Given the 9 deformed elliptical pebbles (i=1-9) in Figure 12.33 (below), estimate the orientation and shape of the strain ellipse. Instructions: Draw the long axis (La) and short axis (Sa) of each pebble. Determine the final shape ratio (R;) for each pebble (Note: Rf = (La)/(Sa). Find the orientation of the long axis of each pebble (0';) with respect to the lower, long edge of Figure 12.33 (this is the reference line!). NOTE: The La and Sa of pebble 1 is already done for you!. The long axis is extended to interest the lower edge of the image to define the acute angle 0', .You do the La and Sa for other ellipses!

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
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ChapterP: Preliminary Concepts
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Given the 9 deformed elliptical pebbles (i=1-9) in Figure 12.33 (below), estimate the orientation and shape of the
strain ellipse.
Instructions:
Draw the long axis (La) and short axis (Sa) of each pebble. Determine the final shape ratio (R;) for each pebble
(Note: Rf = (La)/(Sa).
Find the orientation of the long axis of each pebble (0';) with respect to the lower, long edge of Figure 12.33 (this is
the reference line!).
NOTE: The La and Sa of pebble 1 is already done for you!. The long axis is extended to interest the lower edge of
the image to define the acute angle 0', You do the La and Sa for other ellipses!
3
2
4
5
9
8
Transcribed Image Text:Given the 9 deformed elliptical pebbles (i=1-9) in Figure 12.33 (below), estimate the orientation and shape of the strain ellipse. Instructions: Draw the long axis (La) and short axis (Sa) of each pebble. Determine the final shape ratio (R;) for each pebble (Note: Rf = (La)/(Sa). Find the orientation of the long axis of each pebble (0';) with respect to the lower, long edge of Figure 12.33 (this is the reference line!). NOTE: The La and Sa of pebble 1 is already done for you!. The long axis is extended to interest the lower edge of the image to define the acute angle 0', You do the La and Sa for other ellipses! 3 2 4 5 9 8
What is the angle (e'), measured from the long edge (reference line), for pebble 1?
46
86
20
64
26
Transcribed Image Text:What is the angle (e'), measured from the long edge (reference line), for pebble 1? 46 86 20 64 26
Expert Solution
Step 1: Orientation of line AB according to its angle made with reference line, x-axis

In the figure below:

The orientation of the line AB  (after rotation) is shown in terms of angle θ = α, β, γ made by rotated line AB in counter clockwise direction w.r.t to the reference line i.e. positive x-axis. 

Point A is a origin or a point of rotation. 

 

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