Question

a person is standing on a level floor. his head, upper torso, arms, and hands together weigh 410 n and have a center of gravity that is 1.17 m above the floor. his upper legs weigh 121 n and have a center of gravity that is 0.740 m above the floor. finally, his lower legs and feet together weigh 94.9 n and have a center of gravity that is 0.249 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 \( W_{total}=W_1 + W_2+W_3\), where \(W_1 = 410\space N\), \(W_2=121\space N\), \(W_3 = 94.9\space N\)
\(W_{total}=410 + 121+94.9=625.9\space N\)

Step2: Calculate the weighted - sum of the heights

The formula for the center of gravity \(y_{cm}=\frac{W_1y_1 + W_2y_2+W_3y_3}{W_{total}}\)
Here, \(y_1 = 1.17\space m\), \(y_2=0.740\space m\), \(y_3 = 0.249\space m\)
\(W_1y_1+W_2y_2 + W_3y_3=410\times1.17+121\times0.740 + 94.9\times0.249\)
\(=479.7+89.54+23.6301\)
\(=592.8701\space N\cdot m\)

Step3: Calculate the center of gravity

\(y_{cm}=\frac{592.8701}{625.9}\)
\(y_{cm}\approx0.947\space m\)

Answer:

\(0.947\space m\)