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  • Explain the forces exerted by muscles.
  • State how a bad posture causes back strain.
  • Discuss the benefits of skeletal muscles attached close to joints.
  • Discuss various complexities in the real system of muscles, bones, and joints.

Muscles, bones, and joints are some of the most interesting applications of statics. There are some surprises. Muscles, for example, exert far greater forces than we might think. [link] shows a forearm holding a book and a schematic diagram of an analogous lever system. The schematic is a good approximation for the forearm, which looks more complicated than it is, and we can get some insight into the way typical muscle systems function by analyzing it.

Muscles can only contract, so they occur in pairs. In the arm, the biceps muscle is a flexor—that is, it closes the limb. The triceps muscle is an extensor that opens the limb. This configuration is typical of skeletal muscles, bones, and joints in humans and other vertebrates. Most skeletal muscles exert much larger forces within the body than the limbs apply to the outside world. The reason is clear once we realize that most muscles are attached to bones via tendons close to joints, causing these systems to have mechanical advantages much less than one. Viewing them as simple machines, the input force is much greater than the output force, as seen in [link] .

A forearm of a person holding a physics book is shown. The biceps and triceps muscles of the arm are visible. The elbow joint is the pivot point. The upper part of the arm is vertical and the lower part is horizontal. Biceps muscles are applying a force F B upward. The vertical bone of hand exerts a force F E on the pivot. At the midpoint of the lower part of the hand, the center of gravity of the hand is shown where the weight of the hand acts. The midpoint of the front face of the book is its center of gravity, where its weight acts downward. A free body diagram is also shown and the distances of the three forces F-B, C-G of arm, and C-G of book from the pivot are shown as r one, r two and r three.
(a) The figure shows the forearm of a person holding a book. The biceps exert a force F B to support the weight of the forearm and the book. The triceps are assumed to be relaxed. (b) Here, you can view an approximately equivalent mechanical system with the pivot at the elbow joint as seen in [link] .

Muscles exert bigger forces than you might think

Calculate the force the biceps muscle must exert to hold the forearm and its load as shown in [link] , and compare this force with the weight of the forearm plus its load. You may take the data in the figure to be accurate to three significant figures.


There are four forces acting on the forearm and its load (the system of interest). The magnitude of the force of the biceps is F B size 12{F rSub { size 8{B} } } {} ; that of the elbow joint is F E size 12{F rSub { size 8{E} } } {} ; that of the weights of the forearm is w a size 12{w rSub { size 8{a} } } {} , and its load is w b size 12{w rSub { size 8{b} } } {} . Two of these are unknown ( F B size 12{F rSub { size 8{B} } } {} and F E size 12{F rSub { size 8{E} } } {} ), so that the first condition for equilibrium cannot by itself yield F B size 12{F rSub { size 8{B} } } {} . But if we use the second condition and choose the pivot to be at the elbow, then the torque due to F E size 12{F rSub { size 8{E} } } {} is zero, and the only unknown becomes F B size 12{F rSub { size 8{B} } } {} .


The torques created by the weights are clockwise relative to the pivot, while the torque created by the biceps is counterclockwise; thus, the second condition for equilibrium net τ = 0 size 12{ left ("net "τ rSub { size 8{"cw"} } ="net "τ rSub { size 8{"ccw"} } right )} {} becomes

r 2 w a + r 3 w b = r 1 F B . size 12{r rSub { size 8{2} } w rSub { size 8{a} } +r rSub { size 8{3} } w rSub { size 8{b} } =r rSub { size 8{1} } F rSub { size 8{B} } } {}

Note that sin θ = 1 size 12{"sin"θ=1} {} for all forces, since θ = 90º size 12{θ="90"°} {} for all forces. This equation can easily be solved for F B size 12{F rSub { size 8{B} } } {} in terms of known quantities, yielding

F B = r 2 w a + r 3 w b r 1 . size 12{F rSub { size 8{B} } = { {r rSub { size 8{2} } w rSub { size 8{a} } +r rSub { size 8{3} } w rSub { size 8{b} } } over {r rSub { size 8{1} } } } } {}

Entering the known values gives

F B = 0 . 160 m 2 . 50 kg 9 . 80 m/s 2 + 0 . 380 m 4 . 00 kg 9 . 80 m/s 2 0 . 0400 m size 12{F rSub { size 8{B} } = { { left (0 "." "16"" m" right ) left (2 "." "50"" kg" right ) left (9 "." "80"" m/s" rSup { size 8{2} } right )+ left (0 "." "38"" m" right ) left (4 "." "00"" kg" right ) left (9 "." "80"" m/s" rSup { size 8{2} } right )} over {0 "." "04"" m"} } } {}

which yields

F B = 470 N . size 12{F rSub { size 8{B} } ="470"" N"} {}

Now, the combined weight of the arm and its load is 6.50 kg 9.80 m/s 2 = 63.7 N size 12{ left (6 "." "50"`"kg" right ) left (9 "." "80"`"m/s" rSup { size 8{2} } right )="63" "." 7`N} {} , so that the ratio of the force exerted by the biceps to the total weight is

F B w a + w b = 470 63 . 7 = 7 . 38 . size 12{ { {F rSub { size 8{B} } } over {w rSub { size 8{a} } +w rSub { size 8{b} } } } = { {"470"} over {"63" "." 7} } =7 "." "38"} {}


This means that the biceps muscle is exerting a force 7.38 times the weight supported.

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Questions & Answers

what is fluid
Anthony Reply
anything that flows is Liquid.
a substance that has no specific shape
How submarines floats one water the same time sink in water
Courage Reply
A submarine has the ability to float and sink. The ability to control buoyancy comes from the submarine'strim or ballast tanks which can be filled with either water or air, depending on whether the submarine needs to floator sink. When the submarine floats it means its trim tanks are filled with air
what is work
Ojo Reply
Force times distance
product of force and distance...
Is physics a natural science?
Adebisi Reply
what is the difference between a jet engine and a rocket engine.
Samuel Reply
explain the relationship between momentum and force
Joseph Reply
A moment is equivalent multiplied by the length passing through the point of reaction and that is perpendicular to the force
How to find Squirrel frontal area from it's surface area?
Pooja Reply
how do we arrange the electronic configuration of elements
Muhammed Reply
hi guys i am an elementary student
benedict Reply
are you an elementary student too?
no bro
what is the four equation of motion
what is strain?
Change in dimension per unit dimension is called strain. Ex - Change in length per unit length l/L.
strain is the ratio of extension to length..=e/l...it has no unit because both are in meters and they cancel each other
How is it possible for one to drink a cold drink from a straw?
Karanja Reply
most possible as it is for you to drink your wine from your straw
state the law of conservation of energy
Sushma Reply
energy can neither be destroy or created,but can be change from one form to another
it can neither be created nor destroyed
its so sample question dude
what is the difference between a principle and a law?
Mary Reply
where are from you wendy .?
you are beautiful
are you physics student
laws are ment to be broken
hehe ghulam where r u from?
principle are meant to be followed
south Africa
here Nigeria
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
Rules are meant to be broken while principals to be followed
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
what is momentum?
prakash Reply
is the mass times velocity of an object
it is the product of mass and velocity of an object.
The momentum possessed by a body is generally defined as the product of its mass and velocity m×v
momentum is the product of the mass of a body of its velocity
what about kg it is changing or not
vijay Reply
no mass is the quantity or amount of body so it remains constant everywhere
remains constant
mass of an object is always constant. and that is universally applied.
mass of a body never changes but the weight can change due to variance of gravity at different points of the world
what is hookes law
mass of an object does not change
Is weight a scalar quantity
esther Reply
weight is actually a force of gravity with which earth attracts us downwards so it is a vector quantity. and it has both direction and magnitude
weight is the earth pull of the body
why does weight change but not mass?
Theo, the mass of an object can change but it depends on how you define that object. First, you need to know that mass is the amount of matter an object has, and weight is mass*gravity (the "force" that attracts object A to the object B mass).
So if you face object A with object B, you will get a different result than facing object A with object C, so the weight of object A changes but not its mass.
Now, if you have an object and you take a part away from it, you are changing it mass. Lets use the human body and fat loss process as an example.
When you lose weight by doing exercise, you are being attracted by the same object before and after losing weight so the change of weight is related to a change of mass not a change of gravity.
The explanation of this is simple, we are composed of smaller particles, which are itself objects, so the loose of mass of an object actually is the separation of one object is two different ones.
But if you define an object because of its form and characteristics and not the amount of mass, then the object is the same but you have taken a part of it mass away.
Theo, weight =mass. gravity, here mass is fixed everywhere but gravity change in different places so weight change not mass.
yup weight changes and mass does not. That's why we're 1/3 our weight on the moon
weight is the product of mass × velocity w=m×v = m(v-u) but v=u+1/2at^ weight is a scalar quantity mass of an obj is the amount of particles that obj cont
mass is fixed always while weight is dynamic
Why does water wet glass but mercury does not?
thanks guys
Yusuf Shuaibu, for water the Adhessive force between water molecules and glass is greater than the cohessive force between it's own molecules but for Mercury the cohessive force will be greater in comparison with adhessive force. For this water wet glass but Mercury does not.

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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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