$($a$)$ Correct plank form

$($b$)$ Incorrect plank form

Figure $1$: Side view of $(a)$ correct $(,)=(90,80)$ and $(b)$ incorrect $(,)=(60,60)$ plank forms held by the person ABCDEF.

A: hands; B: elbows; C: neck; D: core; E: heels; F: toes; $m$ : mass of person; $L$ : height of person.

Planks are a recent exercise fad designed to strengthened the core muscles near $D$ of the person ABCDEF in figure $1.$ In this exercise, the

person ABCDEF holds the plank form without moving for as long as possible, typically more than $1$ minute. It is a hard exercise for most. At

a party, a friend said that planks are easy, claiming to be able to hold it for $10$ minutes, and then proceeded to demonstrate the claim by holding

the form in figure $1(b).$ As the only engineer in the room, you proceeded to explain that the form in figure $1(b)$ is incorrect, whereas the form in

figure $1(a)$ is correct. Calculate the internal moments $M_D$ at D required to hold either forms in figures $1(a)$ and $(b)$ and explain in one sentence

to the friend why figure $1(a)$ is the correct form. In your calculations, make the simplifying assumption that the centroids of the normal ground

reactions, $N_B$ and $N_F,$ are located at the elbows B and toes F $,$ respectively. Take $m=90kg,L=1\mathrm{.}75m$ and $g=9\mathrm{.}81\frac{m}{s^2}.$ Hint: first show

$N_B=\frac{0\mathrm{.}1sin+0\mathrm{.}425sin}{0\mathrm{.}35sin+0\mathrm{.}5sin}mg$