Question

Calculate the mass m needed in order to suspend the leg shown in (Figure 1) . Assume the leg (with cast) has a mass of 16.0 kg , and its CG is 36.5 cm from the hip joint; the sling is 78.0 cm from the hip joint.

Answer 1

Hard to visualize. Assume M = 16 kg, which by the definition of CG we can assume lies on the CG. The pivot point is at the hip; so l = .365 m is the small lever arm to CG and the mass M. L = .78 m is the large lever arm from the hip to the mass m = ? you are looking for.

In which case, m/M = l/L = (.365/.78)*16 = 7.4871

\ of the forces w/W = mg/Mg = m/M where mg and Mg are the forces acting on the masses due to gravity. So your system is in balance when wL = mgL = Mgl = Wl and that's where the ratios come from