Lecture one part 2: forces on and in the body

Lecture one part 2: forces on and in the body

Friction in the body
The Walking:-
As the heel of the foot touch the ground a force is transmitted from the foot to the ground Fig (a), we can resolve this force into horizontal (Fh ) and vertical components. The max. Force of friction (F) is:
Fh = ?N
Fh= the horizontal reaction component supplied by frictional forces.
N= normal force supplied by the forces.
When the foot touch the ground Fh between the heel and surface prevent the foot from slipping forward fig(a).while when it leaves the ground , Fh prevents the toe from slipping backward fig (b).


Measurement of Fh:-
The value of the horizontal force component (Fh) of the heel as it strikes
the ground when a person is walking is given by: Fh ? 0.15W
W=mg (persons weight). When ? less than 0.15, his foot slips.
- The coefficient of friction in the boon joints is usually much lower than
in engineering type material. If a disease of the joint exists the friction
may become large, the synovial fluid in the joint involved in the lubrication.
Example :- The mass of (10 kg)is pulled along a horizontal surface at
constant velocity by a force 50N and which make an angle of 25? with
horizontal what is the coefficient of ?k between block (mass) and the
plane ?





Dynamic
The force on the body under the constant acceleration or deceleration of one dimensional motion. The Newton s second law, force equal mass times acceleration, can be written without vector notation as:-
F=ma where: F= The force (N, dyne) , m= The mass (Kg, g) , a= acceleration (cm /sec2 or m/ sec2)
Also F = The change of momentum (p) over a short interval of time (t).

?p= change of momentum =?(m?) , m=mass, ?= velocity of this mass
?t = interval of time
Example:-
A 60 Kg person walking at 1 m/sec bumps into a wall and stops in a distance of 2.5 cm in about 0.05sec what is the force developed on impact?
Solution:-
?(m?)= momentum before impact- momentum after impact




Accelerations can produce a number of effects such as

1- An apparent increase or decrease in body weight
2- Changes in internal hydrostatic pressure
3- Distortion of the elastic tissues of the body
4- If the acceleration become large may pool in various regions of the body, the location of the pooling depends upon the direction of acceleration. If a person is accelerated head first the lack of blood flow to the brain can cause blackout.
5-Tissue can be distorted by acceleration, if the forces are large, tearing or rupture can take place.
Pain symptoms of human subjected to vibrations from 1 to 20Hz
Each of our major organs has its own resonant frequency (or natural period) which depends on its mass and elastic forces that act on it. Pain or discomfort occurs if particular organ is vibrated strongly and its resonant frequency

Example:-
A 60 Kg person walking at 1 m/sec bumps into a wall and stops in a distance of 2.5 cm in about 0.05sec what is he force developed on impact?
Example:-
A person walking at 1 m/sec hits his head on a steel beam . Assume his head stops in 0.5 cm in about 0.01 sec . If the mass of his head is 4kg, what is the force developed ?
The centrifuge way:-



Is way to increase apparent weight, it is especially useful for separating in a liquid, the centrifuge works using the sedimentation principle. It speed up the sedimentation that occur at a slow rate under the force of gravity. In a laboratory centrifuge that uses sample tubes, the radial acceleration causes denser particles to settle to the bottom of the tube, while low-density substances rise to the top
Stock law
Let us consider sedimentation of small spherical objects of density P in a solution of density P? in a gravitational field(g). We know that falling objects reach a maximum terminal velocity due to viscosity effects. Stock has shown that for a spherical object of radius(a), the retarding force Fd and terminal velocity (?) are related by :-


Stokes law makes the following assumptions for the behavior of a particle in a fluid:
•?Spherical particles
•?Homogeneous (uniform in composition) material
•?Smooth surfaces
•?Particles do not interfere with each other.
when the particle is moving at a constant speed, the Fd is an equilibrium with the difference between the downward (Fg)and the upward buoyant force (FB) :

H.W : calculate the terminal velocity ?


In some forms of disease such as rheumatic fever, rheumatic heart disease, and gout, the red blood cells clump together and the effective radius increases; thus an increased sedimentation velocity occurs.
In other diseases such as sickle cell anemia, the red blood cells change shape or break. The radius decrease; thus the rate of sedimentation of these cells is slower than normal.
Hematocrit (packed cell volume PCV) is the percent of red blood cells in the blood.


Since the sedimentation velocity is proportional to the gravitational acceleration, it can be greatly enhanced if the acceleration is increased. We can increase g by means of a centrifuge, which provides an effective acceleration geff

Where f is the rotation rate in revolution per second and r is the position on the radius of the centrifuge where the solution is located.
Hematocrit depends upon:
• Radius of centrifuge.
• Speed of centrifuge.
• Duration of centrifuge.
The medical use of terminal velocity:-
* In some forms of disease such as :
1 - rheumatic fever
2 - rheumatic heart disease
3 - gout
the RBCs clump together and the effective radius increase ; thus
an increased sedimentation velocity occurs
In other disease such as :
1 - hemolytic jaundice .
2 - skill cell anemia
the RBCs change or break , the radius decrease , then the rate of
sedimentation is slower than normal
NOTE :
A related medical test that also depend on the ? = ?2a?^2/9? ?(?-?_(0)) equation indetermination of the hematocrit (the present of RBCs in blood). Since v increase with g it can be greatly enhanced if g increase. We can increase by means of a centrifuge :
geff = 4 ?2 f 2 r
where f = in the rotation rate of revolutions per second ( rbm )
r = in the position on the radius of centrifuge
A normal hematocrit is 40 - 60 .
a lower value than 40 indicates animia .
a high value than 60 indicates poly cythemia
Polycthmia ??( high number of RBCs in the blood )
Prove the terminal velocity (sedimentation velocity) is equal to :
? = ?2a?^2/9? ?(?-?_(0)) ?

Find the effective acceleration at radius r = (22) cm for a centrifuge rotating at (3000) rpm ?