a complete description o± the behavior and the attributes o± an ideal particle.” There±ore, we must have units o± each o± these ([L], [T], and [M]) in some combination in any system o± units that we use. I± we take length, mass, and density as our ±undamental units, we have [length] [L] , [mass] [M] , [density] [M] [L] 3 . As you can see, we have no units o± time [T] so we cannot take these as the three ±undamental units. I±, however, we take length, mass, and speed, we have [length] [L] , [mass] [M] , [speed] [L] [T] . Here, we have all the necessary units, and this is a valid choice ±or the three ±undamental units. It is important to remember that we must be able to “separate” the ±undamental units ±rom each other. For example, mass and speed alone contain all the necessary units but there would be no way to separate [L] ±rom [T] with just these two. By having length, mass, and speed, we can extract each ±undamental unit on its own (±or example, by dividing length by speed to get [T]). Problem 1.3 ( Thickness of a Sheet of Paper ) a) Thickness = 10.0 mm b) Absolute uncertainty = ± 0 . 5mm c) Relative uncertainty = absolute uncertainty measurement = 0 . 10 . 0mm = 5% d) There’s 85 pages, so the thickness o± one page is 10 . 0 ± 0 . 85 = 118 ± 6 μ m . e) Absolute uncertainty = 6 μ m 1
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f) The relative uncertainty is unchanged – 5% . g) Diferent students will apply diferent amounts oF pressure when measuring the thickness. Another Factor is the humidity oF the room in which the measurement is done, as this will afect the thickness oF the paper. Also, there is a possibility that the paper is slightly diferent From book to book. Problem 1.4 ( Relative Uncertainties ) The relative uncertainty is the absolute uncertainty divided by the value oF the measure- ment. Let’s pick the antelope as our bone. It has a measured thickness oF 18.3 mm with an uncertainty oF 1.0 mm; thereFore, its relative uncertainty is 1 .
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sol1 - Massachusetts Institute of Technology - Physics...

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