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Section summary

  • Statics plays an important part in understanding everyday strains in our muscles and bones.
  • Many lever systems in the body have a mechanical advantage of significantly less than one, as many of our muscles are attached close to joints.
  • Someone with good posture stands or sits in such as way that their center of gravity lies directly above the pivot point in their hips, thereby avoiding back strain and damage to disks.

Conceptual questions

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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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?

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Certain types of dinosaurs were bipedal (walked on two legs). What is a good reason that these creatures invariably had long tails if they had long necks?

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Swimmers and athletes during competition need to go through certain postures at the beginning of the race. Consider the balance of the person and why start-offs are so important for races.

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If the maximum force the biceps muscle can exert is 1000 N, can we pick up an object that weighs 1000 N? Explain your answer.

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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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Explain one of the reasons why pregnant women often suffer from back strain late in their pregnancy.

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Problems&Exercises

Verify that the force in the elbow joint in [link] is 407 N, as stated in the text.

F B = 470 N; r 1 = 4.00 cm; w a = 2.50 kg; r 2 = 16.0 cm; w b = 4.00 kg; r 3 = 38.0 cm F E = w a r 2 r 1 1 + w b r 3 r 1 1 = 2.50 kg 9.80 m / s 2 16.0 cm 4.0 cm 1 + 4.00 kg 9.80 m / s 2 38.0 cm 4.00 cm 1 = 407 N alignl { stack { size 12{F rSub { size 8{B} } ="470"" N ; "r rSub { size 8{1} } =4 cdot "00"" cm ; "w rSub { size 8{a} } =2 cdot "50"" kg ;"} {} #r rSub { size 8{2} } ="16" cdot 0" cm ;" {} # w rSub { size 8{b} } =4 cdot "00"" kg ; "r rSub { size 8{3} } ="38" cdot 0" cm" {} #F rSub { size 8{E} } times r rSub { size 8{1} } =w rSub { size 8{a} } left ( { {r rSub { size 8{2} } } over {r rSub { size 8{1} } } } - 1 right )+w rSub { size 8{b} } left ( { {r rSub { size 8{3} } } over {r rSub { size 8{1} } } } - 1 right ) {} # = left (2 cdot "50 kg" right ) left (9 cdot "80 " {m} slash {s rSup { size 8{2} } } right ) left ( { {"16" cdot "0 cm"} over {4 cdot "0 cm"} } - 1 right ) {} #+ left (4 cdot "00 kg" right ) left (9 cdot "80 " {m} slash {s rSup { size 8{2} } } right ) left ( { {"38" cdot "0 cm"} over {4 cdot "00 cm"} } - 1 right ) {} # = {underline {"407"" N"}} {}} } {}

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Two muscles in the back of the leg pull on the Achilles tendon as shown in [link] . What total force do they exert?

An Achilles tendon is shown in the figure. A vertical dotted line is shown at the middle of the top part. Two vectors inclined at twenty degree each with respect to the vertical dotted line are shown.
The Achilles tendon of the posterior leg serves to attach plantaris, gastrocnemius, and soleus muscles to calcaneus bone.
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The upper leg muscle (quadriceps) exerts a force of 1250 N, which is carried by a tendon over the kneecap (the patella) at the angles shown in [link] . Find the direction and magnitude of the force exerted by the kneecap on the upper leg bone (the femur).

The figure shows a side view of the bones of a knee and the quadriceps muscle. The upper bone is inclined at fifty five degrees to the horizontal and the tension exerted by the quadriceps muscle is one thousand two hundred and fifty newtons. The tendon from the knee cap to the lower bone is inclined at seventy five degrees below the horizontal. The force in this direction is the same as that provided by the quadriceps.
The knee joint works like a hinge to bend and straighten the lower leg. It permits a person to sit, stand, and pivot.

1.1 × 10 3 N θ = 190 º ccw from positive x axis alignl { stack { size 12{1 "." 1 times "10" rSup { size 8{3} } `N} {} #θ="190"°`"ccw"`"from"`"positive"`x`"axis" {} } } {}

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A device for exercising the upper leg muscle is shown in [link] , together with a schematic representation of an equivalent lever system. Calculate the force exerted by the upper leg muscle to lift the mass at a constant speed. Explicitly show how you follow the steps in the Problem-Solving Strategy for static equilibrium in Applications of Statistics, Including Problem-Solving Strategies .

A machine for leg exercise is shown. A wire is tied to a cuff around the lower part of a leg. This wire passes over three pulleys and is connected to a ten kg weight. The tension in the wire is shown near the leg in the direction of the wire. On the leg, a point on knee is shown as the pivot. The distance between the pivot and the point where the wire is tied to the leg is thirty five centimeters. A free-body diagram of the leg, represented as a pole, is shown.
A mass is connected by pulleys and wires to the ankle in this exercise device.
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A person working at a drafting board may hold her head as shown in [link] , 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 F V size 12{F rSub { size 8{V} } } {} to hold the head stationary, assuming that this force acts along a line through the center of mass as do the weight and muscle force.

The head of a person working at a drafting board in relaxed position is shown. The inclination of the head is theta to the horizontal and the center of gravity is near the top of the head. The weight of the head is fifty newtons and is acting downward at the center of gravity. Three major forces are shown. The force exerted along the neck is sixty newtons.

F V = 97 N, θ = 59º size 12{F rSub { size 8{V} } ="97"`N,`θ="59"°} {}

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Questions & Answers

Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
Widad Reply
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Ariel
?
Ariel
What is economics
Widad Reply
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn Reply
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn
what is ecnomics
Jan Reply
this is the study of how the society manages it's scarce resources
Belonwu
what is macroeconomic
John Reply
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
etc
husaini
difference between firm and industry
husaini Reply
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from Qd  120 3P to Qd  90  3P and the supply function has shifted from QS  20  2P to QS 10  2P . a) Find the effect of this change on price and quantity. b) Which of the changes in demand and supply is higher?
Toofiq Reply
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innocent Reply
factors influencing supply
Petrus Reply
what is economic.
Milan Reply
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Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Zarshad Reply
Why qualify 28 supplies
Milan
what are explicit costs
Nomsa Reply
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
David Reply
economic overview notes
Amahle Reply
identify a demand and a supply curve
Salome Reply
i don't know
Parul
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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