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

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 aWo = 160–N object. The spine and upper body are represented as a uniform horizontal rod of weight Wb = 320 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°.

(a) Find the tension in the back muscle.
kN

(b) Find the compressional force in the spine. (Enter the magnitude.)
kN

Explanation / Answer

let the length of the spine as 1 unit. You have a horizontal bar with the forces

here reactions at the hips Rx and Ry at x = 0

(weight of spine) = 0.5

so 320 N down at x = 0.5

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 * 320 + 1 *160 = 0.6667 * T sin 12

T = 2308. 55 N = 2.308 kN

so Horrizontal force Rx = T cos 12 = 0.478 kN

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