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1
General Physics course
(PHY 101)
Dr. Zyad Mohammed
Email : [email protected]
Web site:zyadinaya.wordpress.com
mailto:[email protected]
2
"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.
3
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
4
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.
5
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
6
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
7
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
8
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
9
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
10
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
11
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
12
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
13
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
14
weakcohesive
Weight الوزن
work الشغل
Work done الشغل المبذول
X-Ray إكس ) السينية(اشعة
15
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
16
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
17
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
18
Ch 1 (1.1. Vector)
19
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
20
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
21
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
22
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
23
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
24
Third: To calculate the resultant vector by component method
25
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
26
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
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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
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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
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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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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
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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
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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