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Chapter 9: Q14 CQ (page 315)

Explain why the forces in our joints are several times larger than the forces we exert on the outside world with our limbs. Can these forces be even greater than muscle forces?

Short Answer

Expert verified

The joints in human bodies act as a third-class lever. The mechanical advantage is less than 1.

Step by step solution

01

Human hand as lever

The action of muscles when an object is placed on human hand palm is depicted as below:

Human hand as lever

The arm is represented by EP, Elbow at E, palm at P. The load of weight L is at palm.

The muscles exert a forceFMupward, at a distance l1from E. The center of mass of the forearm and the load are at distances l2and l3from E.

02

Calculation of force

Under the equilibrium of forces, we can write,

FM=FE+W+L..…(1)

Here, W is the weight of the fore-arm.

Under the equilibrium of the moments about the point E,

FMl1=Wl2+Ll3FM=WI2l1+Ll3l1........2

We can write from equation (1) that,

FE=FM-W+L=Wl2l1+Ll3l1-W+L=Wl2l1-1+Ll3l1-1

As the factors,I2l1-1andI3l1-1are greater than unity,

FE>W+L

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Most popular questions from this chapter

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?

Suppose we replace the 4.0kg book inExercise 9.31of the biceps muscle with an elastic exercise rope that obeys Hooke’s Law. Assume its force constant k = 600N/m. (a) How much is the rope stretched (past equilibrium) to provide the same force FB as in this example? Assume the rope is held in the hand at the same location as the book. (b) What force is on the biceps muscle if the exercise rope is pulled straight up so that the forearm makes an angle of 25owith the horizontal? Assume the biceps muscle is still perpendicular to the forearm.

(a) What is the mechanical advantage of a wheelbarrow, such as the one inFigure\({\rm{9}}{\rm{.24}}\), if the center of gravity of the wheelbarrow and its load has a perpendicular lever arm of \({\rm{5}}{\rm{.50}}\;{\rm{cm}}\), while the hands have a perpendicular lever arm of \({\rm{1}}{\rm{.02}}\;{\rm{m}}\)? (b) What upward force should you exert to support the wheelbarrow and its load if their combined mass is\({\rm{55}}{\rm{.0}}\;{\rm{kg}}\)? (c) What force does the wheel exert on the ground?

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\(300\;{\rm{N}}\)?

Suppose you pull a nail at a constant rate using a nail puller as shown inFigure 9.23. Is the nail puller in equilibrium? What if you pull the nail with some acceleration – is the nail puller in equilibrium then? In which case is the force applied to the nail puller larger and why?
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