A person bending forward to lift a load \"with his back\" (Figure (a)) rather th

Question

A person bending forward to lift a load "with his back" (Figure (a)) rather than "with his knees" can be injured by large forces exerted on the muscles and vertebrae. The spine pivots mainly at the fifth lumbar vertebra, with the principal supporting force provided by the erector spinalis muscle in the back. To see the magnitude of the forces involved, and to understand why back problems are common among humans, consider the model shown in Figure (b) of a person bending forward to lift a Wo = 170-N object. The spine and upper body are represented as a uniform horizontal rod of weight Wb = 385 N, pivoted at the base of the spine. The erector spinalis muscle, attached at a point two-thirds of the way up the spine, maintains the position of the back. The angle between the spine and this muscle is 12.0

Explanation / Answer

Take the length of the spine as 1 unit. You have a horizontal bar with the forces Rx and Ry at x = 0 (reactions at the hips) 350N down at x = 0.5 (weight of spine) T at angle 12 degrees, at x = 0.6667 (muscle) 200N down at x = 1 (weight being lifted). Take moments about x = 0. 0.5 x 350 + 1 x 200 = 0.6667 x T sin 12 T = 2705 N Resolve horizontally Rx = T cos 12 = 2646 N

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