Homework 4 Solution

Homework 4 Solution - MEEN 260 Introduction to Engineering...

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MEEN 260 Introduction to Engineering Experimentation Homework 4: Measurement Uncertainty Assigned: Thursday, 12 Feb. 2009 Due: Thursday, 19 Feb. 2009, 9:00am Homework Problems: Problem 1) Given the relationship 3 5 5 y x d = , find an expression of uncertainty d μ as a function of the means ( x and y ) and the uncertainties u x , and u y . Problem 2) A company is considering manufacturing a pipe with a cross-sectional area of 0.64 m 2 . The pipe will have a significant wall thickness. However, due to the manufacturing process, uncertainty affects the inner and outer dimensions. Two shapes are available, a square pipe (with outer side o l and inner side i l ) and a rectangular pipe, (with outer length of o l and inner dimensions of 1 i l and 2 i l ) with the following dimensions and manufacturing tolerances (uncertainties): Square Pipe: o l =1m ± 0.01m and i l =0.8m ± 0.05m Rectangular Pipe: o l =2m ± 0.02m, 1 i l =1.6m ± 0.05m, and 2 i l =0.4m ± 0.1 What is the uncertainty of the cross-sectional area for each of the pipes? Which is the better design? Problem 3) Stiffness of coil springs is defined as k=F/d , where F is an applied force and d is a deflection of the spring. The larger the stiffness, the smaller the deflection for applied force. Table below presents the measured forces and deflections of 11 compression springs. Measurement Deflection, d (mm) Force, F (N) 1 2.3 18 2 1.6 15 3 1.95 15.6 4 2.05 17.2 5 2.22 17.6 6 1.85 16.1 7 1.95 16.3 8 2.07 17.2 9 2.03 17.2 10 1.95 16.6 11 1.99 17.2
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a) Calculate mean and standard deviation of F and d using formula for mean and standard deviation in the lecture note. Don’t use built-in functions in Excel or your calculators; show all work.
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This note was uploaded on 07/28/2010 for the course MEEN 260 taught by Professor Langari during the Fall '08 term at Texas A&M.

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Homework 4 Solution - MEEN 260 Introduction to Engineering...

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