Refer to Herman Figure 1.20 for Problems 8 and 9. You can measure the location o

Question

Refer to Herman Figure 1.20 for Problems 8 and 9. You can measure the location of the anatomical center of mass of the body using the arrangement in Fig. 1.20a. The weight (w_1) and location of the mass (x_1) of the balance board are known along with the entire body weight w_2. The location of the body center of mass relative to the pivot point is x_2. The distance from the pivot to the scale is x_3. With the body center of mass to the left of the pivot point there is a measurable force S on the scale (under the head). Show that: x_2 = sx_3 - w_1 x_1/w_2

Explanation / Answer

from figure 1 we can see
from force balance
S = w1 + w2 [ w4 is included in body weight, w2]
from moment balance about the pivot
Sx3 = W2*x2 + w1*x1
so
x2 = (sx3 - w1x1)/W2
so basically, contribution of W4 has to be ignored assuming that effect of w4 is included in the whole bodyu weight w2

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