Homework Help is Here – Start Your Trial Now!
Engineering
Civil Engineering
5. Calculate the centroid of a wire rod bent into the shape of an arc defined by x(y) = 3y² from the origin to point (x,y) = (12,4). Hint: follow the procedure outline in Example 9.1 and SHOW EVERY DETAIL of your work.

5. Calculate the centroid of a wire rod bent into the shape of an arc defined by x(y) = 3y² from the origin to point (x,y) = (12,4). Hint: follow the procedure outline in Example 9.1 and SHOW EVERY DETAIL of your work.

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
5th Edition
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Saeed Moaveni
Chapter7: Length And Length-related Variables In Engineering
Section: Chapter Questions
Problem 42P
See similar textbooks
icon
Related questions
Question
5.) see photos for details
EXAMPLE 9.1 Locate the centroid of the rod bent into the shape of a parabolic arc as shown in Fig. 9-8a. SOLUTION Differential Element. The differential element is shown in Fig. 9-8a. It is located on the curve at the arbitrary point (x, y). Area and Moment Arms. The differential element of length dL can be expressed in terms of the differentials dx and dy, Fig. 9-8b, using the Pythagorean theorem. dL = V V(dx)² + (dy)² Since x = y², then dx/dy= 2y. Therefore, expressing dL in terms of y and dy, we have 302 = y = dL = √(2y)² + 1 dy As shown in Fig. 9-8a, the centroid of the element is located at x = x, y = y. Integrations. Applying Eq. 9-5 and using the integration formula to evaluate the integrals, we get 1 m 1 m [√x dL [" "xV4y² + 1 dy [ "3² √4y² + 1 dy 0 x = 1 m TAL dL 0.6063 1.479 0 dx dy 1 m V V4y² + 1 dy = 0.410 m + 1 dy 1 m fydl flyv fyV4y² + 1 dy dL 1 m dLV4y² + 1 dy √4y² √4y² + 1 dy (6 800X) 0.8484 1.479 = 0.574 m Ans Ans. NOTE: These results for C seem reasonable when they are plotted on Fig. 9-8a. on 01 y = y O (x, y) x = x 1 m- C(x, y) dL (a) = y² dL aldy dx (b) Fig. 9-8 1 m
Transcribed Image Text:EXAMPLE 9.1 Locate the centroid of the rod bent into the shape of a parabolic arc as shown in Fig. 9-8a. SOLUTION Differential Element. The differential element is shown in Fig. 9-8a. It is located on the curve at the arbitrary point (x, y). Area and Moment Arms. The differential element of length dL can be expressed in terms of the differentials dx and dy, Fig. 9-8b, using the Pythagorean theorem. dL = V V(dx)² + (dy)² Since x = y², then dx/dy= 2y. Therefore, expressing dL in terms of y and dy, we have 302 = y = dL = √(2y)² + 1 dy As shown in Fig. 9-8a, the centroid of the element is located at x = x, y = y. Integrations. Applying Eq. 9-5 and using the integration formula to evaluate the integrals, we get 1 m 1 m [√x dL [" "xV4y² + 1 dy [ "3² √4y² + 1 dy 0 x = 1 m TAL dL 0.6063 1.479 0 dx dy 1 m V V4y² + 1 dy = 0.410 m + 1 dy 1 m fydl flyv fyV4y² + 1 dy dL 1 m dLV4y² + 1 dy √4y² √4y² + 1 dy (6 800X) 0.8484 1.479 = 0.574 m Ans Ans. NOTE: These results for C seem reasonable when they are plotted on Fig. 9-8a. on 01 y = y O (x, y) x = x 1 m- C(x, y) dL (a) = y² dL aldy dx (b) Fig. 9-8 1 m
5. Calculate the centroid of a wire rod bent into the shape of an arc defined by x(y) = 3y² from the origin to point (x,y) = (12,4). Hint: follow the procedure outline in Example 9.1 and SHOW EVERY DETAIL of your work.
Transcribed Image Text:5. Calculate the centroid of a wire rod bent into the shape of an arc defined by x(y) = 3y² from the origin to point (x,y) = (12,4). Hint: follow the procedure outline in Example 9.1 and SHOW EVERY DETAIL of your work.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Unit conversion
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Engineering Fundamentals: An Introduction to Engi…
Engineering Fundamentals: An Introduction to Engi…
Civil Engineering
ISBN:
9781305084766
Author:
Saeed Moaveni
Publisher:
Cengage Learning
Structural Analysis
Structural Analysis
Civil Engineering
ISBN:
9781337630931
Author:
KASSIMALI, Aslam.
Publisher:
Cengage,
Fundamentals Of Construction Estimating
Fundamentals Of Construction Estimating
Civil Engineering
ISBN:
9781337399395
Author:
Pratt, David J.
Publisher:
Cengage,
Residential Construction Academy: House Wiring (M…
Residential Construction Academy: House Wiring (M…
Civil Engineering
ISBN:
9781285852225
Author:
Gregory W Fletcher
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS