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
Want to see more full solutions like this?
Chapter 5 Solutions
Vector Mechanics for Engineers: Statics
- The distance of the centroid of an isosceles triangle of base b and height h from its vertex is Select one: 2b/3 2h/3 h/3 b/3arrow_forwardA- Locate the centroid (X only) of the shaded area _>| w B Fig.1.A 'arrow_forwardDetermine the coordinates of the centroid of the trapezoidal area shown.Assume a = 220 mm, b = 365 mm, c = 365 mm.arrow_forward
- Q1: Determine the area A, the centroid y of the parabolic area (Fig 1).arrow_forwardv) What is the distance, d5y, of shape 5’s centroid from axis Yo?w) What is the distance, d2y, of shape 2’s centroid from axis Yo?y) What is the distance, d4y, of shape 4’s centroid from axis Yo?arrow_forward3. The roof of a water tower is composed of eight equal isosceles triangles whose vertices meet at the center of the roof. If the inclined edges measure 4.6 m and the height of the roof is 3 m, determine the surface area of the roof. 4. How many square meters of canvass are required for a conical tent 5.5 m high and 3 m. diameter if 10% of the material is wasted?arrow_forward
- Engineering Mechanics - CentroidsUsing Centroid by Composite Shapes, determine the x- and y-coordinates of the centroid of the shaded area.arrow_forwardKnowing that the distance h has been selected to maximize the distance y from line BB, to the centroid of the shaded area, show that y = 2h/3.arrow_forwardA homogeneous wire is bent into the shape shown. Determine by direct integration the x coordinate of its centroid.arrow_forward
- 1. An architect wants to build a wall with the profile shown. To estimate the effects of wind loads, he must determine the wall’s area and the coordinates of its centroid. Determine the x coordinate of the centroid of the area. 2. An architect wants to build a wall with the profile shown. To estimate the effects of wind loads, he must determine the wall’s area and the coordinates of its centroid. Determine the y coordinate of the centroid of the area.arrow_forwardA vertical trapezoidal gate that is used as an automatic valve is held shut by two springs attached to hinges located along edge AB . Knowing that each spring exerts a couple of magnitude 1470 N.m determine the depth d of water for which the gate will open.arrow_forwardthe centroid of the plane region shown is at c. use the method of composite area to determine the radius (r)arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY