1. You are finding Young's modulus of a sample of wood, using the simply supported and centrally loaded model we discussed in class in Lecture 1. You collect the seven data points below: Load (N) 0.49 0.98 1.47 1.96 2.45 2.94 3.43 Deflection (mm) 0.15 0.38 0.46 0.74 0.78 1.00 1.13 You know the relationship between the two is proportional and linear: d = slope x f where d is deflection and f is the applied load. Using the computer aid of your choice (in class we demonstrated MATLAB's backslash (mldivide) and curve_fit with Python) find the slope of the best fit regression line. NOTE: We know from the physics involved that this line passes through the origin - there is no y- intercept. Set up your calculation in such a way that no intercept is possible. It is not correct to find a regression line with a y-intercept and simply drop the term from the equation. 2. You wish to calculate the density of a marble. You have measured its radius to be 6 ± 0.005 mm and its mass to be 2.9 ± 0.05 g. Equation 1 expresses density as a function of mass and volume; Equation 2 expresses volume as a function of radius. m p=v (1) V = ¼¤r³ Using the propagation of error method discussed in class, find the uncertainty in the calculated value of density. (2)
1. You are finding Young's modulus of a sample of wood, using the simply supported and centrally loaded model we discussed in class in Lecture 1. You collect the seven data points below: Load (N) 0.49 0.98 1.47 1.96 2.45 2.94 3.43 Deflection (mm) 0.15 0.38 0.46 0.74 0.78 1.00 1.13 You know the relationship between the two is proportional and linear: d = slope x f where d is deflection and f is the applied load. Using the computer aid of your choice (in class we demonstrated MATLAB's backslash (mldivide) and curve_fit with Python) find the slope of the best fit regression line. NOTE: We know from the physics involved that this line passes through the origin - there is no y- intercept. Set up your calculation in such a way that no intercept is possible. It is not correct to find a regression line with a y-intercept and simply drop the term from the equation. 2. You wish to calculate the density of a marble. You have measured its radius to be 6 ± 0.005 mm and its mass to be 2.9 ± 0.05 g. Equation 1 expresses density as a function of mass and volume; Equation 2 expresses volume as a function of radius. m p=v (1) V = ¼¤r³ Using the propagation of error method discussed in class, find the uncertainty in the calculated value of density. (2)
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:1. You are finding Young's modulus of a sample of wood, using the simply supported and centrally
loaded model we discussed in class in Lecture 1. You collect the seven data points below:
Load (N)
0.49
0.98
1.47
1.96
2.45
2.94
3.43
Deflection
(mm)
0.15
0.38
0.46
0.74
0.78
1.00
1.13
You know the relationship between the two is proportional and linear:
d = slope x f
where d is deflection and f is the applied load.
Using the computer aid of your choice (in class we demonstrated MATLAB's backslash (mldivide) and
curve_fit with Python) find the slope of the best fit regression line.
NOTE: We know from the physics involved that this line passes through the origin - there is no y-
intercept. Set up your calculation in such a way that no intercept is possible. It is not correct to find a
regression line with a y-intercept and simply drop the term from the equation.
2. You wish to calculate the density of a marble. You have measured its radius to be 6 ± 0.005 mm and
its mass to be 2.9 ± 0.05 g. Equation 1 expresses density as a function of mass and volume; Equation 2
expresses volume as a function of radius.
m
p== //
V = πr³
Using the propagation of error method discussed in class, find the uncertainty in the calculated value
of density.
(1)
(2)
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