Solved: Determine the location (x, y) of the centroid C of

Chapter 9, Problem 9-65

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QUESTION:

Determine the location \((\bar{x}, \bar{y})\) of the centroid C of the area.

Questions & Answers

QUESTION:

Determine the location \((\bar{x}, \bar{y})\) of the centroid C of the area.

ANSWER:

Step 1 of 4

In this problem we need to find out the  centroid  of the area shown.

Step  2 of 4

We can imagine this area as a superposition of square of sides 3 in. with a positive area and triangle with sides 1.5 in. and quarter circle with radius 1.5 in. both with negative areas.

This way we get our original body but composed of simpler parts.

We  marked these parts with red numbers in picture below.

Also we need to find centroids of each part. Centroid of a square is in the middle of it but for the triangle we need to go back to example 9.3. to find that centroid of triangle is located 1/3 of its height above its base (this works for every every side of the triangle and for every triangle). Finally for the quarter circle we can look at the example 9.4 to get that its centroid is  from its center. We  marked centroids of each part with red dot in the picture below.

Step  3 of 4

In the table below I put everything we need to calculate

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