To keep the calculations fairly simple, but still reasonable, we shall model a h

Question

To keep the calculations fairly simple, but still reasonable, we shall model a human leg that is 92.0long (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 70.0 person, the mass of the upper leg would be 8.60 , while that of the lower leg (including the foot) would be 5.25 . a. Find the -coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally. b. Find the -coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally. c. Find the -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 -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.

Explanation / Answer

set x=0 as the position of the hip joint xcm = (x1 m1 + x2 m2)/(m1+m2) where x1=23 cm; m1=8.35kg (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=5.05kg xcm=(23*8.35+69*5.05)/(8.35+5.05) xcm=40.33 cm for second problem x1=23cm and x2=46 cm since the lower part lies along the line x=46 cm xcm=(23 * 8.35 + 46 * 5.05)/13.4= 31.66 cm in third problem y1=0 and y2=-23 cm ycm=(y1 m1 +y2 m2)/(13.4) ycm=(0+(-23)(5.05))/13.4 = -8.66cm

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