Problem $2$

It is required to estimate the force at the facet joint and its location together with the normal force at the disc between lumbar vertebrae $1$ and $2$ for the loading condition shown in the figure below. Knowing that,

Facet joint force makes an angle of $70$ with the $x-$axis.

The line of centers between L$1$ and L$2$ makes an angle of $10$ with the z$-$axis due to spine tilt.

Muscle force $=15N$ and muscle moment $=0\mathrm{.}675N-m.$

$.x$ and $z$ are the local coordinates of $L2.$