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