Question

17 BIO A person bending forward to lift a load "with his back" (Fig. P8.17a) 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, con- sider the model shown in Figure P8.17b of a person bending forward to lift a 200-N object. The spine and upper body are represented as a uniform horizontal rod of weight 350 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 mus- cle is/ 12.0 . Find (a) the tension in the back muscle and (b) the compressional force in the spine. Back muscle Ry 12.0 Pivot R, le 200 N 350 N

Answer 1

Taking moment,

(350 x L/2) + (200 L) = 375 L ....... (1)

T sin 12 x 2L/3 = 0.139 TL ........ (2)

From equation (1) and (2)

375 L = 0.139 TL

A)

T = 2697.84 N

B)

F = T cos12 = 2638.89 N

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