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 = 180-N object. The spine and upper body are represented as a uniform horizontal rod of weight Wb = 340 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

Let the spine has length L
and that the center of mass of the back is at L/2

Moments along Clockwise:
345N * L/2 + 175N * L = 347.5N * L --- (1)

Moments along Clockwise:
T*sin12 * 2L/3 = 0.139 T*L ---- (2)

From (1) & (2)
0.139 T*L = 347.5N * L

(a)
T = 2500 N
T = 2.5 KN

(b)
F = T * cos12
F = 2500* cos 12
F = 2445.37 N
F = 2.445 KN

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