Concept explainers
5.137 and 5.138 Locate the centroid of the plane area shown.
Fig. P5.137
Fig. P5.138
The centroid of the plane shown.
Answer to Problem 5.138RP
The centroid of the plane area
Explanation of Solution
Refer Figures 1 and 2.
Figure 1
Figure 2
The plane is considered as three separate sections as in figure 1. Section 1 is a perpendicular triangle, section 2 is a square and section 3 is a quarter of a circle.
Write an expression to calculate the area of section 1.
Here,
Write an expression to calculate the area of section 2.
Here,
Write an expression to calculate the area of section 3.
Here,
Write an expression to calculate the area of the plane.
Here,
Write an expression to calculate the x component of the centroid of the plane.
Here,
There are three sections in the plane. Rewrite equation (V) according to the plane.
Here,
Write an expression to calculate the y component of the centroid of the plane.
Here,
There are two sections in the plane. Rewrite equation (VII) according to the plane.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the centroid of the plane area
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Chapter 5 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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