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 92.0cm 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 5.25kg .

Part A

Find the x-coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally.

Explanation / Answer

given that ::

mass of a person, mp = 70 kg

length of the human leg (measured from the hip joint) = 46 cm + 46 cm = 92 cm

mass of the upper leg, m1 = 8.6 kg

mass of the lower leg (including the foot), m2 = 5.25 kg

x-coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally is given as ::

at x=0 as the position of the hip joint

xcm = (x1 m1 + x2 m2) / (m1 + m2) { eq. 1 }

where, x1 = location of mass 1

m1 = mass of upper leg

x2 = location of mass 2

m2 = mass of lower leg

x1 = 23 cm, m1 = 8.6kg (x1 = 23 cm, since the upper part is 46 cm & a uniform object has its center of mass at the midpoint)

x2 = 69 cm, m2 = 5.25kg

xcm = (23 cm x 8.6 kg + 69 cm x 5.25 kg) / (8.6 kg+ 5.25 kg)     

xcm = 40.4 cm

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