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# Even when the head is held erect, as in Figure 9.41, its ISBN: 9780130606204 3

## Solution for problem 32PE Chapter 9

Physics: Principles with Applications | 6th 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 32PE Step-by-step solution Step 1 of 3 Apply the condition of static equilibrium. The net torque and the net force acting on the system is zero if it is in the state of static equilibrium. Step 2 of 3 (a) Refer to the figure 9.41 provided in the text book. Take counter clockwise torques as positive and the clockwise torques as negative. The muscles at the back of the neck create counter clockwise torque and the weight of the head at the centre of the gravity creates clockwise torques. For the static equilibrium, the net torque acting on the head is zero. Let the pivot at CG, net torque about pivot point is zero , Substitute 50 N for w solve for , Therefore, the force exerted by muscles at the back of the neck is in downward direction.

Step 3 of 3

##### ISBN: 9780130606204

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