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A person is standing on a level floor. His head, upper torso, arms, and hands together weigh 458 N and have a center of gravity that is 1.31 m above the floor. His upper legs weigh 101 N and have a center of gravity that is 0.785 m above the floor. Finally, his lower legs and feet together weigh 88.8 N and have a center of gravity that is 0.215 m above the floor. Relative to the floor, find the location of the center of gravity for the entire body.

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Answer:

1.07804 m

Explanation:

W = Weight of upper body = 458 N

[tex]x_1[/tex] = Location of upper body = 1.31 m

W' = Weight of upper legs = 101 N

[tex]x_2[/tex] = Location of legs = 0.785 m

W'' = Weight of lower legs = 88.8 N

[tex]x_3[/tex] = Location of lower legs = 0.215 m

The center of gravity is the concentrated point of a body. It is given by

[tex]X=\frac{Wx_1+W'x_2+W''x_3}{W+W'+W''}\\\Rightarrow X=\frac{458\times 1.31+101\times 0.785+88.8\times 0.215}{458+101+88.8}\\\Rightarrow X=1.07804\ m[/tex]

The center of gravity of the person is 1.07804 m from the floor.

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