Question

a person is standing on a level floor. his head, upper torso, arms, and hands together weigh 481 n and have a center of gravity that is 1.34 m above the floor. his upper legs weigh 145 n and have a center of gravity that is 0.720 m above the floor. finally, his lower legs and feet together weigh 90.5 n and have a center of gravity that is 0.224 m above the floor. relative to the floor, find the location of the center of gravity for the entire body.

Explanation:

Step1: Calculate the total weight

The total weight \(W_{total}\) is the sum of the weights of all parts.
\(W_{total}=481 + 145+90.5=716.5\space N\)

Step2: Calculate the weighted - sum of the heights

Let \(y_1 = 1.34\space m\) (height of head, upper torso, arms, and hands), \(y_2 = 0.720\space m\) (height of upper legs), \(y_3=0.224\space m\) (height of lower legs and feet).
The weighted - sum \(S\) is \(S = 481\times1.34+145\times0.720 + 90.5\times0.224\)

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Step3: Calculate the center of gravity \(y_{cg}\)

Using the formula \(y_{cg}=\frac{S}{W_{total}}\), substitute \(S = 769.212\) and \(W_{total}=716.5\)
\(y_{cg}=\frac{769.212}{716.5}\approx1.07\space m\)

Answer:

\(1.07\space m\)