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Shafts ab and ce are support by pillow bearing blocks as shown. Compute the angle of twist at point a. Report your answer in degrees to two decimal places. 35 in 12. X e 5 in-k bearing 25 in d bearing 30 in b bearing bearing 2 in-k A a gear c: gear b: shaft ab: shaft ce: all shafts: radius 2.0 in radius= 5.0 in radius = 0.5 in radius - 0.7 in = G= 12000 ksi

Shafts ab and ce are support by pillow bearing blocks as shown. Compute the angle of twist at point a. Report your answer in degrees to two decimal places. 35 in 12. X e 5 in-k bearing 25 in d bearing 30 in b bearing bearing 2 in-k A a gear c: gear b: shaft ab: shaft ce: all shafts: radius 2.0 in radius= 5.0 in radius = 0.5 in radius - 0.7 in = G= 12000 ksi

Elements Of Electromagnetics
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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### Problem Statement: Shafts \(ab\) and \(ce\) are supported by pillow bearing blocks as shown. Compute the angle of twist at point \(a\). Report your answer in degrees to two decimal places. ### Diagram Explanation: - **Layout and Measurements:** - Shaft \(ab\) is on the right side with a length of 35 inches. - Shaft \(ce\) is on the left side composed of two segments: - Segment \(cd\) with a length of 30 inches. - Segment \(de\) with a length of 25 inches. - **Torque:** - A torque of 2 in-k (inch-kilopounds) is applied at the right end of shaft \(ab\). - A torque of 5 in-k is applied between the bearings on shaft \(ce\). - **Bearings:** - Shaft \(ab\) is supported by two bearings between points \(b\) and \(c\). - Shaft \(ce\) is supported by two bearings between points \(d\) and \(e\). - **Gears:** - Gear \(c\) has a radius of 2.0 inches. - Gear \(b\) has a radius of 5.0 inches. ### Shaft Specifications: - **Shaft \(ab\):** Radius = 0.5 inches. - **Shaft \(ce\):** Radius = 0.7 inches. ### Material Properties: - **All Shafts:** Shear Modulus \(G = 12000\) ksi (kilo-pounds per square inch). The task is to calculate the angle of twist at point \(a\) and express it in degrees, accurate to two decimal places.
Transcribed Image Text:### Problem Statement: Shafts \(ab\) and \(ce\) are supported by pillow bearing blocks as shown. Compute the angle of twist at point \(a\). Report your answer in degrees to two decimal places. ### Diagram Explanation: - **Layout and Measurements:** - Shaft \(ab\) is on the right side with a length of 35 inches. - Shaft \(ce\) is on the left side composed of two segments: - Segment \(cd\) with a length of 30 inches. - Segment \(de\) with a length of 25 inches. - **Torque:** - A torque of 2 in-k (inch-kilopounds) is applied at the right end of shaft \(ab\). - A torque of 5 in-k is applied between the bearings on shaft \(ce\). - **Bearings:** - Shaft \(ab\) is supported by two bearings between points \(b\) and \(c\). - Shaft \(ce\) is supported by two bearings between points \(d\) and \(e\). - **Gears:** - Gear \(c\) has a radius of 2.0 inches. - Gear \(b\) has a radius of 5.0 inches. ### Shaft Specifications: - **Shaft \(ab\):** Radius = 0.5 inches. - **Shaft \(ce\):** Radius = 0.7 inches. ### Material Properties: - **All Shafts:** Shear Modulus \(G = 12000\) ksi (kilo-pounds per square inch). The task is to calculate the angle of twist at point \(a\) and express it in degrees, accurate to two decimal places.
Expert Solution
Step 1: Given

We must apply the relation shown below to get the angle of twist at point a:

T over J equals final sigma over r equals fraction numerator G theta over denominator l end fraction

where,

T = torque acting at that point

J = the polar moment of inertia of the shaft.

r = the radius of the shaft.

G = the modulus of rigidity of the shaft.

l = the shaft length.

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