a therapist tells a 80.0 {kg} patient with a broken leg that he must have his le

Question

a therapist tells a 80.0 {kg} patient with a broken leg that he must have his leg in a cast suspended horizontally. for minimum discomfort, the leg should be supported by a vertical strap attached at the center of mass of the leg-cast system. (see the figure below .) in order to comply with these instructions, the patient consults a table of typical mass distributions and finds that both upper legs (thighs) together typically account for 21.5 % of body weight and the center of mass of each thigh is 18.0 {cm} from the hip joint. the patient also reads that the two lower legs (including the feet) are 14.0 % of body weight, with a center of mass 69.0 { m cm} from the hip joint. the cast has a mass of 5.50 {kg}, and its center of mass is 78.0 { m cm} from the hip joint 1.how far from the hip joint should the supporting strap be attached to the cast? (in cm)

Explanation / Answer

mass of thigh   = 0.5 * 0.215 * 80    = 8.6 kgs

centre =   18 cm   or 0.18 m

mass of lower leg = 0.5 * 0.14* 80 = 5.6 kgs

centre = 69 cm   or 0.69 m

mass of cast = 5.5 kg

centre =   78 cm or 0.78 m

now use the formula for centre of mass

as

Xcm   = m1x1 + m2x2 + m3x3/(m1+ m2+ m3)

Xcm = (8.6 * 0.18) + (5.6 * 0.69) + ( 5.5* 0.78)/(8.6 + 5.6 + 5.5)

Xcm = 49.24 cm --------------<<<<<<<<<<<<Answer

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