One yoga exercise, known as the \"Downward-Facing Dog,\" requires stretching you
ID: 1974722 • Letter: O
Question
One yoga exercise, known as the "Downward-Facing Dog," requires stretching your hands straight out above your head and bending down to lean against the floor. This exercise is performed by a certain 740 N person, as shown in the simplified model in the figure below. When he bends his body at the hip to a 90.0 angle between his legs and trunk, his legs, trunk, head and arms have the dimensions indicated. Furthermore, his legs and feet weigh a total of 260 N, and their center of mass is 41.0 cm from his hip, measured along his legs. The person's trunk, head, and arms weigh 480 N, and their center of gravity is 65.0 cm from his hip, measured along the upper body.
Find the normal force that the floor exerts on each foot, assuming that the person does not favor either hand or either foot and find the normal force that the floor exertson each hand, assuming that the person does not favor either hand or either foot.
Explanation / Answer
Total length of upper body = 75 + 60 = 135 Angle of legs with ground = invtan 135/90 = 56.31 degrees Angle of hands with ground = 90 - 56.31 = 33.69 degrees Horizontal components from hands and legs cancel each other out Let leg force be L, arm force be H cos 56.31 L = cos 33.69 H Vertical components from hands and legs are equal to weight sin 56.31 L + sin 33.69 H = 740 solving for the trigonometry, the two simultaneous equations are 0.5547 L = 0.8321 H 0.8321 L + 0.5547 H = 740 Solving the simultaneous equations, 0.8321 * 0.8321 / 0.5547 H + 0.5547 H = 740 H = 410.4, L = 615.7 For each hand, force = H/2 = 205.2 For each foot, force = L/2 = 307.85
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