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Chapter 9: Q 32PE (page 318)

Question: Even when the head is held erect, as inFigure 9.41, its center of mass is not directly over the principal point of support (the atlantooccipital 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?

Short Answer

Expert verified

(a) The force exerted by the muscles is 25N.

(b) The force exerted by the pivot on the head muscles is 75N upward.

Step by step solution

01

Force

A force is an external factor that can change the rest or motion of a body. It has a size and a general direction.

02

Diagram

The diagram for the biceps muscle is shown below:

The weight is w = 50N.

03

Calculation of the force

(a)

As the force applied by the biceps muscle is perpendicular to the forearm, applying the condition of equilibrium under torque, we can write,

FM0.050-w0.025=0FM=w0.0250.050=50N×0.0250.050=25N

Hence, the force is 25N.

04

Calculation of the force by the pivot

(b)

Applying the condition of equilibrium under force, we can write,

FJ-FM-w=0FJ=FM+wFJ=25+50FJ=75N

Hence, the force by the pivot is 75N.

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Most popular questions from this chapter

Suppose you needed to raise a\(250\;{\rm{kg}}\)mower a distance of\(6.0\;{\rm{cm}}\)above the ground to change a tire. If you had a\(2.0\;{\rm{m}}\)long lever, where would you place the fulcrum if your force was limited to\(300\;{\rm{N}}\)?

Two children push on opposite sides of a door during play. Both pushes horizontally and perpendicular to the door. One child push with a force of 17.5 N at a distance of 0.600 m from the hinges, and the second child pushes at a distance of 0.450 m. What force must the second child exert to keep the door from moving? Assume friction is negligible.

Why are the forces exerted on the outside world by the limbs of our bodies usually much smaller than the forces exerted by muscles inside the body?

Two muscles in the back of the leg pull on the Achilles tendon as shown inFigure\({\rm{9}}{\rm{.37}}\). What total force do they exert?

Why are the forces exerted on the outside world by the limbs of our bodies usually much smaller than the forces exerted by muscles inside the body?
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