Even when the head is held erect, as in Figure 9.41, its center of mass is not directly over the principal point of support (the atlanto-occipital joint). 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. (a) Calculate the force exerted by these muscles using the information in the figure. (b) What is the force exerted by the pivot on the head?
Solution
Step 1 of 2
a) We need to calculate the force exerted by the muscles at the back of the neck.
Consider the figure,
From the second condition of equilibrium
So
Implies
We have the value of
The force exerted by the muscle is and it is in the downward direction.
