1.8 THE BACK When the trunk is bent forward, the spine pivots mainly on the fift

Question

1.8 THE BACK When the trunk is bent forward, the spine pivots mainly on the fifth lumbar ver- tebra (Fig. 1.16a). We will analyze the forces involved when the trunk is bent at 60 from the vertical with the arms hanging freely. The lever model representing the situation is given in Fig. 1.16. The pivot point A is the fifth lumbar vertebra. The lever arm AB represents the back. The weight of the trunk W1 is uniformly distributed along the back; its effect can be represented by a weight suspended in the middle. The weight of the head and arms is represented by W2 suspended at the end of the lever arm.

Explanation / Answer

W2 becomes= 160+20*9.8=356 N

Take moments about pivot A

356*d*cos30 + 320*d/2* cos30 = T sin 12* (2d/3)

T=3223.99 N ,approximately= 3220 N

Now balance the forces along vertical and Honrizontal

356+320+ T sin 18 =Ny

T cos18= Nx

Ny=1672 N

Nx=3066 N

Net N = Sqrt( 1672^2+3066^2) = 3492 N , Approx= 3490 N

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