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Chapter 9: Q 34PE (page 319)

Question: A father lifts his child as shown inFigure. What force should the upper leg muscle exert to lift the child at a constant speed?

Short Answer

Expert verified

The total force exerted by the upper leg muscle is 2254N.

Step by step solution

01

Define the 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

Free-body diagram

The diagram for the leg muscles is shown below:

03

Calculation of the force on the upper leg muscle

The net torque about the pivot point which is knee, is zero in equilibrium. We can write

FQ×2=wleg×20+wchild×38

Here, the weight of the child is,

wchild=10×9.8=98N

The weight of the leg is,

FQ×2=39.2×20+98×38FQ=39.2×20+98×382FQ=2254N

Hence, the force is 2254N.

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Most popular questions from this chapter

Question: A \({\rm{75}}\;{\rm{kg}}\) man stands on his toes by exerting an upward force through the Achilles tendon, as inFigure. (a) What is the force in the Achilles tendon if he stands on one foot? (b) Calculate the force at the pivot of the simplified lever system shown—that force is representative of forces in the ankle joint.

Calculate the magnitude and direction of the force on each foot of the horse inFigure\({\rm{9}}{\rm{.31}}\)(two are on the ground), assuming the center of mass of the horse is midway between the feet. The total mass of the horse and rider is \({\rm{500}}\;{\rm{kg}}\). (b) What is the minimum coefficient of friction between the hooves and ground? Note that the force exerted by the wall is horizontal.

What is the mechanical advantage of a nail puller—similar to the one shown inFigure\({\rm{9}}{\rm{.23}}\)—where you exert a force \({\rm{45}}\;{\rm{cm}}\)from the pivot and the nail is \({\rm{1}}{\rm{.8}}\;{\rm{cm}}\)on the other side? What minimum force must you exert to apply a force of \({\rm{1250}}\;{\rm{N}}\) to the nail?

Question: A person working at a drafting board may hold her head as shown inFigure 9.40, requiring muscle action to support the head. The three major acting forces are shown. Calculate the direction and magnitude of the force supplied by the upper vertebrae Fvto hold the head stationary, assuming that this force acts along a line through the center of mass as do the weight and muscle force.

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 (see previous Question)?
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