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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

A sandwich board advertising sign is constructed as shown inFigure\({\rm{9}}{\rm{.35}}\). The sign’s mass is \({\rm{8}}{\rm{.00}}\;{\rm{kg}}\). (a) Calculate the tension in the chain assuming no friction between the legs and the sidewalk. (b) What force isexerted by each side on the hinge?

Consider a method for measuring the mass of a person’s arm in anatomical studies. The subject lies on her back, extends her relaxed arm to the side and two scales are placed below the arm. One is placed under the elbow and the other under the back of her hand. Construct a problem in which you calculate the mass of the arm and find its center of mass based on the scale readings and the distances of the scales from the shoulder joint. You must include a free body diagram of the arm to direct the analysis. Consider changing the position of the scale under the hand to provide more information, if needed. You may wish to consult references to obtain reasonable mass values.

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.

The upper leg muscle (quadriceps) exerts a force of\({\rm{1250 N}}\), which is carried by a tendon over the kneecap (the patella) at the angles shown inFigure\({\rm{9}}{\rm{.38}}\). Find the direction and magnitude of the force exerted by the kneecap on the upper leg bone (the femur).

Suppose the biceps muscle was attached through tendons to the upper arm close to the elbow and the forearm near the wrist. What would be the advantages and disadvantages of this type of construction for the motion of the arm?
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