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

College Physics | 1st Edition | ISBN: 9781938168000 | Authors: Paul Peter Urone, Roger Hinrichs ISBN: 9781938168000 42

Solution for problem 32PE Chapter 9

College Physics | 1st Edition

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College Physics | 1st Edition | ISBN: 9781938168000 | Authors: Paul Peter Urone, Roger Hinrichs

College Physics | 1st Edition

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Problem 32PE

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?

Step-by-Step Solution:

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.

Step 2 of 2

Chapter 9, Problem 32PE is Solved
Textbook: College Physics
Edition: 1
Author: Paul Peter Urone, Roger Hinrichs
ISBN: 9781938168000

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