G is the gravitational constant = 6.67 x 10 -11 Nm 2 /Kg 2

Medical Physics

Bio-Mechanics

Force in and on the

BODY

Medical Physics

G is the gravitational constant = 6.67 x 10-11 Nm2/Kg2

Force of gravity

Medical Physics

Biomechanics and Force

Medical application of gravitational force:

* Following of blood against the gravitational force in varicose veins (vein near the surface of the skin that has become stretched and swollen with blood) in human legs toward heart.

* Deposition of calcium and other minerals on bones that enhance the bone health

* The body weight is the force exerted by the gravitational force downward

Medical Physics


Force on the bodyBody can be in two force statesStatic : when the body is in equilibriumDynamic (متحرك) : when the body is in acceleration

F1 F2

W

STATICin equilibrium all forces vector sum has to be ZEROSO,

F1 + F2 – W = zeroF1 + F2 = W

Torque (τ) = F x d

= force x perpendicular distance

(ساكن)

Medical Physics


Levers

Lever is “the simple machine consisting of a relatively rigid bar-like body that may be made to rotate about an axis”.

FulcrumForce

Resistance

FulcrumForce

Resistance

Fulcrum

Force

Resistance

1st1st 2nd 2nd 3rd 3rd

Medical Physics


Levers

Medical Physics


First Class Lever

In first class lever fulcrum (pivot point) is between force (effort) and load

In second class lever fulcrum is closed to the

weight (load)

A third class lever has the effort (force) between fulcrum and the load.

Medical Physics


Lever functions :

•Increasing force using of small force to move heavy load

•Increasing distance using force to move an object to longer distance•Increasing speed using force to increase the speed of an object•Moving the force from one place to another•Performance accuracy as we use tweezers to pick up a very small object•Avoiding danger ex. Heat, cold and poisons

How can you know the type of the lever

• Imagine how the lever works• Arrange the force, resistance and fulcrum

o If fulcrum is in the middle First classo If force of resistance is in the middle Second classo If force of effort is in the middle Third class

Medical Physics


The force x its arm = the resistance x its arm

The left side of the equation has to equal the right side

SO,• When force and resistance are equal, force and resistance arms are equal• When the force arm is longer than the resistance arm, force will be smaller than resistance• When the force arm is shorter than the resistance arm, force will be larger than the resistance

Example : calculate the resistance arm when a 10 N force push a lever resistance of 6 N, knowing that the force arm is 3 cm ?

10 x 3 = 6 x ?? = 5 cm

The lever law

Medical Physics


Force Force arm Resistance Resistance arm

5 10 25 ?

40 2 ? 8

3 ? 6 2

9 2 ? 6

Example : Give the missing parts of the table

Example : where you can put one square to equalize each color ?…………………………………………………………………………………………………………………………………………………………………...…………………………………………………………………………………

1 cm2 cm3 cm

Medical Physics


What is the most lever type conserve effort and has a mechanical benefit ?First Class Lever:

• If the force arm is longer than the resistance arm : force will be smaller than resistance SO, it has a mechanical benefit (conserve effort)• If the force arm is equal the resistance arm : force will be equal resistance SO, it has no mechanical benefit.• If the force arm is shorter than the resistance arm : force will be larger than resistance SO, it has no mechanical benefit

Second Class Lever• Force arm is always longer than resistance arm : force always smaller than resistance SO it has a mechanical benefit

(conserve effort)

Third Class Lever• Force arm is always shorter than resistance arm : force always larger than resistance SO it has no mechanical benefit (does not conserve effort)

Medical Physics


Lever application in the human body

First Class Second Class

Third Class

Medical Physics


Mechanical advantage of a force is its ability to do its work and it is related to the distance between the force and its arm :

Mechanical advantage =

Medical PhysicsUnit Coordinator : Dr. Bassem M. RaafatBiomechanics and Force

30 cm14 cm

5 cm

M

H

R

Forearm as a lever system

In biceps muscle :• The effort is the contraction power

of the biceps muscle to bring the arm upward.

• The weight (load) (W) in the palm is 30 cm apart from pivot point.

• Weight of tissue and bones of the hand and arm (H) is 14 cm apart from pivot point.

• The muscle effort (M) arm is 5 cm apart from the pivot point

W

Medical Physics


30 W + 14 H – 5 M = Zero30 W + 14 H = 5 MM = (30W +14H)/5 = 6W + 2.8H (Dyne)

In biceps movement the power M remain constant but the power arm is changed (elongated or shortened) to keep the power constant

Medical Physics


Forearm with plain position

α is the angle by which shoulder move or pivot

T sinα

Tcosα

Total torque = Στ = (18Tsinα) - (36H) - (72W) = zero

18Tsinα - 36H - 72W = zero

18Tsinα = 36H + 72W

Tension in the deltoid muscle (T) = (36H + 72W)/18sinα

(T) = (2H + 4W)/sinα

(H) is the weight of the arm,

(W) is the weight in the palm

(T) is tension in deltoid muscle

(T) = (2H + 4W)/sinα

Medical Physics


Spinal Pressure

Spinal lumber disc pressure is minimum while a person lying on his back. It becomes maximum when he sitting forward.

125 Kg/Sq. cm 125 Kg/Sq. cm250 Kg/Sq. cm 250 Kg/Sq. cm 250 Kg/Sq. cm 250 Kg/Sq. cm

123

Position of the body

Pre

ssure

Medical Physics


fF

N

W = mg = N

Friction force

f = µN = μmg

where N is the force and µ is the friction coefficient

Medical application of friction force :• Bones of joints are separated by anti-lubricants

(synovial fluid) to minimize bone friction.

• Saliva also act as anti-lubricants during food chew

• Lungs movement in chest

• Slippery mucus materials covering intestine during rhythmic (regular) motion to minimize the effect of friction force.

Exerted force Friction force

Direction of motion

Vertical reaction force, supplied by surface

Surface

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Dynamics

We have two cases of dynamic motion : • With constant acceleration or declaration

F = maWhere F is the motion force, m is the mass of moving object and a is the acceleration.

• With change in time and velocity

F =

where v is the velocity and t is the motion time

= m (vf - vi)/Δt

Medical Physics


Problems•A 60 Kg person (mass) walking at 1 m/sec (velocity) bumps into a wall and stops

in a distance of 2.5 cm in about 0.05 sec (time) what is the force developed on impact ?

F =

•A person walking at 1 m/sec (velocity) hits his head on a steel beam. Assume his head stops in 0.5 in about 0.01 sec. If the mass of his head is 4 kg, what is the force developed ?

F = = - 400 (Kg

m/sec2)

= - 1200 (Kg m/sec2)

05.0

)1(0 60)(V m f

t

Vi

01.0

)1(0 4)(V m f

t

Vi

Medical Physics


ViscosityGravitational force Fg= Buoyant force Fb + Retarding (friction) force F

R is the sphere’s radius, is the density of the particle, o is the fluid density, g is the

acceleration due to gravity, is the fluid viscosity coefficient. V = 2R2 g

V is the sedimentation rate by which particles of a solution is precipitated Medical application of sedimentation and centrifugation force:

• When red blood cells shape and size are changed in case of some diseases, blood sedimentation and centrifugation forces are changed, e.g. rheumatoid fever, rheumatic heart and gout in which RBCs are clump together increasing their effective radius and sedimentation rate.

• In hemolytic anemia and sickle cell anemia RBCs break and sedimentation rate is decreased.

Medical Physics


Types of Fluid motionFluid flow is generally broken down into two different types of flows, laminar flow and turbulent flow.

Laminar flow : is fluid motion in which all the particles in the fluid are moving in a straight line. For example, the thin layer of fluid in contact with the wall of a pipe travels very slowly due to the friction at the wall.Turbulent flow is an irregular flow of particles. For example, the fluid layers of increasing speed, reaching the maximum speed at the center of the pipe.

Both types of flow occur inside an object or outside an object, for example, fluid flow inside a pipe or fluid flow around a baseball.

Medical Physics


The Reynolds number is dimensionless quantity defined as the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions.

Reynolds Number (RN)

laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion; turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces

Laminar Flow Turbulent FlowReynolds Number

Low High

Medical Physics


Bernoulli's principleBernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid’s potential energy.

constant 2

1 2 ghP V

Where : P is the pressure is the densityg is the free acceleration constant (9.8)V is the speedH is the elevation

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G is the gravitational constant = 6.67 x 10 -11 Nm 2 /Kg 2