CG OF MULTI-SEGMENT SYSTEMS (IRREGULAR SHAPE) Example One: If we need to locate the CG of the whole leg using the $CG_{thigh}$, $CG_{leg}$ and $CG_{foot}$ we can use the same equations, provided that we pre-calculate the length and mass of each segment, as well as each segment CG. $x_{CG} = \frac{m_1x_1 + m_2x_2 + ... + m_nx_n}{M}$ $y_{CG} = \frac{m_1y_1 + m_2y_2 + ... + m_ny_n}{M}$
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This can be done by adding the masses of the thigh, leg, and foot segments. Show moreā¦
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(I) Calculate the mass $m$ needed in order to suspend the leg shown in Fig. 9-47. Assume the leg (with cast) has a mass of 15.0 kg, and its $_{CG}$ is 35.0 cm from the hip joint; the cord holding the sling is 78.0 cm from the hip joint. FIGURE 9ā47 Problem 2. (Figure can't copy)
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(I) Calculate the mass $m$ needed in order to suspend the leg shown in Fig. 9-47. Assume the leg (with cast) has a mass of 15.0 kg, and its $_{CG}$ is 35.0 cm from the hip joint; the cord holding the sling is 78.0 cm from the hip joint.
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EXAMPLE 3 Find the moments and center of mass of the system of objects that have masses 4, 3, and 6 at the point (-1, 1), (2, -1), and (3, 2), respectively. SOLUTION We use the following equations to compute the moments: My = 4(-1) + 3(2) + 6(3) = Mx = 4(1) + 3(-1) + 6(2) = Since m = 4 + 3 + 6 = , we use these equations to obtain x = My / m = y = Mx / m = Thus the center of mass is (x, y) = . (See the figure.)
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