ch 10, bio mechanics in bio medical engineering

7/28/2019 Ch 10, Bio Mechanics in Bio Medical Engineering

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BIO-MEDICALENGINEERINGGUIDE.INC

2013

[BIO-MECHANICS IN BIO-

MEDICAL ENGINEERING,

CH-10: LINEAR-

KINEMATICS-OF-

HUMAN-MOVEMENT:-]MOHAMMAD-SIKANDAR-KHAN-LODHI

[ 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 Y S I K A N D A RK H A N - L O D H I


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[BIO-MECHANICS IN BIO-MEDICAL ENGINEERING, CH-10: LINEAR-

KINEMATICS-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 Y

S I K A N D A R - K H A N - L O D H I ]

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Table of ContentsCHAPTER 10 : ................................................................................................................................................ 3

LINEAR-KINEMATICS-OF-HUMAN-MOVEMENT:- ......................................................................................... 3

KINEMATICS: ............................................................................................................................................. 3

UNIT-OF-DISTANCE-AND-DISPLACEMENT:- .............................................................................................. 5

SPEED AND VELOCITY:- ............................................................................................................................. 5

SPEED:- ...................................................................................................................................................... 5

VELOCITY:- ................................................................................................................................................. 6

DIAGRAM: Fig # 10.2 ............................................................................................................................. 6

ACCELERATION:- ....................................................................................................................................... 8

LINEAR-ACCELERATION:-........................................................................................................................... 8

ACCELERATION IS ZERO ( a= 0 m/s2 ):- .................................................................................................... 11

PROJECTILE:- ........................................................................................................................................... 11

Fig # 10.4 : ........................................................................................................................................... 11

FACTOR THAT EFFECTING THE PROJECTILE MOTION:- ............................................................................... 13

Fig # 10.5 : ........................................................................................................................................... 13

Fig # 10.6 VERTICAL TRAJECTORY AT 90 DEGREE ANGLE WITH RESPECT TO [ w.r.t ] X-AXIS: ........... 15

FIG # 10.7 OBLIQUE-TRAJECTORY :- ................................................................................................ 16

Fig # 10.8 [ Horizontal Trajectory [ at zero degree angle with respect to x-axis]. .............................. 17

Fig # 10.10 : ......................................................................................................................................... 19

3. RELATIVE-HEIGHT OF PROJECTILE:- ................................................................................................ 19

Fig # 10.11 ........................................................................................................................................... 20

Fig # 10.12 ........................................................................................................................................... 21

Fig # 10.13 : ......................................................................................................................................... 22


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CHAPTER 10 :

LINEAR-KINEMATICS-OF-HUMAN-MOVEMENT:-

KINEMATICS:

In the Kinematics wecan described the Motion [

under the influence of forces ] of a Mechanical-system.

The Kinematic Quantities (i-e)

1.Displacement, distance.2.Velocity.3.Acceleration.

DISTANCE:-

Definition : The Distance are define as when a body covered ortravels from the actual path, so the measured length covered by

the body of that actual path is known as Distance.

The Distance has no any direction but it has its magnitude.Therefore, the Distance is a Scalar-Quantities.

DISPLACEMENT:-


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The term Displacementcan be define as : The Displacement isthe shortest distance covered by the body from its starting

position towards its final position.So, the displacement is a Vector-Quantities because , its shows

us he shortest magnitude of the body covered nd the direction

from its initial o its final position.

1.There is a case in which a runner completed its 2-labs so, eachlabs is about 800m, so, the distance covered by the runner is

about ( [800+800]m=1600m ) and the displacement covered is

zero, because the initial and final position of runner is same.

Diagram: Fig # 10.1


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UNIT-OF-DISTANCE-AND-DISPLACEMENT:-

The Unit of distance and displacement is same as the unit of length .

That is meter ( In metric form)

Km = 1000 m => [.] mx10+3 .Centimeter = 1/100 m => [] mx10-2 .Millimeter = 1/1000 m => [] mx10-3 .

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

SPEED AND VELOCITY:-

SPEED:-

The distance covered by the body per that time which has taken to

covered that distance, is known as speed.

Its a scalar quantities, [ its has no involved any direction but it has

involved the magnitude because its a scalar quantities ].

{-> Speed = S = Distance/ [ Change in Time ] };[

];

Unit:

[

];

-----------


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VELOCITY:-

DIAGRAM: Fig # 10.2

The Displacement or ( Change in Position ) that occursduring a given period of time .

[ V = Displacement/Change in time ];

In the description of Velocity must include the indication ofboth direction and magnitude of the motion.

There are two direction of that motion will be present , so ifthe direction of that motion is positive with there magnitude

so, the velocity is positive.


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DIAGRAM EXPLANING POSITIVE AND NEGATIVE DIRECTION:-

And , If the direction of that motion is negative with theremagnitude , than the velocity is negative as shown in above

diagram.

UNIT OF VELOCITY:-

The unit of velocity is same as unit of speed.

[-> V = displacement/change in time ];

[ ];

Unit :


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[

];

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

ACCELERATION:-

LINEAR-ACCELERATION:-

The Linear-Acceleration is define as following

The rate of change in velocity is called as a Acceleration.

Formula:

[

];


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Unit :

[

];

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

Example:

Consider a body which can accelerated in a constant acceleration.

That is : At the initial time when race will be started its initialvelocity is 0m/s so, its acceleration is also 0m/s

2.

After the one second when this car increased its velocity about 2m/s , then its acceleration is 2m/s

2.

Than , after the 2nd second when this car or body increased itsvelocity about 4m/s, now , this car or body gain a constant

acceleration that is 2m/s2

.

Than after the third second , when this car or body increased itsvelocity about 6m/s , so in the third second its velocity is 6m/sand its acceleration will be remain constant about 2m/s

2.

Key-point: The Acceleration of a car or body is remain constantbecause the difference of increased velocity in each seconds will

remain constant [ or same ] that is [ 2m/s2 => its the constant

acceleration of Car or body.

Q) If a car which has its variable ( increase or decrease ) its acceleration

, so how we expressed it as followed:

That is :

SOLUTION:


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Page 10-OF-22

Let, consider a car , at initial time its at a resting position, than , itwill be speed up , will a variable acceleration.

Than , in 1

st

second its velocity is about 2 m/s, and itsacceleration is about 2m/s

2.

[

];

Now,

In the 2nd -second its velocity will be increased is about 10m/s ,so its acceleration will be increased is about

[

];

So,

Its Acceleration is increased is about 8m/s2 in the 2nd second.Than , On the 3rd second, its velocity will be increased about

25m/s.

Than, its acceleration will be increased is about on that 3rd-secondis about ,

[

];

Now, if this car velocity cause to slow down , than on the 4thsecond its velocity will be decreased is about 10m/s.

Than its acceleration will be decreased is about ,[

];


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

ACCELERATION IS ZERO ( a= 0 m/s2 ):-

When ever the car is running than its velocity will be same in each

second , than its acceleration will become zero.

That is

Example:-

[

];

--------------Finished-here----------------

PROJECTILE:-

Fig # 10.4 :


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Discription:

The projectile is a free falling bodies , which experiencesthe gravitational and air resistance forces during the

performances of projectile motion.

It make a certain some angle with the horizontal surface.That is :

[ ];

When ever any body which performed this motion is called aprojectile motion.


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Those body which perform this projectile motion are called asProjectile.

FACTOR THAT EFFECTING THE PROJECTILE MOTION:-

There are three factor that determined the Projectile motion.

1.Projection angle.2.Projection speed.3.Relative height of projection.

Fig # 10.5 :


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1.PROJECTION ANGLE:-The projectile trajectory shape ( or flying path shape ) depend

upon , the projection angle (or direction (slope) of theprojection).

Key-Point: ANGLE OF PROJECTION [ ] : The direction [ ] atwhich the body is projected with respect to the horizontal

surface .

There are three different types of projectile trajectory shapeare present , so these three different types of projection

trajectory shape are formed by the three different possibleprojection-angles .

That is

i. When projection angle is 90 with respect tohorizontal surface ( x-axis ) then the shape of

Projectile trajectory is vertical up and down ward

direction. That is see in below fig # 10.6


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Fig # 10.6 VERTICAL TRAJECTORY AT 90 DEGREE ANGLE WITH

RESPECT TO [ w.r.t ] X-AXIS:

2.When projection angle is nearly between about ( 0 to 90 ) withrespect to horizontal surface (x-axis) , than the shape of projectile

trajectory is like a parabola. That is see in below fig # 10.7 ;


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FIG # 10.7 OBLIQUE-TRAJECTORY :-

3.When projection angle is about zero ( ) with respect tohorizontal surface (x-axis) { or the direction of projectile is parallel

with horizontal surface {x-axis}, than the shape of projectile

trajectory is like a one-half of Parabola as shown in below fig #

10. 8 .


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Fig # 10.8 [ Horizontal Trajectory [ at zero degree angle with

respect to x-axis].

2.PROJECTION SPEED:-The projection speed determined the length [ or size ] of the projection

trajectory. That is :

Example No 1 :

When a body is projected up-ward , vertical direction , than the initial

speed ( projection speed ) determined the maximum height obtained

by the projectile.


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fig # 10.9

{:. Trajectory = Path = or flying Path };

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

Example No 2 :

When the body is projected at a oblique angle with respect to x-axis

between [ ] . than at this condition the speed of projectiledetermined the maximum height obtain by the projectile [ which is

called as Apex ] and the maximum horizontal distance covered by the

projectile determined by the projectile angle , as shown in below fig #

10.10:


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Fig # 10.10 :

3.RELATIVE-HEIGHT OF PROJECTILE:-The Relative-height-of-Projectile is define as its the difference

in vertical distance [ or height ] in which when the a projectile will

be projected at initial time than this projectile will be land on its

final position .The difference between this two position height is known as

Relative height of projectile.


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Fig # 10.11


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Fig # 10.12

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

Q ) SAMPLE PROBLEM:

A swimmer crossing a lake that is 0.9km wide in 30 minute ? what was

his average velocity? Can his average speed be calculated?

Solution:

Sketch :-

Now we sketch the General idea which given on this question that is

shown in fig # 10.13 below;


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Fig # 10.13 :

DATA :

Displacement covered by the swimmer is that [ 0.9 km = d ] Total time

covered by the swimmer for covering the lake => [ T = 30 min ];

Required:-

[

];

[

];

FOR AVERAGE VELOCITY :-


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[

];

[

];

Also

FOR AVERAGE SPEED:-

We do not be able to calculate the average speed of the swimmer,

because the actual distance covered by the swimmer were not given;

----------------Finished-here---------------

-----------CH-10 , on Bio-Mechanics in Bio-medical engineering finished

here-------------

XMUHAMMAD-SIKANDER-KHAN-LODHI

OWNER OF MY PERSONAL NOTES Tuesday, June 18, 2013


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ch 10, bio mechanics in bio medical engineering

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