Even when the head is held erect, as in the figure below, its center of mass is

Question

Even when the head is held erect, as in the figure below, its center of mass is not directly over the principal point of support (the atlanto-occipital joint, point A). The muscles at the back of the neck should therefore exert a force to keep the head erect. That is why your head falls forward when you fall asleep in the class If the head weighs 53 N, calculate the force exerted by the muscles, FM, using the information in the figure. Number What is the force exerted by the pivot on the head, Fj? Number Xi= 4.5 cm Fwl=53 N x,-2.3 cm

Explanation / Answer

Given

F_W = 53 N

x1 = 4.5 cm = 0.045 m

x2 = 2.3 cm = 0.023 m

now the moments equal to zero

the moments about A is  

F_M*x1 -F_W*x2 = 0

F_M = F_W*x2/x1

F_M = 53*0.023 /(0.045) N

F_M = 27.08 N

The force exerted by the muscle ,F_M = 27.08 N

now the moment about left end is

F_J*x1 = F_W*(x1+x2)

F_J = F_W*(x1+x2) /x1

F_J = 53(0.023+0.045)/(0.045) N

F_J = 80.08 N

The force exerted by the pivot on the head , F_J = 80.08 N

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