A person bending forward to lift a load “with his back” rather than “with his kn

Question

A person bending forward to lift a load “with his back” 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 free-body diagram for a person bending forward to lift a 200 N object.

The spine and upper body are represented as a uniform horizontal rod of weight 350 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) What is the tension T in the erector spinalis muscle?

(b) What is the compressional force R in the spine?

Explanation / Answer

They give us the diagram of force so, first we do summing of momentum in the point R.

the distance of all is assumed as "D"

350 N is in the center because is the weigth (we always assume this)

so..

-(1/2)*D*350-200*D+(2/3)*D*T*sin(12.5°)=0, D is the same of all, so we simplificated this:

-(1/2)*350-200+(2/3)*T*sin(12°)=0

so, T is: 2705.47 N

For Y:

-350 N -200 N + Ry + T*sin(12°) = 0

we know T, so Ry is...

Ry=-12.5 N

For x:

Rx - T*cos(12°) = 0

2646.28 N

So R is

R=(Rx^2 + Ry^2)^(1/2) = 2646.3 N

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