Question

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.

Answer 1

1.07804 m

Step-by-step explanation:

W = Weight of upper body = 458 N

`x_1` = Location of upper body = 1.31 m

W' = Weight of upper legs = 101 N

`x_2` = Location of legs = 0.785 m

W'' = Weight of lower legs = 88.8 N

`x_3` = Location of lower legs = 0.215 m

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

`X=(Wx_1+W'x_2+W''x_3)/(W+W'+W'')\\\Rightarrow X=(458* 1.31+101* 0.785+88.8* 0.215)/(458+101+88.8)\\\Rightarrow X=1.07804\ m`

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