Centroids - Composite Area Method
Conceptual Questions - Centroid of a Single Area
[br]How would you expect the location of the x-coordinate, x̄ of the centroid of a rectangle to change if its height is doubled while the width remains the same?
How would you expect the location of the y-coordinate, ȳ of the centroid of a rectangle to change if its height is doubled while the width remains the same?
How would you expect the location of the x-coordinate, x̄ of the centroid of a rectangle to change if its width is doubled while the height remains the same?
How would you expect the location of the y-coordinate, ȳ of the centroid of a rectangle to change if its width is doubled while the height remains the same?
If the rectangle is changed to a trapezoid, how would you expect the location of the centroid to change?
Centroid of a Composite Body
Use the image below to answer the following questions.
The above trapezoidal composite body can be broken into a rectangle (shape 1) and triangle (shape 2).[br][br]If the above units are in mm, use the above figure and coordinate system to answer the following questions.[br][br]What is the x-coordinate of the centroid, x̄[sub]1 [/sub]of the rectangle?
What is the y-coordinate of the centroid, ȳ[sub]1 [/sub]of the rectangle?
The correct expression for the product A[sub]1[/sub] x̄[sub]1[/sub] is most nearly...
The correct expression for the product A[sub]1[/sub] ȳ[sub]1[/sub] is most nearly...
The x-coordinate of the centroid, x̄[sub]2 [/sub]of the triangle is most nearly...
The y-coordinate of the centroid, ȳ[sub]2 [/sub]of the triangle is most nearly...
The correct expression for the product A[sub]2[/sub] x̄[sub]2[/sub] is most nearly...
The correct expression for the product A[sub]2[/sub] ȳ[sub]2[/sub] is most nearly...
The location of the centroid of the trapezoid (x̄, ȳ) is most nearly...
If the width of the rectangle were doubled while the triangle remained unchanged, which coordinate of the centroid x̄ or ȳ would you expect to increase by a greater amount?
Use the interactive Figure to Observe Changes in the Centroid of the Composite Body
Click and drag the corners of each individual shape to change its location, size, and area. [br][br]Note the changes in each shapes individual area [i]A[sub]i [/sub][/i]and centroid location (x̄[sub]i[/sub], ȳ[sub]i[/sub]) in the spreadsheet. Observe how the coordinates of the centroid of the composite body (x̄, ȳ) change as a result. [br][br]The centroid of each individual shape and the composite body can be toggled on and off with the check boxes in the top left corner.
How would you anticipate the location of the x-coordinate, x̄ of the centroid of the composite shape would change if the area of shape 3 were greatly increased while the others remained the same?
How would you anticipate the location of the y-coordinate, ȳ of the centroid of the composite shape would change if the area of shape 3 were greatly increased while the others remained the same?