A girl of mass, m = 40 kg has osteoporosis which weakens herbones. From a kneeling position, she topples forward onto herelbows with her upper arms extended vertically downwards on impactwith the ground. In falling forward, her centre of mass lowers by aheight, h = 50 cm and she absorbs all of her kinetic energy fromher fall into her two humerus bones (one bone in each upperarm).
Determine an equation for the stress in each humerus bone, ?, interms of m, h, the acceleration due to gravity, g, Young’s modulusfor bone, Y, the cross sectional area of each humerus bone, A andthe length of each humerus bone, l. State any laws used. Now,determine the minimum rupture strength required for the girl’shumerus bones such that she doesn’t break them, given in units ofN/m2 . Take l = 20 cm, A = 3.0 cm2 and Y = 1.4 x10^10 N/m2 .
