o keep the calculations fairly simple, but still reasonable, we shall model a hu

Question

o keep the calculations fairly simple, but still reasonable, we shall model a human leg that is 92.0cm long (measured from the hip joint) by assuming that the upper leg and the lower leg (which includes the foot) have equal lengths and that each of them is uniform. For a 70.0kg person, the mass of the upper leg would be 8.60kg, while that of the lower leg (including the foot) would be 5.30kg. A, Find the x-coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally. B, Find the y-coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally. C, Find the x-coordinate of the center of mass of this leg, relative to the hip joint, if it is bent at the knee to form a right angle with the upper leg remaining horizontal. D, Find the y-coordinate of the center of mass of this leg, relative to the hip joint, if it is bent at the knee to form a right angle with the upper leg remaining horizontal. please help!

Explanation / Answer

a) set x=0 as the position of the hip joint xcm = (x1 m1 + x2 m2)/(m1+m2) where x1=location of mass 1; m1=mag of mass1 x2=location of mass 2; m2=mag of mass2 x1=23 cm; m1=8.6kg (x1=23 cm since the upper part is 46 cm, and a uniform object has its center of mass at the midpoint x2=69cm; m2=5.25kg xcm=(23*8.6+69*5.25)/(8.6+5.25) xcm=40.44 cm b) x1 is the same in this case, but now x2=46 cm since the lower part lies along the line x=46 cm xcm=(23 * 8.6 + 46 * 5.25)/13.85= 31.72 cm c) here, y1=0 since the upper part lies along the line y=0 y2=-23 cm ycm=(y1 m1 +y2 m2)/(13.85) ycm=(0+(-23)(5.25))/13.85 = -8.72cm

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