A human leg that is 92.0 cm long (measured from the hip joint) by assuming that

Question

A human leg that is 92.0 cm 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 70.0 kg person, the mass of the upper leg would be 8.60 kg , while that of the lower leg (including the foot) would be 5.30 kg. 1.Find the x-coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally. 2.Find the y-coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally. 3.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. 4.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.

Explanation / Answer

a)take 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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