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A student flexes her neck to 40 degrees from vertical while studying for her final exam. She pivots her head around the upper vertebra, approximated as point P (in the middle of the picture). Her head has a mass of 4.5 kg, and its center of mass is 11 cm away from point P. Her neck muscles are 1.5 cm from point P, measured perpendicular and pulling straight down. How much force do the neck muscles have to exert to keep the head still

Answer :

okpalawalter8

Answer:

[tex]T=208N[/tex]

Explanation:

From the question we are told that:

Neck flex angle [tex]\angle_n=40 \textdegree[/tex]

Head mass [tex]M_h=4.5kg[/tex]

Center of mass [tex]M_c= 11cm[/tex]

Distance of neck from P [tex]d_p=1.5cm[/tex]

Let

[tex]T_g=Gravitational\ force\ torque\\T_{nm}=Tension\ on\ neck\ muscle\ torque[/tex]

Generally the net Torque T_n is mathematically given by

[tex]T_n=0[/tex]

Therefore

[tex]T_g-T_{nm}=0[/tex]

Generally the equation for Torque T is mathematically given by

[tex]T=\frac{M_h*g*l_g}{d_p}[/tex]

where

[tex]l_g=M_c*sin\angle_n[/tex]

[tex]l_g=11*10^{-2}*sin40[/tex]

[tex]l_g=0.07m[/tex]

Therefore

[tex]T=\frac{4.5*9.8*0.07}{1.5*10^{-2}}[/tex]

[tex]T=208N[/tex]

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