ch-12 , on bio-mechanics in bio-medical engineering

7/28/2019 Ch-12 , On Bio-mechanics in Bio-medical Engineering

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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-

12 , LINEAR-KINETICS OF

HUMAN MOVEMENT: ]TEXT-BOOK: BIO-MECHANICS BY SUSAN-JHALL , 3rd

edition.

6/19/2013

BIO-MEDICAL ENGINEERING GUIDE.INC

MOHAMMAD-SIKANDER-KHAN-LODHI

MY BLOG :www.medical-image-processing.blogspot.ca
http://www.medical-image-processing.blogspot.ca/http://www.medical-image-processing.blogspot.ca/http://www.medical-image-processing.blogspot.ca/http://www.medical-image-processing.blogspot.ca/


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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-12 , LINEAR-

KINETICS OF HUMAN MOVEMENT: ]

[ W W W . M E D I C A L - I M A G E - P R O C E S S I N G . B L O G S P O T . C A B YS I K A N D A R - K H A N - L O D H I ]

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ContentsLINEAR-KINETICS-OF-HUMAN-MOVEMENT:- ............................................................................................... 3

MECHANICAL-BEHAVIOR-OF-BODIES-IN-CONTACT:- ............................................................................... 3

FRICTION-FORCE:- ..................................................................................................................................... 3

See in below Fig # 12.1 . ....................................................................................................................... 4

Fig # 12.2 [ GRAPHICAL-REPRESENTATION ] :- ..................................................................................... 5

NORMAL-REACTION-FORCE (R) :- ............................................................................................................. 7

Diagram : [ fig # 12.3 ] .......................................................................................................................... 7

COEFFICIENT-OF-FRICTION [ ]:- ............................................................................................................. 8MOMENTUM :- ......................................................................................................................................... 9

IMPULSE :- ............................................................................................................................................... 10

IMPACT : .................................................................................................................................................. 11

1. PERFECTLY-ELASTIC-IMPACT:- ........................................................................................................ 11

Fig # 12.4 [Perfectly Elastic impact ]: .................................................................................................. 12

2. PERFECTLY PLASTIC IMPACT:- ....................................................................................................... 12

Fig # 12.5 [ perfectly Plastic Impact ]. ............................................................................................... 13

CASE-I : .................................................................................................................................................... 14

Fig # 12.6 [ Case- I ]: ............................................................................................................................ 15

Case-A : ................................................................................................................................................... 15

Case-B :.................................................................................................................................................... 16

Diagram: fig # 12.7 [1m = Drop-Hight , and some Bounced hight ] : .................................................. 18

WORK, POWER AND ENERGY RELATIONSHIP:- ...................................................................................... 21

WORK:- .................................................................................................................................................... 22

POWER :- ................................................................................................................................................. 22

Diagram:- [ fig # 12.8 ] ........................................................................................................................ 24

ENERGY :- ................................................................................................................................................ 25

a. STRAIN-ENERGY:- ............................................................................................................................ 27

GENERAL-CONCEPT:- .............................................................................................................................. 28


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LINEAR-KINETICS-OF-HUMAN-MOVEMENT:-

MECHANICAL-BEHAVIOR-OF-BODIES-IN-CONTACT:-

Whenever a body which cause to connected with other

body during motion then a friction force will be generated between

these two bodies against the direction of motion.

FRICTION-FORCE:-

The friction force will be produced when the twobodies will be contact during the motion and thedirection of both bodies are opposite .

Then , when these bodies will be contact with eachother so, a force will be generated at the contacting

surfaces of bodies , which is in the opposite

direction of motion.

The friction force cause to stop the motion forcewhich cause to perform the motion.


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See in below Fig # 12.1 .


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Fig # 12.2 [ GRAPHICAL-REPRESENTATION ] :-

Consider a box which are lie on the horizontal plane that is a tablein (above) fig #1 so, there are two forces act on it the first one is

the box weight itself and the opposite force by the horizontal

plane by table is reactant force [ R ] .

These both forces are opposite in direction but equal inmagnitude which act on that static position box and keeping the

bok in static state then.


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Now see fig 12.1 (fig # 2 ) in this figure we applied a small externalapplied force [ Fa ] to the box , then this force will produced a

opposite equivalent small friction force which cause to canceltheir effect of small applied force [ Fa ].

In this way we increased the magnitude of the applied force [ Fa ]which cause to produce a opposite indirection but equal in

magnitude of this static-friction force on the box .

There is a point will be come where at that point (on abovegraph ) the value of this Static-friction force will become

maximum,This point is known as Maximum-static-friction force point (on

the above graph).

Until this maximum-static friction point , the value of Appliedexternal-force and value of the static friction force will directly

proportional to each other,

Then, after , when we increase the value of applied force justbeyond the maximum-static-force-point ( maximum static

friction force point ) than the value of friction force will be goes

down and become a constant value but just below the

maximum-static-friction-point.

At that point the friction is the dynamic friction and its known asKinetic-friction point so, in this kinetic-friction point , there is

a movement will be occurs on the static box .

Then, if we increased the external applied force then there is aconstant kinetic-friction force which will act on the box

continuously during the motion of the box .


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NORMAL-REACTION-FORCE (R) :-

Statement: The Reaction force which are the major

factor which effecting the magnitude of friction force is called theReaction-Force [ R ] .

Process: When two bodies are come to contact with each other at rest

, then the Reaction force * R + act on the contact surfaces of these two

bodies .

Key-point when an box is placed on smooth horizontal surface at

rest then there is a weight of that box act on the horizontal smoothsurface , also the equal in magnitude but opposite in direction , the

reaction force [ R ] act on the box.

Diagram : [ fig # 12.3 ]


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COEFFICIENT-OF-FRICTION [ ]:-The Coefficient of friction * + define as ,when ever the two

bodies come in contact during motion then there is a mechanicaland molecular interaction will be occur between two contacting

surfaces , this mechanical and molecular interaction is known as

Coefficient of friction *+ , so, according to above graph *friction [ y-axis] & applied force [ x-axis ] Graph ] .

Inthis graph there are two types of friction are occur when weapplied the external force. That is

1.Maximum-Static-Friction[ Fm+ .2.Kinetic-Friction [ Fk ].

There are two coefficient that is :

a.Coefficient of static friction [ ]..b.Coefficient of Kinetic-friction [ ] .1.The magnitude of maximum static friction force is depend upon

the coefficient of static friction and reactant and weight force.

That is

a)Fm = max-static friction force =>[ ];

b)Fk = Kinetic friction force =>[[ ];

So, when ever the two bodies will come in contact with each

other so, then [ ];------------------------finished-here-----------


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Q ) WHY KINETIC FRICTION FORCE ( FK) IS ALWAYS SMALLER

THAN MAXIMUM-STATIC-FRICTION-FORCE [ Fm+ :-

Because the coefficient of kinetic friction [] is alwayssmaller than the coefficient of static friction [ ] .

Due to this the magnitude of kinetic friction force [ Fk ] , isalways less than the magnitude of maximum static friction

force [ Fm ].

Mathematically:-

When [ ];Than [ ];KEY-POINT the synovial-fluid which present in between the two

articulated surfaces of two bones in the joint so this fluid cause to

reduced the friction between the articulated surfaces of these bones .

----------------finished-here---------------

MOMENTUM :-

The momentum is generally used to measured the motion of anany object so, will be measured of any object under the certain

motion .

By taking the product of the mass of that object which performedthe certain motion & velocity of that object so , then we can

calculated the momentum , its denoted by M .Momentum is a vector quantity , and momentum is used to

measured the motion of any object.

Mathematically:


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[ ];UNIT :-

[ ---------------finished-------------

IMPULSE :-

Its the product of forces and time interval over which the force act on

any object .

Mathematically :-

[ ];Unit :

[ ];Example:

[ ];[ ];

[ ];[

];

[ ];Or

[ ];


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{:. =change in Momentum }[

];

The impulse is equal to the change in momentum .

-------------finished-here----------

IMPACT :

Impact is defined as the collision of two bodies over a extremely

small time interval , and during this interval this two bodies

exerted relative large forces from each other .

EXPLINATION:

When two moving bodies come in contact with each other so,during the extremely small time interval at which they comes in

contact these two bodies will exerted ( released ) forces on each

other .

There are two types of impact are present in bio-mechanics .

That is :

1.Perfectly Elastic impact.2.Perfectly Plastic impact.

1. PERFECTLY-ELASTIC-IMPACT:-Whenever two bodies will be collied [or hit each other ]

then they regain their velocity [I mean initial velocity before the


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impact ] which are present before the impact of these two bodies is

called perfectly elastic impact *see in below fig # 12.4 +.

Fig # 12.4 [Perfectly Elastic impact ]:

2.PERFECTLY PLASTIC IMPACT:-When the two bodies will come in contact , then both or one of

these two bodies , should be deforms from its original shapeand they do not regain its original shape .

And the velocity after the collision of these two bodies becomeszero , then this event is called as Perfectly Plastic-Impact .


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Fig # 12.5 [ perfectly Plastic Impact ].

COEFFICIENT-OF-RESTITUTION [ e OR c ] :-

Well the Coefficient-Of-Restitution *e or c + is the particleapplication of the perfectly plastic and perfectly elastic

impact.

This Coefficient-Of-Restitution * e or c + is the any number inbetween [ 0 to 1 ] .

We can easily analysis that , if the Coefficient-Of-Restitution [ eor c + is near to 1 so, then this impact is called as Perfectly-

Elastic impact .


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if the Coefficient-Of-Restitution * e or c + is near to 0 so, thenthis impact is called as a Perfectly-Plastic impact .

we have two condition in which the two object will come incontact in the Impact, which are explain in following Case-I ,

Case-A, Case-B and Case-II .

that is :

CASE-I :

In this condition , the impact will occurred by the collision of twomoving object , they were comes in contact .

It will be calculated by as following formula in eq-A, also see fig #12.6 below.

[ ];Where :

u1 and u2 = Velocity of object with mass m1 and m2 just beforethe Impact ( before the collision ) of these two object with massm1 and m2 .

V1 and V2 = velocity of that same object with mass m1 and m2just after the Impact ( after the collosion) , of these two object

with mass m1 and m2 .


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Fig # 12.6 [ Case- I ]:

Note :-

Case-A :

The Coefficient of restitution of any Elastic-Impact isnearly to 1 , because in the Elastic-Impact the velocity of

two bodies after the impact is approximately slightly lower

then the velocity of these two bodies just before the impact

.


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Let consider the two bodies in which one body is in motionwith mass [ m1 ] and the other 2

ndbody lies in a resting state

with mass [ m2 ].The velocity of 2nd body with mass [ m2 ] which lies in the

resting state , and its velocity is zero before the impact , its

a fixed ridged body so it velocity tend to be zero just after

the impact .

When the 1st moving body with mass [ m1 ] which cause tohit [or collide ] with the 2

ndstationary fixed body with mass [

m2+ , so, then if this impact is Perfectly Elastic so, thenthere Coefficient of restitution is near to 1 .

Case-B :

In this case there are two bodies , now if these bothbodies will be collide ( impact ) then as the result of

it the both or any one of these two bodies becomes

deformed from its original shape and also there

velocity just after the impact become to zero then it is

the Perfectly-Plastic-Impact .

The Coefficient-Of-restitution * e OR c + which causeto measure [ or examine ] what types of this impact

its , so , if the velocity of these two bodies [ or any

one body ] become zero just after the impact so, its

coefficient of restitution is equal to nearly to zero*0+ and this type of impact is known as Perfectly

Plastic-Impact .

Now ,


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CASE-II :-

In this condition where a moving body with mass [ m1 ] cause tocollide [ or hit ] on a stationary body with mass [ m2 ].

Before the impact [or collision ] the velocity of the moving body isu1 so, if the 2

ndbody with mass [ m2 ] is a fixed structure then we

can calculated the Coefficient-Of-Restitution * e OR c + just

after the impact by the square root on the ratio ofbounced

height over the drop height which is given below.

[ ]; its the formula of Coefficient-Of-Restitution * e OR c +.

So, if the coefficient of restitution is nearly to be zero, so thisimpact is called as Perfectly-Plastic-Impact .

So, if the Coefficient of Restitution is nearly to 1 then thisimpact is called as Perfectly-Elastic-Impact.

[ ];

[ ];

[ ];


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Diagram: fig # 12.7 [1m = Drop-Hight , and some Bounced hight

] :

Key point -> the increased the velocity before the impact and also

increase the internal molecular temperature of the impacted bodies

cause to increase the Coefficient of restitution* e OR c +.

------------finished-here-------------

COEFFICIENT OF RESTITUTION *e OR c +

SAMPLE-PROBLEM:-


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Q) A basket ball is dropped from a height of about 2m on the floor, if

the coefficient of restitution between the ball and the floor on the

impact 0.9 , so,

a. How , higher will the ball bounced ?

b. also, explained what type of impact its ?

c. and which condition it form the previously explained two condition

?

SOLUTION :-

DATA :-

Drop-Height -> [ ];The Coefficient Of Restitution of the Impact is => * ];Also

Required :

Hb = Bounced Height = ?What type of Impact its = ?Which condition its = ?

SOLUTION:

Its those condition in which there is a body is in static condition and theother 2

ndbody in the motion .

On this condition we used the following formula to determined the

coefficient of Restitution.


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FORMULA:-

[

];

So,

Part-b :- [ what type of Impact its ]:-

Its given that the coefficient of restitution to the particular Impact

is [ e = c = 0.9 ] , so

As , we see that * e = 0.9 + is approximately nearly to 1 , so this typeof Impact is called as Perfectly Elastic Impact .

FOR PART-a

How higher the ball will bounced?

Solution:

The ball bounced back nearly to the original falling position from whereit [ ball ] drop on the floor.

FOR Hb :-

Where :

e = c = 0.9 , Hd = 2m ,

FORMULA :

[

];Put the value and get the answer .


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[

];

[ ];

[ ];

[ ];..

[ +; its the bouncing height of the ball , so the Impact iscalled as Perfectly-Elastic in its nature.

-----------finished-here-------

FACTOR THAT EFFECT THE COEFFICIENT OF RESTITUTION ( e OR c ) :-

1)The factor are the nature like Gravity-force, the body weight ,size , shape and material characteristic of the both

Impacted-Bodies.

2)Kinematics of moving system.3)Kinetic .4)Effect of increasing the temperature and velocity which cause to

increase the coefficient of restitution *e OR c +.

--------------finished-here-----------

WORK, POWER AND ENERGY RELATIONSHIP:-


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WORK:-

The work is the product of force into displacement .

FORMULA:

[ = Force.displacement ];Unit :-

Joules = N-meter = Newton-Meter.There are two types of work that is :

1)Positive-Work.2)Negative-Work.

1)POSITIVE WORK:- when we applied force on any object then thisobject move with in the direction of applied force , so this is called

as Positive-Work.2)NEGATIVE-WORK:- When we applied the force on any object then

the object move in the opposite direction as compare to the

direction of the applied force , this type of work is known as

Negative-Work.

----------------finished-here------------

POWER :-The power is the capacity of system , to produced the certain amount

of mechanical work over the interval of time is known as the Power

of that system.

MATHEMATICALLY:


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[ ];[

];

FORMULA:-

[ ];--------------finished-here------------

SAMPLE-PROBLEM:

Q) A 580 N- person runs up to 30 stairs of riser, each stairs height is

about (25cm) , so this person runs the total 30 stairs within 15 seconds,

1)How much work is done ?2)How much Mechanical power is generated?

----------------

A 580 V person runs up a flight of 30 stairs of riser ( height) of 25cm

during a 15-second period

a.How much mechanical work is done ?b.How much mechanical power is generated?

------------


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Diagram:- [ fig # 12.8 ]

Solution:-

DATA:-

[ ];[ ];[ ];FOR MECHANICAL WORK :-

[ = Force.displacement ];


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{:. Displacement = d = ht = ht = 750 cm }

{ d = ht = 750 cm }

{ F = wt = 580 N }

[ = Force.displacement ];[ ];[ ];FOR MECHANICAL POWER:-

[ ];[ ];[ ];------------finished-here---------------

ENERGY :-

The energy is means that , the capacity ( or ability) of any body to

performed work is known as energy .

There are following types of energy are as followed that is

1.Mechanical-Energy .2.Electrical Potential energy .3.Thermal energy

1.MECHANICAL ENERGY :-


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The mechanical energy are those energy by which it can performed the

some mechanical work, there are two types of mechanical energy are

present.

That is

a.Kinetic-Energy .b.Potential-Energy.

a.KINETIC-ENERGY:-

As we know that Kinetic-energy will be developed when thebody performed some kind of motion .

If the body become in resting state where its [ body ] velocity isequal to be zero [ V = 0 ] then its motion will become zero.

So, this body is not remain in the state of motion so, here theKinetic-energy [ K.E ] of the body becomes zero [ K.E = 0 ].

As we know that the Kinetic energy is equal to the half of mass ofbody into and the velocity square .

So, where the mass of body is a constant , there is only one factorthat is velocity .

If we (increased or decreased ) the velocity of the body so, itcause to increased or decreased the K.E of the body .

FORMULA:-

[ ];b.POTENTIAL-ENERGY [P.E]:-


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As we know that the potential energy is depend on the position ofthe body with respect to ground .

If we want to increased the P.E so we displaced that object fromthe ground with certain height .

At that height we can calculated the Potential-Energy of thatobject by the following formula.

[ ];[ ];{:. F = m.a }

[ ]; answer.----------------finished-here-----------

Where :

Mass = constant of a body .

Acceleration due to gravity = constant of the earth = 9.81 m/s2 =ag .

h = variable .--------------finished-here-----------

There is a another type of potential energy is called that is : Strain-

energy.

a.STRAIN-ENERGY:-The strain energy is a type of P.E its called as Elastic-energy .

FORMULA:


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[ ];Where :

k = Spring constant.x = distance over which material of spring is deformed.

-------------------

GENERAL-CONCEPT:-

Strain-energy is those energy in any elastic material which help it when

these structure cause to deformed , so after that this body cause toreturn it Original-shape .

----------------finished-here-------

2.ELECTRICAL-POTENTIAL ENERGY:-If those energy [ E.M.F ] which provide by the voltage source to unit

positive test charge to flow through the circuit.

3.THERMAL-ENERGY :-The Thermal-Energy is the heat energy of any object .

Example : if we give the heat to any material or any gas so, then the

internal molecular energy [ ] will be increased.------------------finished-here------------

-------------------CH-12, ON BIO-MECHANICS IN BIO-MEDICAL

ENGINEERING FINISHED-HERE-----------------


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XMUHAMMAD-SIKANDER-KHAN-LODHIOWNER OF MY PERSONAL UNIVERSITY NOTES Wednesday, June 19, 2013


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ch-12 , on bio-mechanics in bio-medical engineering

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