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 43 N, calculate the force exerted by the muscles, FM, using the information in the figure.

O 4/1/2017 11:55 PM A 3.1/6 4/3/2017 09:44 PM Gradebook Print Calculator Question 11 of 17 ncorrect Map Openstax College Physics presented by Sapling Learning openstax n when the head is held erect, as in the figure below, its center of mass is not directly over the principal oint 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 43 N, calculate the force exerted by the muscles, FM, using the information in the figure. Number Tools x 102 What is t ed by the pivot on the head, Fu? Number x, 4.9 cm FTW 43 N x, 2.1 cm O Previous ® Give Up & View solution Check Answer Next H Ext Hint

Explanation / Answer

Given x1=4.9cm,x2=2.1cm

Fw=43N

Force exerted by the muscles of the back of the neck

Fmuscle x(x1)=Fw x x2

Fmuscle x4.9=43x2.1

Fmuscle=18.4 N

The ratio of the force exerted by the muscles to the total weight held by the muscles

Fmuscle/Fhead=18.4/43

=0.43N

Force acting on the pivot of the head Fj

Fjoint=Fhead+Fmuscle

Fj=43+18.4

=61.4N

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