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Solved: Even when the head is held erect, as in Figure

Chapter 9, Problem 32

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QUESTION:

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?

                

Figure \(9.41\) The center of mass of the head lies in front of its major point of support, requiring muscle action to hold the head erect. A simplified lever system is shown.

Equation Transcription:

Text Transcription:

9.41

Questions & Answers

QUESTION:

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?

                

Figure \(9.41\) The center of mass of the head lies in front of its major point of support, requiring muscle action to hold the head erect. A simplified lever system is shown.

Equation Transcription:

Text Transcription:

9.41

ANSWER:

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.

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