Assume a person bends forward to lift a load \"with his back\" as shown in Figur

Question

Assume a person bends forward to lift a load "with his back" as shown in Figure (a). 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, consider the model shown in Figure (b) for a person bending forward to lift a wi = 195-N object. The spine and upper body are represented as a uniform horizontal rod of weight = 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 = 10.0°. Back muscle livol Rx W (a) Find the tension T in the back muscle. AI (b) Find the compressional force in the spine.

Explanation / Answer

In equilibrium net torque about left = 0

T*sintheta*(2/3)L - W1*L - W2*L/2 = 0

T*sin10*(2/3) - 195 - 320 /2= 0

T = 3066.5 N

tension T in the back muscle = T = 3066.5 N <<<--------------ANSWER

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part(b)

In equilibrium Fnet = 0

along horizontal

Fx = 0

Rx - T*costheta = 0

Rx = T*costheta = 3066.5*cos10 = 3020 N

along vertical

Fy = 0

Ry + T*sintheta - W - W2 = 0

Ry = W1 + W2 - T*sintheta

Ry = 195 + 320 - (3066.5*sin10) = -17.5 N

compressional force R = sqrt(Rx^2+Ry^2)

compressional force R = sqrt(3020^2 + 17.5^2) = 3020 N <<<--------------ANSWER

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