Physics, Someone please help me!

A person bending forward to lift a load with his back, as shown in the figure, 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 the figure of a person bending forward to lift a 160 N object. The spine and upper body are represented as a uniform horizontal rod of weight 420 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°. Find the tension in the back muscle (T).

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  1. I do not have your picture but if it is a cantilever beam with a cable making a 12 degree angle with the boom 2/3 of the way out we can make some progress.

    first what force up is required 2/3 of the way out? Lets call the back 10 units long so there is a 420 N force down at 5 units from the base and a 160 N force down at the tip.
    the moments around the base are 420*5+160*10
    = 2270 Nm
    that must be balanced by the upward component of the muscle tension T
    T sin 12 * 6.67 units = 2270

    so the tension T = 1637 N or about ten times the weight we are lifting

    Now of course we alsoget a compression in the boom(spine) equal to T cos 12 = 1601 N

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