A woman ( ) stands on one leg

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Biophysics & Medical Physics · Bioelectricity, the senses and the physics of the body

Life at Thermal Energy, Ch Bones, muscles, blood and body size

Problem

65\,\mathrm{kg}

woman (

g = 9.8\,\mathrm{m\,s^{-2}}

) stands on one leg. The weight of the body above the stance hip,

(5/6)W

, acts at a horizontal distance of

11\,\mathrm{cm}

from the centre of the femoral head, on the side away from the abductor muscles; the abductor muscles pull at a horizontal distance of

4.4\,\mathrm{cm}

from the femoral head, on the near side. Take moments about the femoral head, and take the joint reaction force to be the sum of the abductor force and the weight carried above the hip (as in the single-leg-stance model of the text). ((a)) Find the abductor force and the hip joint reaction force, each as a multiple of body weight

W

, with no walking aid. ((b)) She now carries a cane in the opposite hand, through which the ground pushes up on her with a force of

0.12W

at a horizontal distance of

28\,\mathrm{cm}

from the femoral head, on the far side (the same side as the body weight above the hip). Using torque balance about the femoral head and force balance on the pelvis, find the new abductor force and joint reaction force, each as a multiple of

W

, and hence in newtons. ((c)) Some years later, she lands stiff-legged from a small jump. The peak force transmitted through this same femur is

6.0

times her body weight, and the cortical bone of the femoral shaft has a cross-sectional area of

2.9\,\mathrm{cm^2}

. Find the peak compressive stress in the femoral shaft and express it as a safety factor against the measured compressive strength of compact bone,

170\,\mathrm{MPa}

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