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General Physics course

(PHY 101)

Dr. Zyad Mohammed

Email : zmohammed@inaya.edu.sa

Web site:zyadinaya.wordpress.com

mailto:zmohammed@inaya.edu.sa

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"Why should I study physics?" Sometimes asked with emotional overtones ranging from anguish to anger, this is one of

the questions most frequently heard by physics teachers. It seems appropriate therefore to

begin this book by attempting an answer. One reason this question is asked so often is that

many people who have not studied physics—and some who have—lack a clear notion of

what physics is. Dictionaries are not much help. A typical short dictionary definition says

that physics is the branch of science that deals with matter, energy, and their interactions.

This is vague and general enough to include what is usually considered to be chemistry; in

any case, it does not give any real feeling for what is involved. Longer dictionary entries

usually expand the definition by noting that physics includes subfields such as mechanics,

heat, electricity, and so forth. They give no clues as to why some subfields of science are

included and others are not. A better approach to defining physics is to ask what physicists

are concerned about. Physicists attempt to understand the basic rules or laws that govern

the operation of the natural world in which we live. Since their activities and interests evolve

with time, the basic science called physics also changes with time. Many of the most active

contemporary subfields of physics were undreamed of a generation or two ago. On the other

hand, some parts of what are now considered to be chemistry or engineering were once

considered to be physics. This is because physicists sometimes gradually abandon a field

once the basic principles are known, leaving further developments and practical applications

to others.The fact that physics deals with the basic rules governing how the world works

lets us see why people with varied interests may find the study of physics interesting and

useful. For example, a historian who wants to understand the origins of our contemporary

society will find significance in the story of the development of physics and its relationship

to other human activities. Similarly, a philosopher concerned about concepts of space and

time will profit greatly from understanding the revolutionary twentieth-century advances in

physics. However, since we have written this book primarily for students majoring in the

sciences, we have not stressed the historical or philosophical aspects of physics. Instead, we

have tried to make clear in every chapter the connection between physics and the other

biological and physical sciences. Perhaps the most obvious impact of physics on science is

at the level of instrumentation. A knowledge of physics helps in the intelligent use of

everything from light microscopes and centrifuges to electron microscopes and elaborate

radiation detection systems used in nuclear medicine. Physics also enters in more

fundamental ways. The physical laws governing the behavior of molecules, atoms, and

atomic nuclei are the basis for all of chemistry and biochemistry. Physiology offers many

examples of physical processes and principles: diffusion within cells, the regulation of the

body temperature, the motion of fluids in the circulatory system, and electrical signals in

nerve fibers are just a few. In comparative anatomy, the physics associated with an

anatomical feature often helps to clarify the evolutionary process.

Athletic activities ranging from running and jumping to karate can be studied and sometimes

optimized with the aid of physical principles.

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Physical principles explain the motion of the atmosphere, and the structure of astronomical

objects. In the course of developing and illustrating the basic principles of physics, we

discuss all these applications and many others. A few remarks about how one studies

physics may be helpful. More than any other science, physics is a logical and deductive

discipline. In any subfield of physics, there are just a few fundamental concepts or laws

derived from experimental measurements. Once one has mastered these basic ideas, the

applications are usually straightforward conceptually, even though the details may

sometimes become complicated. Consequently, it is important to focus one's attention on

the basic principles and to avoid memorizing a mass of facts and formulas. Most of the basic

laws of physics can be expressed rather concisely in the form of mathematical equations.

This is a great convenience, since a tremendous amount of information is implicitly

contained in a single equation. However, this also means that any serious attempt to learn

or apply physics necessitates a willingness to use a certain amount of mathematics. High

school algebra plus a bit of geometry is adequate for everything covered in this book, but a

reasonable level of facility is required. A student who has become rusty at these

mathematical skills may want to begin with the Mathematical Review in Appendix B. One

post-high school mathematical technique, differentiation, is introduced in the first chapter.

However, except in definitions, its use is restricted to a few derivations located in the

Supplementary Topics. None of the exercises or problems requires this mathematical

tool. In summary, we believe the student will benefit in two major ways from studying

physics. The student will gain an understanding of the basic laws that govern everything in

our world from the subatomic to the cosmic scale and will also learn much that will be

important in his or her work in the sciences. The study of physics as a basic science is not

particularly easy, but we believe it is rewarding, particularly for students planning further

training in related sciences. We hope that all who use this book will agree.

J. W. K

M. M. S

From book : Physics by Kane and Sternhiem. Publisher Wiley; 7 edition (March 17,

2006) ISBN-13: 978-0471663157

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Course Description: This course serves as an introduction to the basic principles of physics and also this

course is designed for students in Health Science to enable them to appreciate the

basic concepts of Physics which are relevant to their further studies.

Student Learning Outcomes

Upon completion of this course, the students are expected to:

1. understand the essential elements of physics needed by premedical students.

2. Recognize the basic principles of physics in the branches of mechanics, movement, forces, fluid mechanics, electric and magnetic phenomena and

radiation.

3. Describe the nature phenomena by using the language of physics. 4. develop the ability to solve problems and think critically by applying the

acquired knowledge of physics to the various problems.

5. know how to conduct a series of practical experiments for the study of

physical phenomena related to some previous knowledge.

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List of Topics

Vectors

-Addition: Geometrical method & Analytical method -Product of vector: Scalar and Cross product

Newton’s laws of Motion:

Definition of force.

Equilibrium state.

Newton’s laws of motion.

Fundamental forces: Weight and friction.

Work, Energy and Power:

Work and Kinetic energy.

Conservative forces and potential energy.

Observations of work and energy.

Power.

Mechanics of non-Viscous Fluid

The Equation of continuity, Stream line flow. Bernoulli’s equation and its static consequences. Role of gravity in blood circulation. Pressure measurement using manometer.

Direct Electric Current (DC)

Basic concept of DC Electric current. Ohm’s law. Electric safety

Nerve Conduction:

Structure of nerve. Electric characteristics of axon. Ionic concentration and the resting potential. Response to weak stimuli. The action potential.

Wave properties of light: The Index of Refraction. Reflection of Light. Refraction of Light. Ionizing Radiation Exposure , Absorbed Dose and Radiation Quantities, Units

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Vocabulary

ENGLISH ARABIC

Acceleration تسارع –عجلة

Activity نشاط أشعاعى

Air pressure ضغط الهواء

Ampere أمبير

Analytical تحليلى

Analytical Method الطريق التحليلية

Angle زاوية

Angle of Deviation زاوية االنحراف

Angle of Incidence زواية السقوط

Angle of reflection زاوية االنعكاس

Angle of refraction زاوية األنكسار

Archimedes's Principle مبدأ أرخميدس

Atmospheric pressure الضغط الجوي

Atom الذرة

Axoplasm ِجْبلَةُ اْلِمْحَواِر

Axons محاور عصبيّة

Balanced Force القوة المتزنة

Bernoulli's Principle law مبدأ )قانون( برنولي

Binding Energy طاقة الربط

Blood pressure ضغط الدم

blood vessel وعاء دموى

Buoyancy الطفو

Buoyant force قوة الطفو

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Capacitance سعة المكثف

Capacitor المكثف

Coefficient of friction معامل األحتكاك

Charge شحنة

Circuit دائرة

cohesion قوة التماسك بين جزئيات السائل

components of a vector مكونات متجه

compression ضغط , كباس , أنضغاط

conduction توصيل

conductivity معامل الموصلية الحرارية

Conductor الموصل

Conservation of Energy حفظ الطاقة

conservation of momentum حفظ كمية الحركة

consumed مستهلك

Coulomb كولوم

cube مكعب

Current تيار

deceleration تباطؤ

Density الكثافة

Dendrites التشعبات العصبية

diffraction حيود الضوء

dimensions االبعاد

Dispersion تشتت , تفرق

direction إتجاه

directly proportional يتناسب طرديا

displacement اإلزاحة

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distance المسافة

Drag السحب )المقاومة )اللزوجية( التي يبديها المائع لجسم متحرك

عبره(

drift )انسياق )حركة حامالت التيار الكهربائي، في شبه الموصل

dynamics الديناميكا

efficiency كفاءة

effort arm ذراع القوة

Electric Charge شحنة كهربائية

Electric Circuit دائرة كهربائية

Electric Current التيار الكهربى

Electric Energy طاقة كهربائية

Electric field المجال الكهربي

Electrical Conductivity توصيل كهربائى

Electric Potential جهد كهربائى

Electrical Resistance مقاومة كهربائية

electricity الكهرباء

electrode قطب كهربائى

Electromagnetic Field مجال كهرومغناطيسي

electromagnetic induction الحث الكهرومغناطيسي

Electromotive Force القوة الدافعة الكهربية

Electron اإللكترون

Electron Diffraction اإللكترونحيود

Energy الطاقة

Energy Level مستويات الطاقة

Energy Transformations تحوالت الطاقة

Equation of continuity معادلة اإلستمرارية

Equilibrium إتزان

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ev إلكترون فولت

Farad الفاراد )وحدة السعة الكهربة( كولوم لكل فولت

Field مجال

Fluid , السائلالمائع

Fluid Dynamics ديناميكا الموائع

flow rate معدل السريان

Force قوة

force exerted القوة المبذولة

Frequency التردد

Friction اإلحتكاك

Friction forces قوة االحتكاك

fusion دمج -إنصهار

Geometric Method طريق الرسم الهندسى او البيانى

graph الرسم البيانى

Gravitational Force قوة الجاذبية

Gravitational potential energy الطاقة الكامنة لمجال الجذب الكوني

Gravity الجاذبية

Heat حرارة

Heat Energy الطاقة الحرارية

Heat Transfer انتقال الحرارة

Heavy Water الماء الثقيل

History of Physics تاريخ الفيزياء

Hooke's Law قانون هوك

horizontal أفقى

Impedance المقاومه الكهربائيه

Ideal Gas Law قانون الغاز المثالي

inclined مائل

inertia القصور الذاتى

Infinity النهائية

intensity الشدة

interference التداخل

International System of Units الوحدات الدولينظام

inversely proportional يتناسب عكسى

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Ion أيون

ionic concentration التركيز األيوني

Ionizing التأين

Ionizing Radiation أشعة مؤينة

Joule )الجول )الوحدة الدولية لقياس الطاقة

Kelvin كلفن: درجة الحرارة المطلقة

Kinetics علم الحركة

Kinetic Energy الطاقة الحركية

kinetic friction االحتكاك الحركي

Laminar flow تدفق المنار

laser الليزر

law of conservation of mechanical

energy قانون حفظ الطاقة الميكانيكية

laws of motion قوانين الحركة

leakage resistance مقاومة التسرب

Light year الضوئيةالسنة

Light الضوء

Liquid السائل

longitudinal wave الموجه الطوليه

Luminosity سطوع

Magnetic Field مجال مغناطيسي

Magnetic Flux تدفق مغناطيسي

Magnetic Moment عزم مغناطيسي

magnitude معيار & قيمة

manometer مقياس ضغط الدم

mass الكتلة

matter مادة

mechanics ميكانيكا

mechanical energy الطاقة الميكانيكية

medium وسط

metal معدن

molecules جزئيات

Motion حركة

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Movement حركة

net force محصلة القوة

neutron النيوترون

Nerve عصب

Nerve cells (neuron) خاليا عصبية

Nerve conduction التوصيل العصبى

newton نيوتن

Newton's first law قانون نيوتن األول

Newton's first law of motion قانون نيوتن األول للحركة

Newton's first law of motion

(Inertia) قانون نيوتن األول للحرآة قانون القصور الذاتي

newton's law of gravitation قانون نيوتن للجاذبية

newton's second law of motion قانون نيوتن الثاني للحركة

newton's third law of motion قانون نيوتن الثالث للحركة

normal force قوة عمودية

nuclear radiation اإلشعاع النووي

nucleus نواة

Ohm أوم

Ohms Law قانون

Optics البصريات

particle جسيم

pendulum بندول

photoelectric effect التأثير الكهروضوئي

photon فوتون

physics الفيزياء

pipeline خط انابيب

position موضع

Potential Difference فرق الجهد

Potential Energy طاقة الوضع

power القدرة

pressure الضغط

pressure in liquids الضغط في السوائل

Proton بروتون

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Pulses ومضات

pull سحب

pulling force قوة السحب

quantity كمية

radiation اإلشعاع

radius نصف القطر

reaction رد الفعل

reflection أنعكاس

refraction األنكسار

refractive index معامل االنكسار الضوئي

relativity النسبية

resistance المقاومة

resistance force قوة مقاومة

resistivity المقاومة النوعية

resistor المقاوم

Rest Energy طاقة السكون

Resultant ناتج

Resultant Force القوة الناتجة

Scalar قياسى

Scalar quantities كميات قياسية

smooth أملس -ناعم

Smooth horizontal surface سطح أفقى املس

sound الصوت

space الفضاء

speed السرعة المطلقة

sphygmomanometer مقياس ضغط الدم

static electricity الكهريبة الساكنة

surface السطح

surface tension التوتر السطحى

tension توتر -شد

terminal velocity سرعة الوصول

Temperature درجة الحرارة

Thermal Physics الفيزياء الحرارية

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thermometer مقياس الحرارة

Turbulence اضطراب

turbulent flow تدفق مضطرب

Transformers المحوالت

Transient Energy الطاقة الزائلة

Transverse Waves الموجات المستعرضة

Ultrasound فوق صوتى

ultraviolet ray االشعة فوق البنفسجية

unbalanced forces قوى غير متزنة

uniform motion حركة منتظمة

Vacuum الفراغ

valence electron إلكترونات التكافؤ

vector متجه

vectors متجهات

Vectors Geometry هندسة المتجهات

Velocity السرعة المتجهة

Viscosity اللزوجة

visual angle زاوية اإلبصار

volt فولت وحدة قياس فرق الجهد الكهربي

voltage الجهد الكهربي

voltmeter الفولتميتر جهاز قياس فرق الجهد الكهربي

Volume الحجم

water pipe انابيب مياه

water pressure ضغط الماء

watt W وحدة قياس القدرة الكهربية -واط

Wave موجة

Wave Function الدالة الموجية

wave length الطول الموجي

Wave Interference التداخل الموجى

Wave Motion الحركة الموجية

Wave Phenomena الظواهر الموجية

wave speed سرعة الموجة

Wave Superposition التراكب الموجى

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weakcohesive

Weight الوزن

work الشغل

Work done الشغل المبذول

X-Ray إكس ) السينية(اشعة

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List of common physics notations Symbol Meaning SI unit of measure

A

area meter squared (m2)

a

acceleration meters per second squared (m/s2)

C

capacitance farad (F)

Cm Capacitance per unit area F/m2

c

speed of light (in vacuum) 299,792,458 meter per second (m/s)

speed of sound 340.29 meter per second (m/s)

viscous damping coefficient kilogram per second (kg/s)

D

displacement meter (m)

d

distance meter (m)

diameter meter (m)

V Volume cubic meter (m3)

v Velocity meter per second m/s

E

Energy Joule (J)

e electron charge 1.60217662 × 10-19 coulomb (C)

F

force newton (N)

f

frequency hertz (Hz)

function

friction newton (N)

g

acceleration due to gravity meter per second squared (m/s2), or

equivalently, newton per kilogramme (N/kg)

h height meter (m)

I electric current ampere (A)

https://en.wikipedia.org/wiki/Areahttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Accelerationhttps://en.wikipedia.org/wiki/Metershttps://en.wikipedia.org/wiki/Capacitancehttps://en.wikipedia.org/wiki/Faradhttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Speed_of_soundhttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Dampinghttps://en.wikipedia.org/wiki/Kilogramhttps://en.wikipedia.org/wiki/Electric_displacement_fieldhttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Distancehttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Diameterhttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Cubic_meterhttps://en.wikipedia.org/wiki/Electric_fieldhttps://en.wikipedia.org/wiki/Elementary_chargehttps://en.wikipedia.org/wiki/Coulombhttps://en.wikipedia.org/wiki/Forcehttps://en.wikipedia.org/wiki/Newton_(unit)https://en.wikipedia.org/wiki/Frequencyhttps://en.wikipedia.org/wiki/Hertzhttps://en.wikipedia.org/wiki/Function_(mathematics)https://en.wikipedia.org/wiki/Frictionhttps://en.wikipedia.org/wiki/Newton_(unit)https://en.wikipedia.org/wiki/Standard_gravityhttps://en.wikipedia.org/wiki/Heighthttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Electric_current

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k kinetic energy joule (J)

KB

Boltzmann constant 1.38× 10-23 joule per kelvin (J/K)

K wavenumber, wave vector radians per meter (m−1)

L length meter (m)

m mass kilogram (kg)

n refractive index

P power watt (W)

p pressure pascal (Pa)

Q

electric charge coulomb (C)

Flow rate = Volume/time cubic meter (m3 ) per second {m3 /s)

q

electric charge coulomb (C)

R

electrical resistance ohm (Ω)

axon resistance ohm (Ω)

R leakage resistance ohm (Ω)

Rm resistance of unit area of

membrane

ohm (Ω )m2

r

radius meter (m)

T Temperature kelvin (K)

t time second (s)

U

potential energy joule (J)

V

voltage ,also called electric

potential difference

volt (V)

v velocity meter per second (m/s)

W

mechanical work joule (J)

w

Weight Kilo gram (Kg)

https://en.wikipedia.org/wiki/Kinetic_energyhttps://en.wikipedia.org/wiki/Joulehttps://en.wikipedia.org/wiki/Boltzmann_constanthttps://en.wikipedia.org/wiki/Joulehttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Lengthhttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Masshttps://en.wikipedia.org/wiki/Kilogramhttps://en.wikipedia.org/wiki/Refractive_indexhttps://en.wikipedia.org/wiki/Power_(physics)https://en.wikipedia.org/wiki/Watthttps://en.wikipedia.org/wiki/Pressurehttps://en.wikipedia.org/wiki/Electric_chargehttps://en.wikipedia.org/wiki/Cubic_meterhttps://en.wikipedia.org/wiki/Electric_chargehttps://en.wikipedia.org/wiki/Coulombhttps://en.wikipedia.org/wiki/Electrical_resistancehttps://en.wikipedia.org/wiki/Ohmhttps://en.wikipedia.org/wiki/Ohmhttps://en.wikipedia.org/wiki/Ohmhttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Temperaturehttps://en.wikipedia.org/wiki/Timehttps://en.wikipedia.org/wiki/Potential_energyhttps://en.wikipedia.org/wiki/Joulehttps://en.wikipedia.org/wiki/Voltagehttps://en.wikipedia.org/wiki/Velocityhttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Mechanical_workhttps://en.wikipedia.org/wiki/Joulehttps://en.wikipedia.org/wiki/Meter

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theta angular displacement

ᵞ gamma photon

gamma ray

delta ∆ a change in a variable (a change of "blank")

lambda

wavelength meter (m)

mu coefficient of friction unitless

pi 3.14159... (irrational number)

rho density kilogram per cubic meter (kg/m3)

resistivity Ohm meter ({\displaystyle \Omega } m)

Ơ sigma electrical conductivity

Cm x 10-2 m

m m x 10-3m

μ m x 10-6m

Liter x 10-3m3

Gram x 10-3 kg

https://en.wikipedia.org/wiki/Theta_(letter)https://en.wikipedia.org/wiki/Angular_displacementhttps://en.wikipedia.org/wiki/Photonhttps://en.wikipedia.org/wiki/Gamma_rayhttps://en.wikipedia.org/wiki/Delta_(letter)https://en.wikipedia.org/wiki/Derivative#Differentiation_and_the_derivativehttps://en.wikipedia.org/wiki/Lambdahttps://en.wikipedia.org/wiki/Wavelengthhttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Mu_(letter)https://en.wikipedia.org/wiki/Coefficient_of_frictionhttps://en.wikipedia.org/wiki/Pi_(letter)https://en.wikipedia.org/wiki/Rho_(letter)https://en.wikipedia.org/wiki/Densityhttps://en.wikipedia.org/wiki/Resistivityhttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Meterhttps://en.wikipedia.org/wiki/Sigmahttps://en.wikipedia.org/wiki/Electrical_conductivity

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Ch 1 (1.1. Vector)

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Part 1: Define scalar and vector quantity.

Part 2: Adding vector

There are three methods to adding Vector

1- Graphical or called (Geometrical Method)

2- Pythagorean Theorem

3- Analytical Method or called Component's Method

1- Graphical or called (Geometrical Method)

Add vectors A and B graphically by drawing them together in a head to

tail arrangement.

Draw vector A first, and then draw vector B such that its tail is on

the head of vector A.

Then draw the sum, or resultant vector, by drawing a vector from the

tail of A to the head of B.

Measure the magnitude and direction of the resultant vector

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Example 1

A man walks at40 meters East and 30 meters north. Find the magnitude

of resultant displacement and its vector angle. Use Graphical Method.

Answer

Given:

A = 40 meters East B = 30 meters North

Resultant (R) =? Angle θ = ?

So from this

Resultant (R) =50 & Angle θ = 37

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2- Pythagorean Theorem

The Pythagorean Theorem is a useful method for determining the result

of adding two (and only two) vectors and must be the angle between

this two vector equal =90

Example2

A man walks at 40 meters East and 30 meters North. Find the magnitude

of resultant displacement and its vector angle. Use Pythagorean

Theorem.

Answer

_____________________________________________________

22 BABAR

)B/A (1Tan

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Notes(1): To calculate the magnitude A+B with angle degree 90 o or 90 o

We use the equation

Example

Given A = 5 and θA = 120o and B = 7,θB = 60o find the magnitude A+B ?

Solution,

1- we find the total angle θ =θA-θB SO θ =120-60 = 60

2-We use the equation

So A+B

Notes(2): To calculate the magnitude A-B with angle degree 90 o or 90 o

We use the equation

Example

Given A = 5 and θA = 120o and B = 7,θB = 60o find the magnitude A-B ?

Solution,

2- we find the total angle θ =θA-θB SO θ =120-60 = 60

2-We use the equation

So A-B

3-Analytical Method or called Component's Method

First: to calculate the components and magnitude of vector for example

the components of vector A are

Ax = A Cos θ and Ay = A sin θ

COSABBABA 222

COSABBABA 222

44.106075275 22 COSxx

COSABBABA 222

COSABBABA 222

24.66075275 22 COSxx

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Example 1

Find the components of the vector A, If A = 2 and the angle θ = 30o ?

Solution,

Since, Ax = A Cos θ and cos 30 = 0.866 so Ax = 2 cos 30 = 2 x 0.866 = 1.73

Also, Ay = A sin θ and sin 30 = 0.500 so Ay = A sin 30 = 2 x 0.5 = 1

Example 2

Given A = 3 and θ = 90o find Ax and Ay?

Solution,

Since, Ax = A Cos θ and cos 90 = 0. so Ax = 3 cos 90 = 3 x 0= 0

Also, Ay = A sin θ and sin 90 = 1 Ay = A sin 90 = 3 x 1 = 3

Second: To calculate the magnitude of vector for example magnitude vector A and

direction angle

We use the equation and

Example

If the components of a vector are defined by Ax =3.46 and Ay =2 find the

magnitude and direction angle of the vector A?

Solution,

1-We use the equation to find the magnitude vector

So the magnitude vector A=3.99

2- To find the direction angle we use the equation

30o So the direction angle θ=30o

22

yx AAA ) /AA( xy1Tan

22

yx AAA

99.3)2()46.3( 22 A

) /AA( xy1Tan

) /3.462(1Tan

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Third: To calculate the resultant vector by component method

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Example: If A= 25 and θA = 50, B=4 and θB = 150, C=6 and θC = 265

1- Calculate the Resultant magnitude by using component method?

2- Calculate the Resultant angle direction?

Answer

solution (1) We use the last equations. So

By using equation so use the equation

(2) we use the equation

so

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Part 3 :Unit Vector Notation and product of vector

Unit Vector Notation

A unit vector is a vector that has a magnitude of one unit and can have any

direction.

1-Traditionally i^ (read “i hat”) is the unit vector in the x direction

2- j^ (read “j hat”) is the unit vector in the y direction. |i^|=1 and |j^|=1, this

in two dimensions

3-and motion in three dimensions with ˆk (“k hat”) as the unit vector in the z

direction

Notes

If A&B are two vectors, where

A = axi + ayj + azk& B = bxi + byj + bzk Then the:

1- To findA+B and A B

A+B= (ax +bx)i + (ay +by)j + (az +bz)k

A B= (axbx)i + (ayby)j + (azbz)k

Example

Two vector A = 3i +2j +3K and B = 5i + 4j +3k find A+B and A B

Solution,

1- According the equation A+B= (ax +bx)i + (ay +by)j + (az +bz)k

So A+B= (3 +5)i + (2 +4)j + (3 +3)k =8i + 6j + 6k

2-According the equation A B= (ax bx)i + (ay by)j + (az bz)k

So A B= (35)i + (24)j + (33)k = -2i –2j + 0k= -2i-2j

_____________________________________________________

2-To find the magnitude of A+B and A B

Example 222 )()()( zzyyxx bababaBA

222 )()()( zzyyxx bababaBA

27

Two vector A = 3i +2j +3K and B = 5i + 4j +3kfind the magnitude for A+B and A B

Solution, 1- To find the magnitude for A+B

According the equation

So =11.66

2- To find the magnitude for AB

According the equation

So =2.82

2-the magnitude of vector in Unit Vector Notation

If A is vectoring, where A = axi + ayj + azk Then the:

To find magnitude of vector Awe use the equation

Example

vector A = 3i +2j +3Kfind magnitude of vector A

Solution,

According the last equation

So

222 )()()( zzyyxx bababaBA

222 )33()42()53( BA

222 )()()( zzyyxx bababaBA

222 )33()42()53( BA

222

zyx aaaA

69.4323 222 A

28

Product of Vectors

There are two kinds of vector product:

1. The first one is called scalar product or dot product because the result of

the product is a scalar quantity.

2. The second is called vector product or cross product because the result is a

vector perpendicular to the plane of the two vectors.

Example on the dot(scalar)and cross product

1- If the magnitude of A is A=4,θA = 35o , and the magnitude of B is B=5 and θB = 70o Find a) A . B c) A x B

Solution,

Θ=θBθA = 70o35o= 35o

So A . B= A B COSθ = 4 x5 x COS 35o=16.38

A x B= A B Sinθ = 4 x5 x Sin 35o=11.47

29

Notes on the scalar product

If A & B are two vectors, where

A = Axi + Ayj + Azk &B = Bxi + Byj + Bzk

Then, their Scalar Product is defined as:

AB = AxBx + AyBy + AzBz Where

&

Example

Two vector A = 2i +3j +4K and B = 5i + 2j +6k find the scalar product A. B

Solution,

According the last equation

So AB =(2x5)+(3x2)+(4x6)=10+6+24= 40

30

Summary low in the chapter

31

Quizzes

1- If the magnitude of A is A=4, θA = 35o, and the magnitude of B is B=5 and θB = 70o find a) A +b b) A - b c) A x B d) A . B

2- Two vector A = 2i +3j +4K and B = 5i + 2j +6k find the magnitude of a) A.B b) A+B c) A-B

3- A man walks at 20 meters East and 15 meters north. Find the magnitude of resultant displacement and its vector angle. Use Graphical Method and Pythagorean

Theorem?

4- If the magnitude of A is A=2, magnitude of B is B=3 and θ =30o Find a) A +b b) A - b c) A x B d) A. B

5- Two vector A= 5i -7j+10k and B= 2i +3j-2k find A.B

6- Vector A has a magnitude of 5 units and direction angle ΘA = 30 find Ax and Ay?

7- the components of a vector are defined by Ax =3.46 and Ay =2 find the magnitude and direction angle of the vector A ?

8- If A= 10 and θA = 30, B=7 and θB = 70, C=8 and θC = 240

Calculate the Resultant magnitude by using component method?

Calculate the Resultant angle direction?

32

Choose the correct answer

Which of the following is a physical quantity that has a magnitude but no direction?

A. Vector B. Resultant C. Scalar D. None

Which of the following is an example of a vector quantity? A. Temperature B. Velocity C. Volume D. Mass

Which of the following is a physical quantity that has a magnitude and direction?

A. Vector B. Resultant C. Scalar D. None

Given |A|=6 and , ӨA =60. Find the Ax and Ay. A. Ax= 2.3 , Ay=1.9 B. Ax= 2, Ay=3. C. Ax= 3 , Ay=5.2 D. Ax= 5.1, Ay=1.7

The magnitude of the resultant of the vectors shown in Figure is: A. 2 N B. 12 N C. 35 N D. −2 N

Given |A|= 5 , ӨA =120o and |B|=7 , ӨB =60o .Find the magnitude |B +A|

A. |B +A|= 5

B. |B +A|=7.2

C. |B +A|=10.44

D. |B +A|=8.6

33

A car travels 90 meters due north in 15 seconds. Then the car turns around and

travels 40 meters due south. What is the magnitude and direction of the car's

resultant displacement?

A. 40 meters, South B. 50 meters, South C. 50 meters, North D. 40 meters, North

A car moved 60 km East and 90 km West. What is the distance it traveled? A. 30 km, West B. 60 km. East C. 90 km D. 150 km

What is magnitude? A. The direction that describes a quantity. B. A numerical value C. A unit of force

150N weight hanging DOWN from a rope. Vector or scalar? A. Scalar B. Vector

What type of quantity is produced by the dot product of two vectors? A. scalar B. vector

Tow vectors A= 3i +5j-2k and B= 4i -3j .Find the scalar product A.B

A. - 6

B. - 8

C. -2

D. -3

34

Ch1 (1.2. Force and Newton's laws)

35

Facts about FORCE

Force unit is the NEWTON (N).

Its definition a push or a pull.

What change the state of object is called “force”.

Means that we can control the magnitude of the

applied force and also its direction, so force is a vector

quantity, just like velocity and acceleration.

What is the Net Force?

The net force is the vector sum of all the forces acting on a body.

321net FFFFF

Adding Forces

Forces are vectors (They have both magnitude and direction)

and so add as follows:

1-Adding Forces In one dimension

2-Adding Forces In two dimensions

36

2- Adding Forces In two dimension

a) The angle between them is 90°.

Example

In this figure shown find the resultant (Net) force

Solution,

According the equation

2

2

2

1 FFF

NF 252015 22

37

B) The angle between them is or 90°.

Example

In this figure shown find the resultant (Net) force

Solution,

According the equation

So

COSFFFFF 212

2

2

1 2

NCOSxxF 5.14301052105 22

38

Unbalanced Forces

Unbalanced forces acting on an object result in a net force and cause a change in the

object’s motion. Show figure

Balanced Forces

Balanced forces acting on an object do not change the object’s motion. Show figure

39

Forces you will need

Applied

Force(Fapp)

An applied force is a force that is applied to an object by a person or another

object. If a person is pushing a desk across the room, then there is an applied

force acting upon the object. The applied force is the force exerted on the

desk by the person.

Gravity

Force(also

known as

Weight)Fg

Gravitational Force is the Weight of the Object (equal to mass x g”(w= mg)

Normal Force(Fn)

Normal force: this force acts in the direction perpendicular to the contact

surface and opposite the weight.

For example, if a book is resting upon a surface, then the surface is exerting

an upward force upon the book in order to support the weight of the book. On

occasions, a normal force is exerted horizontally between two objects that are

in contact with each other. For instance, if a person leans against a wall, the

wall pushes horizontally on the person.

friction

Force

Ffrict

The force of friction is a force that resists motion when two objects are in

contact.

As such, friction depends upon the nature of the two

surfaces and upon the degree to which they are

pressed together. If the surface is smooth, the

friction force, Ff= 0

The level of friction that different materials exhibit

is measured by the coefficient of friction.

Coefficients of friction Coefficient of friction is the ratio between friction force and normal force. Symbol is the Greek letter mu (μ)

μ= Ff / FN and Friction Force = Coefficient of friction Normal Force

Ffriction = Fnormal The coefficient of friction has no units. The coefficient of friction depends on the nature of the two surfaces,

N

w

40

There are two forms of friction, kinetic and static.

1- Static Friction: Static friction is a force that keeps an object at rest.

If a small amount of force is applied to an object, the static friction has an

equal magnitude in the opposite direction.

The equation for this relationship is: Fs = μs Fs & μs=Fs /Fn

2-Kinetic friction

occurs when two objects are moving against one another with some

part of their surfaces in contact. Kinetic friction is the friction that

opposes the sliding motion and tries to reduce the speed at which the

surfaces slide across each other show figure. Kinetic friction opposes

the motion of the object and is proportional to the normal force

acting on an object. The proportionality constant is the coefficient of

friction, µk. The equation for this relationship is: Fk = μk Fn

.

Figure: Upon sliding, the baseball player will come to a complete stop due

to the Force of Kinetic Friction

41

Example

5Kg block is on a flat, horizontal surface.

(a) If a horizontal force Fap = 20 N is applied and the block remains at rest, what is the

static frictional force fs?

(b) The block starts to slide when Fap is increased to 40 N. What is μs ?

(c) The block continues to move at constant velocity if Fap is reduced to 32 N. What is μk?

Answer

(a) Since the block remains at rest when the force Fap is applied, the static frictional force fs

must be equal but opposite to Fap. Consequently

fs = Fap = 20 N

(b) Since the block just begins to slide when the applied

force is increased to 40 N, the maximum frictional force must be fs (max) = 40 N

The vertical forces must add to zero, so the normal force FN is equal to the weight,

W= mg so FN=W=mg=5x10=50 N . Hence μs=Fs /Fn SO & μs=40N /50N=0.8

(c) Since the block moves with constant velocity when Fap= 32N force is applied, the

net force must be zero. Consequently, the kinetic frictional force Fk must equal the

applied force, or Fk = Fap = 32 N . again the normal force FN is equal to the

weight, W= mg so FN=W=mg=5x10=50 N

Hence μk=Fk /Fn SO & μk=32N /50N=0.64

Note the μk

42

Newton’s First Law

An object at rest tends to stay at rest and an object in motion tends to stay in motion with the

same speed and in the same direction unless an external force is acting on it.

Or in other words

Everybody continuous in its state of rest or in uniform motion Unless an external force is

acting on it.

Notes: Newton’s First Law is also called the Law of Inertia

So:

Inertia is a term used to measure the ability of an object to resist a change in its

state of motion.

An object with a lot of inertia takes a lot of force to start or stop; an object with a

small amount of inertia requires a small amount of force to start or stop.

EQUILIBRIUM

Newton's first law tells us that the state of motion of an object remains unchanged

whenever the net force on the object is zero. This can happen if no forces act on an

object. More commonly, it occurs because two or more forces acting on an object

add to zero or "balance." When the state of motion of an object remains unchanged

even though two or more forces act upon it, the object is said to be in equilibrium

Inability of an object to change its position by itself is called Inertia.

43

Example 1

An ice cream vendor (Fig. below) exerts a force of 40 N to overcome friction and push his cart

at a constant velocity. The cart has a mass of 150 kg. Find the forces acting (friction force ) on

the cart.

Solution, The vertical forces acting on the cart are its weight w, which acts downward, and an upward

normal force N exerted on the cart by the floor. The vendor exerts a horizontal force F to the

left. The frictional force f opposes the motion, and is directed toward the right. The net force

on the cart is the sum w + N + F + f, and it is equal to zero since the cart is moving with a

constant velocity.

Ff= Fap = 40 N So the friction force Ffaction is 40 N

FN =W=m g where m= 150 and g=10 So FN = 150 x10=1500N

Example 2

A man is pulling 20Kg suitcase with constant speed on a horizontal rough

floor show figure. The pulling force F1 action is unknown. Find The pulling

force F1 and normal force FN?

Solution,

From figure

F1= F2 = 20 N So the pulling force F1 action is 20 N

FN =m g where m= 20 and g=10 So FN = 20 x10=200N

44

Example 3

In this figure shown, the object is at rest. Find normal force FN

Solution,

From figure

FN + F2 = F1 FN = F1F2 =2510=15 N

So the normal force FN =15 N

_______________________________________________________________________________

Newton’s Second Law When a net external force acts on an object of mass m, the acceleration a that results is

directly proportional to the net force and has a magnitude that is inversely proportional to the

mass. The direction of the acceleration is the same as the direction of the net force.

“Net Force equals mass times acceleration.”

Fnet = ma

What does F = ma mean?

Force is directly proportional to mass and acceleration.

Notes: Newton’s second law states that the net force on an object is proportional to the mass

and the acceleration that the object undergoes.

(a)Acceleration: a measurement of how quickly an object is

changing speed. a= F/m

45

Example 1

A human femur will fracture if the compressional force is 45000N. A person of mass 90 kg

lands on one leg. so that there is a compressional force on the femur, what acceleration will

produce fracture?

Solution,

a= F/m where F=45000 N & m=90kg so a= 45000/90 =500 m/s2

Example 2

The forces F1=10 N and F2=5N are the action on the block of mass 3 kg with 30°.

Find

1. The net force? 2. The acceleration of the block?

Solution,

1: we find the resultant (Net) force According the equation

2: The acceleration of the block (a) a= F/m where F=14.5 N & m=3kg so a= 14.5/3

=4.83 m/s2

Example2: A 10-kg box is being pulled across the table to the right by a rope with an applied force of

50N. Calculate the acceleration of the box if a 12 N frictional force acts upon it.

Solution,

Given: m=10 ,Fa=50 and Ff=12

first: we find the resultant (Net) force

The acceleration (a) a = 𝐹𝑛𝑒𝑡

𝑚=

38

10= 3.8

𝑚

𝑠2

COSFFFFF 212

2

2

1 2

NCOSxxF 5.14301052105 22

46

unbalanced forces pulling without and with angle θ

Example 1

A lady is pulling a 30 kg mass suit case on a rough horizontal floor. The pulling force F=90 N and

the coefficient of friction µk =0.1.

a. Find the magnitude of the normal force?

b. Find the magnitude of the force of friction?

c. Calculate is the acceleration of the suit case?

Solution,

Given: Fp=90 N, m=30 , g=10 m/s2 and µk =0.1

With out angle With angle

1- Friction Force Ff= µk . FN & FN =m . g

2-The acceleration (a)

𝑎 =𝐹𝑛𝑒𝑡𝑚

= 𝐹𝑎 − 𝐹𝑓

𝑚

Fx = F cos θ

Fy = FSin θ

1- Friction Force

Ff= µk . FN & FN=mg Fy

F

2-The acceleration (a)

𝑎 =𝐹𝑛𝑒𝑡

𝑚=

𝐹𝑥 − 𝐹𝑓

𝑚

47

a. FN = W= m . g=30×10=300 N so the magnitude of the normal force = 300 N

b. Ff= µk . FN So Ff= 0.1×300=30 N so the magnitude of the force of friction = 30 N

c. The acceleration (a) a=𝐹𝑛𝑒𝑡

𝑚=

𝐹𝑝 –𝐹𝑓

𝑚=

90−30

30=

60

30= 2

𝑚

𝑠2

so the acceleration of the suit case is 2 mls2

Example2 A man is pulling a bag of 20 Kg mass on a horizontal floor. The pulling force is 40 N inclined

at 30° above the horizontal and the coefficient of friction between the bag and the floor is

0.1. a. Find the magnitude of the normal force?

b. Find the magnitude of the force of friction?

c. Calculate is the acceleration of the suit case?

Given:

m=20kg , Fp =40N , θ=30° =0.1 and g=10

the pulling force F analysis in x and y direction show figure

Fx = F cos θ=40 x cos30° = 34.6 N

Fy = FSin θ=40xsin 30°= 20 N

a. magnitude of the normal force

FN=mg Fy=20x1020 = 180 N

b. magnitude of the force of friction

Ff = FN Ff = 0.1 X 180 =18N so the magnitude of the force of friction = 18 N

c. The acceleration of the suit case

𝑎 =𝐹𝑛𝑒𝑡𝑚

= 𝐹𝑥 − 𝐹𝑓

𝑚=

34.6 − 18

20=

16.6

20= 0.083 𝑚/𝑠2

so the acceleration of the suit case is 0.083 mls2

48

Newton’s Third Law

Whenever one object exerts a force on a second object, the second object exerts

an equal and opposite force on the first OR

“For every action there is always an opposed equal reaction” The statement means that in every interaction, there is a pair of forces acting on the two

interacting objects.

The size of the forces on the first object equals the size of the force on the second object. The

direction of the force on the first object is opposite to the direction of the force on the second

object. Forces always come in pairs - equal and opposite action-reaction force pairs.

For example, suppose you are at rest in a swimming pool. If you push a wall with your legs, the

wall exerts a force that propels you further into the pool. The reaction force the wall exerts on

you is opposite in direction to the force you exert on the wall.

49

Quizzes 1. Calculate the force required to accelerate a 15Kg block along the floor at 3.0 m/s2. m

2. The forces F1=10 N and F2=5N are the action on the block of mass 3 kg. Find the resultant force

and acceleration of the block?

3. An object of mass m=3Kg is subject to a force F=9N. Find:

a) Wight of the object b) the acceleration of the object

4. The forces F1=2 N and F2=4N are the action on the object with 60°. Find the magnitude of the

resultant force?

5. An object of mass m=5Kg is pulled by a force F on a smooth horizontal floor. If the magnitude of

the force F= 16N and its direct 30°above the horizontal. Find :

a) The normal force N. b) The acceleration of the object

6. A man is pulling a bag of 20 Kg mass on a horizontal floor. The pulling force is 40 N inclined at 30°

above the horizontal and the coefficient of friction between the bag and the floor is 0.1.

What is the force of friction?

What is the acceleration of the suite case? 7. A man of 60 Kg sits on a chair while his feet is resting on the ground. The ground exerts a force of

350 N on the feet. Find the force exerted by the chair on him?

8. A man mass is pulling a suitcase of 15Kg on a horizontal rough floor. If the coefficient of friction is

0.2.What is the pulling force ?

9. A man of 80 kg mass is sitting on a chair and his feet is resting against the ground. His feet is

experiencing 300 N force applied by the ground. Find the force applied on him by the chair.

10. A box of 30 Kg mass is pulled with constant speed on a horizontal rough surface. The force of

friction is Fk = 60 N. What is the coefficient of friction µk ?

11. A lady is pulling a 20 kg mass suit case on a rough horizontal floor. The pulling force F=90 N and

the coefficient of friction µk =0.2.

What is the magnitude of the force of friction?

What is the acceleration of the suit case?

12. A 50 N block is on a flat, horizontal surface, if a horizontal force T = 40 N is applied and the block

starts to slide. What is μs?

50

Choose the correct answer? 1. What type of forces do not change the motion of an object?

a. balanced forces b. unbalanced forces c. static forces d. accelerating forces

2. If the net force acting on an object is zero, then the object will remain at rest or move in a straight line with a constant speed is.

a. Newton's first law of motion b. Newton's second law of motion c. Newton's third law of motion d. Newton's fourth law of motion

2. What unit do we use to measure force?

a. Newton b. Meter c. Pascal d. Joule

3. When an unbalanced force acts on an object, the force

a. changes the motion of the object. b. is cancelled by another force. c. does not change the motion of the object. d. is equal to the weight of the object.

4. An object's resistance to change in motion

b. Motion c. Inertia d. Friction e. Mass

5. is the measure of the force of gravity on an object

a. mass b. weight c. density d. equation

6. Forces always act in equal but opposite pairs is .

a. Newton's first law of motion b. Newton's second law of motion c. Newton's third law of motion d. Newton's fourth law of motion

51

7. The force of attraction between any two objects that have mass

a. Energy b. Force c. Gravity d. Speed

8. When you use a boat paddle to push water backwards, the water exerts an opposite force pushing the boat forward. This is an example of:

a. Newton's First Law of Motion b. Pascal's Law c. Newton's Third Law of Motion d. Archimedes Principle

9. Which is the correct equation for Newton's second law? (relationship between mass, acceleration and force)

a. F=ma b. m=Fa c. a/F=m d. m=aF

10. A force that resists motion created by objects rubbing together is . a. gravity b. friction c. speed d. force

11. A box of 30 Kg mass is pulled with constant speed on a horizontal rough surface.

The force of friction is Fk = 60 N. What is the coefficient of friction µk ?

a) 0.5 b) 0.1

c) 0.3 d) 0.2

12. In the figure shown find the resultant (Net) force.

a) 10.6 b) 20.78

c) 14.5 d) 30.4

13.For every action, there’s an equal and opposite reaction.

a. Newton's First Law b. Newton's Second Law c. Newton's Third Law d. Force

52

14.The sum of all the forces acting on an object or system

a. net force b. force c. normal force d. drag force

15. an opposing force caused by the interaction between two surfaces. a. inertia b. mass c. friction d. force

16. State of rest or balance due to the equal action of opposing forces.

a. equilibrium b. force c. inertia d. mass

17.The force perpendicular to the surface that pushes up on the object of concern. a. normal force b. force c. drag force d. net force

18.An object of mass 10 kg is accelerated upward at 2 m/s2. What force is required?

a. 20 N B. 2 N C.5 N D. 0 N

19.Kinetic friction is always

A. lesser than static friction B. greater than static friction

B. equal to static friction C. equal to contact force

20.Which type of friction occurs when objects are not moving?

A. Kinetic B. fluid C. Rolling D. static

21.friction is a force that acts in an ___________ direction of movement.

A. Similar B. Opposite

B. parallel

22.The acceleration of an object is equal to the net force acting on the object divided by its

a) Wight b) Mass

c) Volume d) Distance

25.The coefficient of friction (µ) is the ratio between friction force and--------

a). Friction force b). Normal force

c). Pulling force d). Drag force

53

54

Ch 2 work and energy

55

56

Notes on Work

Work = The Scalar Dot Product between Force F

and Displacement d.

W = F . d

The unit of work is a joule (J) and J = N · m

Calculate work done on an object:

1-Without angle (θ=0)

a) with apply force

The equation used to calculate the work (W) in this case it:

W= F . d

Example

How much work is done pulling with a 15 N force applied at

distance of 12 m?

Solution,

Given F=15 N & d=12m

According the equation W= F . d

So W=15x12=180 J

ntdisplacemeForceWork

57

b) Also with friction force

The equation used to calculate

the work (W) in this case it:

W= -Ff . d -----------1

But Ffriction = Fnormal so you can write this equation (1)

W= -(Fnormal)d ---------2

But Fnormal= m g so you can write this equation(2)

W= -(mg)d ---------3

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

Example

A horizontal force F pulls a 10 kg carton across the floor at

constant speed. If the coefficient of sliding friction between the

carton and the floor is 0.30, how much work is done by F in

moving the carton by 5m?

Solution,

Given: m=10 kg , d=5m ,g=10 and μ=.30 W=?

The carton moves with constant speed. Thus, the carton is in

horizontal equilibrium.

Fp = Ff = μk N = μk mg.

Thus F = 0.3 x 10 x 10= 30 N

Therefore work done W = F .d=30 x 5= 150 J

58

2-With angle

In this case, the work done given by

Example

How much work is done pulling with a 15 N force applied at 20o over

a distance of 12 m?

Solution,

Given F=15 N , θ=20o& d=12m

According the equation W= F . dCos θ

So W=15x12xCos 20o=169.1 J

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

Example

An Eskimo returning pulls a sled as shown. The total mass of the sled is 50.0 kg,

and he exerts a force of 1.20 × 102 N on the sled by pulling on the rope.

a) How much work does he do on the sled if θ = 30° and he pulls the sled 5.0 m?

b) Suppose µk = 0.200, How much work done on the sled by friction,

c) Calculate the net work if θ = 30° and he pulls the sled 5.0 m ?

W = F . d cos

59

Solution,

Given F=1.20 × 102 N, θ=30° , µk = 0.200& d=5m .g=10

a) Calculate work does he do on the sled if θ = 30° and he pulls the sled 5.0 m

b) calculate the work done on the sled by friction.

c) Calculate the net work

J

mN

dFW

520

)30)(cos0.5)(1020.1(

cos.

2

J

N

dFmgxN

dFxFW

kk

fffric

440

)5)(30sin102.11050)(200.0(

).sin(

.)180cos(

2

J

WWWWW gNfricFnet

0.90

00440520

60

Kinetic Energy

Kinetic Energy is: the energy of a particle due to its motion

K.E = ½ mv2

Where

K is the kinetic energy m is the mass of the particle v is the speed of the particle

Also K.E = ½ mv2 so V2 =𝟐𝒌

𝒎 V=√

𝟐𝒌

𝒎

Example 1 A 1500 kg car moves down the freeway at 30 m/s Find the Kinetic Energy?

Solution, Given m=1500kg, v=30m/s

According the equation K.E = ½ mv2

So : K.E. = ½(1500 kg)(30 m/s)2= 675,000 kg·m2/s2 = 675 kJ

Example 2 A 10 kg mass has a kinetic energy of 20 joule. What is the speed?

Solution, Given m=10 kg, K.E. =20 joule , v=?

V=√𝟐𝒌

𝒎=√

𝟐𝒙𝟐𝟎

𝟏𝟎= √

𝟒𝟎

𝟏𝟎= √𝟒 = 2 m/s

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Work and Kinetic Energy

The relationship that relates work to the change in kinetic energy is known as work-

energy theorem. The work-energy theorem states that the work W done by the net

external force acting on an object equals the difference between the object’s final kinetic

energy Kf and initial kinetic energy K0 . in another words the work done by the net force equals the change in kinetic energy of the system.

So W = Kf - K0 ------------1

And also W =½ mvf2 ½ m v02 ------------2 But W= -Ff . d

So -Ff . d=½ mvf2 ½ m v02 ------------3

𝐹f =1

2𝑚𝑣02

𝑑 ------------4 If vf = 0

Example1:

A child of 40kg mass is running with speed 3m/s on a

rough horizontal floor skids a distance 4 m till stopped .

a) Find the force of friction?

b) Find the coefficient of friction?

Solution,

Given: m=40 kg, v0=3m/s , vf=0 , d= 4m and g=10

a) Calculate the force of friction

We apply the equation -Ff . d=½ mvf2 ½ m v02

But vf=0 so ½ mvf2 =0

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-Ff . d=0 ½ m v02 -Ff . d=- ½ m v02

Ff= (½ m v02 )/ d =(½ 4032 )/ 4= 45 N

So the force of friction = 45 N.

b) Calculate the coefficient of friction

According the equation in ch2 μ= Ff / FN

Where Ff= 45 N and FN =mg=4010=400

So μ= Ff / FN μ= 45 / 400 μ=0.1

---------------------------------------------------------------------------- Example 2

A 6.0-kg block initially at rest is pulled to the right along a horizontal,

frictionless surface by a constant horizontal force of 12 N. Find the speed of

the block after it has moved 3.0 m.

Solution,

Given:Fp= 12 N m=6 kg, v0=0, vf=? ,

d= 3m and g=10

W =Fp. d =12x 3 = 36J

Δk = w

½ mvf2 ½ m v02 = w

But vo=0 so ½ mv02 =0

½ mvf2 = W

½ x 6 x vf2 = 36 vf sm / 46.312

63

Example3

woman pushes a toy car. initially at rest, toward a child by exerting a constant

horizontal force F of magnitude 5 N through a distance of 1 m .

(a)How much work is done on the car?

(b) What is its final kinetic energy?

(c) If the car has a mass of 0.1 kg, what is its final speed (vf)? (Assume no work is

done by frictional forces.)

Solution

Given: Fp= 5 N m=0.1 kg, v0=0, d= 1m and g=10

a) The force the woman exerts on the car is parallel to the displacement, so the work she

does on the car is W = F. d = (5 N) x (l m) = 5 J

(b) v0 = 0 so The initial kinetic energy Ko is zero, so the final kinetic energy of the car from the equation (W = Kf - K0 but ) W=5J & K0=0 W = Kf Kf = 5J

c) The final kinetic energy is Kf =½ mvf2 so

Vf=√𝟐𝒌

𝒎=√

𝟐𝒙𝟓

𝟎.𝟏= √

𝟏𝟎

𝟎.𝟏= √𝟏𝟎𝟎 = 10 m/s

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Potential Energy

Potential Energy means the work done by gravity on the object.

The formula for potential energy (U) due to gravity is U = m.g.h

P.E. = mass x height x gravity

The unit of Potential Energy is a joule (J)

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

Example:

A child of 40 kg mass is sitting at the roof a tower 60m high referenced to the

ground. What is the potential energy of child?

Solution,

Given: m=40 kg h= 60m and g=10

According the equation U = m.g.h

So U = 40 x 10x 60=24000 J ---------------------------------------------------------------------------------------------------

Conservation of Energy

1-The law of conservation of mechanical energy states: Energy cannot be created or destroyed,

only transformed

2-Potential energy and Kinetic Energy or the sum of the kinetic

energy and the potential energy is called the total mechanical

energy are mechanical Energy

In this figure below. When a pendulum swings the point which has the highest potential energy is (1.5), and the highest kinetic

energy is (3)

So the final mechanical energy Ef = Kf + Uf is equal to the initial mechanical energy EO = Ko + Uo

EO=EF

Ko + Uo = Kf + Uf---------- 1

K= U so ½ mvf2 ½ m v02 = mg(hfho) -------- 2

vf = √𝟐𝒈(𝒉0 − 𝒉f) --------

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Example

At a construction site a 1.50 kg brick is dropped from rest and hit the ground

at a speed of 26.0 m/s. Assuming air resistance can be ignored, calculate the

gravitational potential energy of the brick before it was dropped?

Solution,

Given: m=1.50 kg v0=0, vf=26 ,Uf=0 Uo=?

According Ko + Uo = Kf + Uf

But vo=0 so Ko =½ mv02 =0 and Uf=0

So Uo = Kf Uo=mgho = ½ mvf2

Uo= ½ x (1.5x 26)2= 507 J -----------------------------------------------------------------------------------------------

Example

A child of 20 kg mass is ON A swing. The swing reaches maximum height 3 m

above her lowest position. Find her speed at the lowest position?

Solution,

Given: m=20 kg v0=0, vf=? ,hf=0 , ho=3 and g= 10

we use the equation vf = √𝟐𝒈(𝒉0 − 𝒉f)= √𝟐𝒙𝟏𝟎(𝟑 − 𝟎)= √𝟔𝟎 =7.74

66

Power Power is: is the rate of doing work. It is the amount of energy consumed per

unit time P =𝑊

𝑡=

𝐹.𝑑

𝑡

Units of Power

Where the unit of work(W) is joule and unit of time(t) is second. So The unit of

power is a Watt

where 1 watt = 1 joule / second

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

Example1

A 100 N force is applied to an object in order to lift it a distance of 20 m within 60 s.

Find the power.

Solution,

Given: F=100 N d=20 m t=60 s

According the equation P =𝑊

𝑡=

𝐹.𝑑

𝑡=

100 𝐱 20

60= 33.33 waat

_________________________________________________________________

Example 2

A 70-kg man runs up a flight of stairs 3 m high in 2 s.

(a) How much work does he do against gravitational forces?

(b) What is his average power output?

Solution,

Given : Given: m=70 Kg h=3 m t=2 s and g=10m/s2

a) The work done, ∆W, is equal to his change in potential energy, mgh. Thus ∆W = m.g.h = 70 x10x 3 = 2100 J

b) His average power is the work done divided by the time,

P =𝑊

𝑡==

2100

2= 1050 waat This is a high power output for a human.

https://en.wikipedia.org/wiki/Work_(physics)https://en.wikipedia.org/wiki/Energy_(physics)

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Example 3

A woman of 50 Kg mass climbs a mountain 4000 m high.

a) . Find the work she did against gravitational forces

b). A Kilogram of fat supplies energy of 3.7x107 J. If she converts fat to

energy with efficiency rate of 25%. How much fat she consumed in the climb?

Solution,

a) Calculate the work she did against gravitational forces

W= F . d where in this case F= m g and d=h

So W= m g . h W= 50 x 10 x 4000=2000000=2 x 106 J

b) Calculate the fat consumed in the climb 1 kg of body fat would provide 3.7x107J of energy

Where The conversion rate to mechanical work is 25% = 0.25

1 kg would therefore provide=(3.7x107) x(0.25)=9250000=9.25 x 106 of

mechanical work.

So (1 kg) of fat would be consumed for 2 x 106 J of mechanical work =2 x 106 J 𝑥 1 𝐾𝑔

9.25 x 106J= 0.216 kg of fat would be consumed.

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Quizzes 1. Find the potential energy of 20 Kg mass child sitting on a roof 10m above the ground?

2. A truck is pulling a box of 20 Kg mass on a horizontal surface, a distance of 10 m with a

constant speed. The force of friction between the box and the surface is 20 N.

Find the work it did against the force of friction.

3. A ball of 3 Kg mass was dropped from rest the top of tower 50 m high.

Find the speed of the ball 20 m above the base of the tower.

4. A car of 800 Kg mass is travelling at 20 m/s speed coasts to a stop in 400 m on a rough

horizontal road. Find the energy loss.

5. A boy of 50 Kg mass climb’s a wall 500 m high.

a) Find the work he did against gravitational forces.

b) A Kilogram of fat supplies energy of 3.7x10^7 J. If he converts fat to energy with

efficiency rate of 25%. How much fat he consumed in the climb.

6. A car of 800 Kg mass is travelling at 20 m/s speed coasts to a stop in 400 m on a rough

horizontal road. Find the force of friction.

7. A car of 800 Kg mass is travelling at 20 m/s speed hits a concrete wall and comes to rest

after smashing 1.5 meter of the front of the car. Find the reactive force acting on the car

body during the crash.

8. A man raises a 10 Kg mass vertically upwards a distance of 0.5 m. He practices that 1000

times.

a) Find the work he did against gravitational forces.

b) A Kilogram of fat supplies energy of 3.7x10^7 J. If the man converts fat to energy

with efficiency rate of 25%. How much fat he consumed in the exercise

9. A child of 30kg mass is running with speed 5m/s on a rough horizontal floor skids a

distance 3 m till stopped . Find the force of friction?

10. A child 0f 25 kg mass climbs a tower 50m height above the ground. Find his potential

energy at the top of the tower ?

11. A car of 100 Kg mass is travelling at 15 m/s, speed hits a concrete wall and comes to rest

after smashing 1.5 meter of the front of the car.

a) Find the kinetic energy of the car

b) Find the reactive force acting on the car body during the crash.

12 A child of mass 30 kg climbs a tower 50 m high above the ground surface ( given that the

acceleration due to gravity g= 10m/s2) .Find his potential energy at top of the tower

69

Choose the correct answer?

Potential energy and kinetic energy are types of A. Electrical energy B. Magnetic energy C. Thermal energy D. Mechanical energy

Work done = Force x _______ A. distance.

B. acceleration

C. velocity

D. speed

1 joule = 1 _______ A. N m2 B. Kg/s2 C. N m D. N2 m2

The unit of power is _______ 1. watt per second 2. joule 3. kilojoule 4. joule per second

A. watt per second B. joule C. kilojoule D. joule per second

A man of mass 50 kg jumps to a height of 1 m. His potential energy at the highest point is (g = 10 m/s2)

A. 50 J

B. 60 J

C. 500 J

D. 600 J

A. B. C. D.

70

A 1 kg mass has a kinetic energy of 1 joule when its speed is

A. 0.45 m/s

B. m/s

C. 1.4 m/s

D. 4.4 m/s

Name the physical quantity which is equal to the product of force and

distance

A. Work

B. energy

C. power

D. acceleration

An object of mass 1 kg has potential energy of 1 joule relative to the

ground when it is at a height of _______.

A. 0.10 m

B. 1 m

C. 9.8 m

D. 32 m

What is kinetic energy?

A. When an object is in motion

B. When an object is not in motion

C. all of the above

D. none of the above

It takes 20 N of force to move a box a distance of 10 m. How much work is done on the box ?

A. 200 J B. 20.0J C. 2 J D. 200 N

Two factors that determine work are A. amount of the force, and effort used B. amount of the force, and type of force C. mass, and distance D. amount of force and distance moved

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What is energy? A. It is measured in watts B. It is power C. It is the ability to do work D. It is fluid motion

What is work? A. The product of force and displacement B. Causes a change in potential energy of an object C. Does not depend on the path traveled, but only starting and ending position D. All of these are true

The law of conservation of energy states A. Energy cannot be created B. Energy cannot be destroyed C. Energy can only be transferred D. All of these

-------- the energy amount of energy consumed per unit time

a). Work b). Volt

c). Charge d). Power

What is the energy of position or shape that depends on weight and height?

a). kinetic energy b). Magnetic energy

c). Electrical energy d). Potential energy

The unit of Potential energy, work and kinetic energy is a) Watt per second b) Watt

c) Joule d) joule per second

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Ch 3 THE MECHANICS OF NON-VISCOUS

FLUIDS

73

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

What is the Fluids?

A fluid is a collection of molecules that are randomly arranged

and held together by weakcohesive forces and by forces exerted

by the Walls of a container.

Both liquids and gases fluids

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

Density and Pressure 1- Density • The density of a fluid is defined as mass per unit volume .

ρ=m/v (uniform density)•Density is a scalar, the SI unit is kg/m3.

2-Pressure

P=F/A (Pressure of uniform force on flat area)

• F is the magnitude of the normal force on area A.• The SI unit of pressure is N/m2 , called the Pascal (Pa).• The tire pressure of cars are in kilopascals.• 1 atm = 1.013x 105 Pa = 76 cm Hg = 760mm Hg

74

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

if there is an incompressible fluid completely fills a channel such as a pipe or an artery.

Then if more fluid enters one end of the channel, So, an equal amount must leave the other

end. This principle, is called

{The Equation of Continuity}.

The Equation of Continuity (STREAMLINE FLOW)

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The flow rate (Q)

𝑄 is The flow rate which is the volume ΔV of the fluid flowing past a

point in a channel per unit time Δt :

The S.I unit of the flow rate 𝑄 is the 𝒎 3 /𝒔.

Example

If the volume of water flows flowing past a point in pipeline in 3

minutes is 5 litters what is the flow rat?

Answer

Given

ΔV= 5 litter =5x10-3 𝒎 3 and Δt=3 minutes=3x60 s= 180 s

So according the last equation

Q = 𝑉

𝑡=

5x10−3

180= 2.7x10−5 𝑚3/𝐬

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84

85

86

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Exercise

89

1. Questions and Answers

What are fluids? A. Solid B. Liquids, and gases

C. A&b D. Non of the above

Flow rate (Q) measures the amount of ……….. that passes through an area per time

a) Volume b) Mass

c) Distance d) Velocity

Bernoulli's principle states that, for streamline motion of an incompressible non-viscous fluid:

A. pressure at any part + kinetic energy per unit volume = constant

B. kinetic energy per unit volume + potential energy per unit volume = constant

C. pressure at any part + potential energy per unit volume = constant

D. pressure at any part + kinetic energy per unit volume + potential energy per

unit volume = constant

If layers of fluid has frictional force between them then it is known as

A. viscous

B. non-viscous

C. incompressible

D. both a and b

If every particle of fluid has irregular flow, then flow is said to be

A. laminar flow

B. turbulent flow

C. fluid flow

D. both a and b

if every particle of fluid follow same path, then flow is said to be

A. laminar flow c. turbulent flow

B. fluid flow d. both a and b

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Which of the following is a fluid? A. helium B. ice C. iron D. gold

Which of the following is NOT a fluid? A. carbon dioxide B. hydrogen C. seawater D. wood

Which of the following properties is NOT a characteristic of an ideal fluid? A. laminar flow B. turbulent flow C. nonviscous D. incompressible

According to equation of continuity, when water falls its speed increases, while its cross sectional area

a-Increases b-Decreases

c-remain same d-different

Simplified equation of continuity is represented as

A. A1V1 = A2V2

B. A1V2 = A2V2

C. A1V1 = A1V2

D. A2V1 = A1V1

Fundamental equation that relates pressure to fluid's speed and height is known as

A. equation of continuity

B. Bernoulli's equation

C. light equation

D. speed equation

Bernoulli’s equation cannot be applied when the flow is a. Rotational b. turbulent

c. unsteady d. all of the above

91

2. What is the fluid?

3. What is the flow rate?

4. Write the equation of continuity?

5. Write the Bernoulli's equation?

6. The brain of a man is 0.5 m above his heart level. The blood density ρ =1059.5

Kg/m3.What is the blood pressure difference between the brain and the heart?

7. Blood flows in to one of an artery of 0.2Cm radius with a velocity o 3 m/s, and leaves the

other end of radius 0.1 Cm. find the velocity of blood out?

8. If a sphygmomanometer were used to measure the blood pressure in the leg of a man

sitting at rest, would the results give the pressure at the heart? Explain.

Answer : No, because the height is different.

9. Why we measure the blood pressure (using the sphygmomanometer) in the upper arm of

a human?

Answer :it is close to the pressure in the heart.

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Ch4 Direct currents

93

Electric current: The electric current in a wire is the rate at which the charge moves in the wire.

Definition of the current:

The S.I. Current unit is the ampere (A)

t

QI

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Ohm’s Law:

For many conductors, current depends on:

Voltage - more voltage, more current

Current is proportional to voltage

Resistance - more resistance, less current

Current is inversely proportional to resistance

Example 3

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Example 4

What is the resistance of the heating element in a car lock deicer that

contains a 1.5-V battery supplying a current of 0.5 A to the circuit?

Resistance (R)

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97

According to Ohm's law, Resistance is equal to to voltage divided by:

A. potential difference B. conduction C. time D. current

What is a circuit? A. A pathway that electricity flows in. It has a load, wire, and a taco B. A pathway that protons flow in. It has a load, wire, and a power source. C. A pathway that electricity flows in. It has a load, wire, and a power

source.

D. A pathway that electricity flows in. It has a load and wire.

What is an Electric Current? A. A. An Electric Field B. B. An Ampere C. C. The flow of electric charge.

What is Ohm's Law? A. I=V/R

B. R=V/I

C. Power= Voltage × Current

D. A&B

A closed path that electric current follows A. Voltage B. Current C. Resistance D. Circuit

This is related to the force that causes electric charges to flow A. Voltage B. Current C. Resistance D. Circuit

What charge does an electron have? A. negative (-) B. positive (+) C. neutral or no charge (0)

Resistance is affected by a material’s A. temperature. B. thickness. C. length. D. all of these.

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The number of electrons flowing is called

A. voltage. B. power. C. current. D. resistance.

When the circuit is______, current does not flow A. resistors B. heat C. closed D. open

Electrons leave the ______ of a battery and enter the ______ of the battery. A. Positive terminal, positive terminal B. Negative terminal, negative terminal C. Negative terminal, positive terminal D. Positive Terminal, Negative Terminal

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Ch5. Nerve Conduction

100

Nerve Conduction

1- What is nerve conduction study?

These include nerve cells (or neurons).

A nerve conduction study (NCS), also called a nerve conduction velocity (NCV) test--is a

measurement of the speed of conduction of an electrical impulse through a nerve. NCS

can determine nerve damage and destruction.

A nerve conduction study (NCS) is a medical diagnostic test commonly used to evaluate

the function, especially the ability of electrical conduction, of the motor and sensory

nerves of the human body.

Neurons are the basic functional units of the nervous system, and they generate electrical

signals called action potentials, which allow them to quickly transmit information over

long distances

2- Structure of nerve Cell Neurons are made up of a cell body, dendrites, and axons.

Dendrites:

-Receive inputs from other cells and conduct signals

towards the cell body.

-Receive information.

Axons:

-Axon: is the information which transmitted in the

human body by electrical pulses in nerve fibers. axon

has a very high resistance. Axon typically 1 to 20

micrometers in diameter.

- send information.

-Larger axons are enclosed by sheaths of myelin produced by Schwann cells.

Narrow gaps in the myelin sheath between Schwann cells are called nodes of Ranvier.

Nerves are cable-like bundles of axons.

A neuron consists of a cell body that receives electrical messages from other neurons

through contacts called synapses located on the dendrites or on the cell body.

Myelinated neurons are covered in myelin sheaths (Schwann Cells). These increase the

speed in which nerve impulses can be transmitted.

Unmyelinated neurons don't have myelin so they pass impulses "slower" than the

myelinated ones (They do not have node of Ranvier)

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3-Nerve electric properties

Axon is responsible for transforming signals between different points of the nervous system.

In neurons and their surrounding fluid, the most abundant ions are:

1- Positively charged (cations): Sodium Na+ , and potassium K+ .

2- Negatively charged (anions): Chloride Cl-, and organic anions

3- In a resting neuron (polarized), the membrane is much more permeable to K+ than

to Na+ .

4- In most neurons K+, and organic anions (such as those found in proteins and amino

acids) are present at higher concentrations inside the cell than outside.

5- In contrast Na+ and Cl- are usually present at higher concentrations outside the cell. This

means there are stable concentration gradients across the membrane for all of the most

abundant ion types.

The electrical properties of neurons can be described in terms of electrical circuits. To

understand the behavior of this circuit, we need to know the behavior of the basic components

of electrical circuit such as resistor and capacitor.

A Resistance: is a component of a circuit that resists the flow of electrical current.

The capacitance: is the ability of a component to store an electrical charge.

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103

104

105

D)- Space parameter

Space parameter : indicate how far a current travels before most of it has leaked out through

membrane . Thus a current pulse can travel much farther without amplification in myelinated

nerve.

So The distance a current can travel without amplification is characterized by the Space

parameter

According to our model the axoplasm resistance R is proportional to length L of the axon