A person bending forward to lift a load \"with his back\" shown in Figure (a) ra

Question

A person bending forward to lift a load "with his back" shown in 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 Fig. (b) of a person bending  forward to lift a Wo = 240 N object. The spine and upper body are represented as a uniform horizontal rod of weight Wb = 305 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 person bending forward to lift a load "with his back" shown in 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 Fig. (b) of a person bending forward to lift a Wo = 240 N object. The spine and upper body are represented as a uniform horizontal rod of weight Wb = 305 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 degree. Find the tension in the back muscle and the compressional force in the spine.

Explanation / Answer

Part A)
Placing the pivot point at the location of R, we can sum the torques

Tsin(12)(2/3) = Wb(.5) + Wo(1)

.667Tsin(12) = (305)(.5) + (240)

T = 2832 N

For the forces in the spine.

Ry will be found from

Ry + T(sin 12) = 305 + 240

Ry + (2832)(sin 12) = 545

Ry = -43.8 N

Rx will be found from

Rx = Tcos(12)

Rx = 2832 (cos 12)

Rx = 2770 N

(In the event that your answer key needs Rx and Ry combined, that is by the pythagoream theorem and you get 2770 N)

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