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 92.0 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 8.80 kg , while that of the lower leg (including the foot) would be 5.35 kg . Take that x-axis is directed horizontally and the y-axis is directed vertically downward.

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.

Part 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.

Part 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.

#Show work

Explanation / Answer

A) from hip:

d1 = centre of upper leg from hip joint= 92/4 = 23 cm

d2 = centre of lower leg from hip joint = (92/2) + (92/4) = 69 cm

Xcm = m1d1 + m2d2 / (m1 + m2)

= (8.80 x 23 + 5.35x69) / (8.80 + 5.35) = 40.4 cm from hip joint.

B) now x1 for upper leg = 92/4 = 23 cm

now x2 fro lower leg = 92/2 = 46 cm

Xcm = (8.80 x 23 + 5.35x46) / (8.80 + 5.35) = 31.7 cm

c) Y1 for upper leg = 0

Y2 for lower leg= 92/4 = 23 cm

Ycm = (8.80 x 0 + 5.35x23) / (8.80 + 5.35) = 8.7 cm

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