1. Determine the coordinate of the center of gravity of the object as shown in the figure below.
Solution :
Divide the object into three parts.
Area of part 1 (A1) = (2)(6) = 12 cm2
The center point lies on the x axis (x1) = 1/2 (2) = 1 cm
The center point lies on the y axis (y1) = 1/2 (6) = 3 cm
Area of part 2 (A2) = (4)(2) = 8 cm2
The center point lies on the x axis (x2) = 2 + (1/2)(4) = 2 + 2 = 4 cm
The center point lies on the y axis (y2) = 2 + (1/2)(2) = 2 + 1 = 3 cm
Area of part 3 (A3) = (2)(6) = 12
The center point lies on the x axis (x3) = 2 + 4 + (1/2)(2) = 2 + 4 + 1 = 7 cm
The center point lies on the y axis (y3) = 1/2 (6) = 3 cm
Coordinate of the center of gravity at x axis :
Coordinate of the center of gravity at y axis :
Coordinate of the center of gravity of the object is at x axis and y axis (x , y) = (4, 3)
[irp]
2. Determine the coordinate of the center of gravity of object , about the x axis.
Solutions
Divide the object into three parts, A, B, C, and D.
Calculate the area of each part :
AA = ½ (base)(height) = ½ (1.5)(3) = (1.5)(1.5) = 2.25
AB = (length)(width) = (4.5-1.5)(1) = (3)(1) = 3
AC = ½ (base)(height) = ½ (6-4.5)(3) = (1.5)(1.5) = 2.25
AD = ½ (base)(height) = ½ (4.5-1.5)(6-3) = ½ (3)(3) = (1.5)(3) = 4.5
yA = 1/3 (3) = 1
yB = 1/2 (1) = 0,5
yC = 1/3 (3) = 1
yD = 3 + (1/3)(6-3) = 3 + (1/3)(3) = 3 + 1 = 4
Coordinate of the center of gravity at y axis :
Coordinate of the center of gravity about the x axis is 2 cm.
[irp]
3. Determine coordinate of the center of gravity of the object, as shown in figure.
Solution :
Divide the object into four parts, A, B, C, and D.
Calculate the area of each part.
AA = (length)(width) = (4)(3) = 12
AB = ½ (base)(height) = ½ (6-4)(3) = ½ (2)(3) = (1)(3) = 3
AC = ½ (base)(height) = ½ (8-6)(3) = ½ (2)(3) = (1)(3) = 3
AD = (length)(width) = (8)(6-3) = (8)(3) = 24
yA = 1/2 (3) = 1.5
yB = 3 – (1/3)(3) = 3 – 1 = 2
yC = 3 – (1/3)(3) = 3 – 1 = 2
yD = 3 + (1/2)(6-3) = 3 + (1/2)(3) = 3 + 1.5 = 4.5
xA = 1/2 (4) = 2
xB = 4 + (1/2)(6-4) = 4 + (1/2)(2) = 4 + 1 = 5
xC = 6 + (1/2)(8-6) = 6 + (1/2)(2) = 6 + 1 = 7
xD = 1/2 (8) = 4
Coordinate of the center of gravity at the x axis :
Coordinate of the center of gravity at y axis :
[irp]