A person is standing on a level floor. His head, upper torso, arms, and hands to

Question

A person is standing on a level floor. His head, upper torso, arms, and hands together weigh 418 N and have a center of gravity that is 1.11 m above the floor. His upper legs weigh 195 N and have a center of gravity that is 0.731 m above the floor. Finally, his lower legs and feet together weigh 82.7 N and have a center of gravity that is 0.279 m above the floor. Relative to the floor, find the location of the center of gravity for the entire body.

(I'm familiar with the setup but for some reason my numbers aren't right...)

Explanation / Answer

Centre of gravity of a system of bodies is

R =   i (mi * ri) / i mi

   = (mu * ru  + mul * rul   + mll * rll) / (mu + mul+ mll)

   = (g * mu * ru  + g * mul * rul   + g * mll * rll) / (g * mu + g * mul+ g * mll)

= (Wu * ru  + Wul * rul   + Wll * rll) / (Wu + Wul+ Wll)

here W represent weight and r is position vector of c.g. subscript u stands for upper part, ul upper leg and ll lower leg and feet.

R = (418 * 1.11 + 195 * 0.731 + 82.7 * 0.279) / (418 + 195 + 82.7)

= 629.60 / 695.70

= 0.905 m above ground level

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