A student is interested in quantifying the resultant force and moment $(F_T$ and $M_T)$ through the talar joint when a ballerina is en pointe. To do this, the student brings a ballerina into the HPL and performs a motion analysis experiment allowing them to determine the centre of pressure and the centre of mass with respect to the foot. The ballerina is then instructed to statically stand en pointe on the surface of a force plate. The resulting force at the centre of pressure $(F_p)$ was determined to be $3500$ N and the mass of the ballerina was measured to be $60$ kg $.$ Use the free body diagram below to determine $F_T$ and $M_T,$ given that $a=100mm,b=70mm,=25,$ and $=45.$

While you're studying for your KNES $363$ exam, you decide to quantify how much of a pain in the neck it really it$.$ You know that your head has a mass of $5$ kg and you've been statically hunched over at $37$ degrees for last few days causing an applying far too much force through your splenius capitis $(F_m)$ and cervical vertebrae $(F_v).$ Use the free body diagram to answer the questions below:

Assuming static equilibrium, calculate the force applied by your splenius capitis $(F_m)$ and cervical vertebrae $(F_v)$

Assuming static equilibrium, calculate the axial $($normal$)$ force and bending moment acting at the centre of the cross section labeled $S_1-S_2.$

Calculate the normal stress on the surface of the cross section at points $S_1$ and $S_2.$ Assume the crosssectional area and areal moment of inertia are $50m{m}^2$ and $180m{m}^4,$ respectively.