A person of weight 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

Forces, Machines and Signals, Ch Bones, blood and body size

Problem

A person of weight

800\,\mathrm{N}

stands on one leg. A torque balance at the hip gives a joint force of

2.4

times body weight acting on the femoral head, offset by

18\,\mathrm{mm}

from the shaft axis. Model the femoral shaft as the standard tube of outer radius

r_o = 13\,\mathrm{mm}

, inner radius

r_i = 7\,\mathrm{mm}

, cross-sectional area

377\,\mathrm{mm^2}

and second moment of area

I = 2.05\times10^{-8}\,\mathrm{m^4}

. For the compressive stress, take the joint force to act along the shaft axis. ((a)) Calculate the compressive stress from the axial component of the joint force spread over the shaft area. ((b)) Calculate the bending moment produced by the offset joint force and the resulting surface bending stress

\sigma = M_br_o/I

. ((c)) State which stress dominates and by roughly what factor.

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