{"id":2245,"date":"2018-04-29T04:30:09","date_gmt":"2018-04-28T20:30:09","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=2245"},"modified":"2023-08-08T14:03:33","modified_gmt":"2023-08-08T14:03:33","slug":"center-of-gravity-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/center-of-gravity-problems-and-solutions.htm","title":{"rendered":"Center of gravity \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Center of gravity \u2013 problems and solutions<\/span><\/p>\n

1. Determine the coordinate of the center of gravity<\/a> of the object as shown in the figure below.<\/span><\/p>\n

Solution :\"Center<\/span><\/p>\n

Divide the object into three parts.<\/span><\/p>\n

Area of part 1 (A1<\/sub>) = (2)(6) = 12 cm2<\/sup><\/span><\/p>\n

The center point lies on the x axis (x1<\/sub>) = 1\/2 (2) = 1 cm<\/span><\/p>\n

The center point lies on the y axis (y1<\/sub>) = 1\/2 (6) = 3 cm<\/span><\/p>\n

Area of part 2 (A2<\/sub>) = (4)(2) = 8 cm2<\/sup><\/span><\/p>\n

The center point lies on the x axis (x2<\/sub>) = 2 + (1\/2)(4) = 2 + 2 = 4 cm<\/span><\/p>\n

The center point lies on the y axis (y2<\/sub>) = 2 + (1\/2)(2) = 2 + 1 = 3 cm<\/span><\/p>\n

Area of part 3 (A3<\/sub>) = (2)(6) = 12 <\/span><\/p>\n

The center point lies on the x axis (x3<\/sub>) = 2 + 4 + (1\/2)(2) = 2 + 4 + 1 = 7 cm<\/span><\/p>\n

The center point lies on the y axis (y3<\/sub>) = 1\/2 (6) = 3 cm<\/span><\/p>\n

Coordinate of the center of gravity at x axis :<\/span><\/p>\n

\"Center<\/span><\/p>\n

Coordinate of the center of gravity at y axis :<\/span><\/p>\n

\"Center<\/span><\/p>\n

Coordinate of the center of gravity of the object is at x axis and y axis (x , y) = (4, 3)<\/span><\/p>\n

2. Determine the coordinate of the center of gravity of object , about the x axis.<\/span><\/p>\n

Solutions\"Center<\/span><\/p>\n

Divide the object into three parts, A, B, C, and D.<\/span><\/p>\n

Calculate the area of each part : <\/span><\/p>\n

AA<\/sub> = \u00bd (base)(height) = \u00bd (1.5)(3) = (1.5)(1.5) = 2.25<\/span><\/p>\n

AB<\/sub> = (length)(width) = (4.5-1.5)(1) = (3)(1) = 3<\/span><\/p>\n

AC<\/sub> = \u00bd (base)(height) = \u00bd (6-4.5)(3) = (1.5)(1.5) = 2.25<\/span><\/p>\n

AD <\/sub>= \u00bd (base)(height) = \u00bd (4.5-1.5)(6-3) = \u00bd (3)(3) = (1.5)(3) = 4.5<\/span><\/p>\n

yA<\/sub> = 1\/3 (3) = 1\"Center<\/span><\/p>\n

yB<\/sub> = 1\/2 (1) = 0,5 <\/span><\/p>\n

yC<\/sub> = 1\/3 (3) = 1<\/span><\/p>\n

yD <\/sub>= 3 + (1\/3)(6-3) = 3 + (1\/3)(3) = 3 + 1 = 4<\/span><\/p>\n

Coordinate of the center of gravity at y axis :<\/span><\/p>\n

\"Center<\/span><\/p>\n

Coordinate of the center of gravity about the x axis is 2 cm.<\/span><\/p>\n

3. Determine coordinate of the center of gravity of the object, as shown in figure.<\/span><\/p>\n

Solution :\"Center<\/span><\/p>\n

Divide the object into four parts, A, B, C, and D.<\/span><\/p>\n

Calculate the area of each part.<\/span><\/p>\n

AA<\/sub> = (length)(width) = (4)(3) = 12<\/span><\/p>\n

AB<\/sub> = \u00bd (base)(height) = \u00bd (6-4)(3) = \u00bd (2)(3) = (1)(3) = 3<\/span><\/p>\n

AC<\/sub> = \u00bd (base)(height) = \u00bd (8-6)(3) = \u00bd (2)(3) = (1)(3) = 3<\/span><\/p>\n

AD <\/sub>= (length)(width) = (8)(6-3) = (8)(3) = 24\"Center<\/span><\/p>\n

yA<\/sub> = 1\/2 (3) = 1.5<\/span><\/p>\n

yB<\/sub> = 3 – (1\/3)(3) = 3 \u2013 1 = 2<\/span><\/p>\n

yC<\/sub> = 3 – (1\/3)(3) = 3 \u2013 1 = 2<\/span><\/p>\n

yD <\/sub>= 3 + (1\/2)(6-3) = 3 + (1\/2)(3) = 3 + 1.5 = 4.5<\/span><\/p>\n

xA<\/sub> = 1\/2 (4) = 2<\/span><\/p>\n

xB<\/sub> = 4 + (1\/2)(6-4) = 4 + (1\/2)(2) = 4 + 1 = 5<\/span><\/p>\n

xC<\/sub> = 6 + (1\/2)(8-6) = 6 + (1\/2)(2) = 6 + 1 = 7<\/span><\/p>\n

xD<\/sub> = 1\/2 (8) = 4<\/span><\/p>\n

Coordinate of the center of gravity at the x axis :<\/span><\/p>\n

\"Center<\/span><\/p>\n

Coordinate of the center of gravity at y axis :<\/span><\/p>\n

\"Center<\/span><\/p>\n

    \n
  1. What is the center of gravity (COG) of an object?<\/strong><\/span>\n