Physics by RM 1st sec 1st term ملزمة فيزياء لغات اولى ثانوي الترم الاول

1. st 2018/2019
–
2018/2019
By: Raneen Medhat
2018/2019
Physics 1st term Secondary 1

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Physical measurements
Types of Measurements and measurements error
Motion
Acceleration
Equations of Motion
: Applications on Motion With uniform acceleration
: Force & Newton’s First Law
Newton’s second Law
Newton’s Third Law

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Unit 1
Chapter 1: Physical Measurements.
Measurements:
Is the process of comparing the amount of an unknown quantity with another Quantity
of same kind To see how many times the first contain the second.
Measurements
requirments.
The physical quantity
Measuring tools
Units of measurements

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A. The physical quantity:
It is any quantity that can be determined and has a unit of measurements in our life.
So: Everything that can be measured is called Physical quantity.
It can be classified into:
-----------------------------------------------------------------------------------------------------------------------------------
The physical (Mathematical) equation:
The simplest form to express the relation between the Physical quantities and shows
the Physical meaning.
Quantities which can’t be derived from
other Physical quantities
Ex:
Length – time
mass – temperature
Application
Length (L) of the line= 4 cm
4cm
Quantities which can be derived from other
Physical quantities
Ex:
Speed – work
energy – force
Area of the shape = Length x Width
= L1 x L2=2 x 4 =8 cm
4cm
2 cm
The physical quantity
Derivable Physical quantitiesThe fundamental Physical quantities

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B. Measuring tools
Some old and recent measurement tools
Length scale Metric tape, ruler, micrometer and
Vernier caliper
Mass scale Roman balance, two pan balance,
one pan balance and digital balance
Time scale Hourglass, pendulum clock,
stopwatch and digital clock
C. Measuring Units
You can’t say the mass of something =10
10 what? Gram or kilogram
So we say the mass of something =10 Kg or 10 g to Know the amount
the fundamental "Basic"
Physical quantities
French System
C.G.S
British System
F.P.S
Metric System
M.K.S
Length cm Foot Meter
Mass gram Pound Kg
Time sec sec sec

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International system of units (SI units)
(Modern Metric system)
Physical quantity Unit
1) Length (L) Meter (m)
2) Mass (m) Kilogram (Kg)
3) Time (T) Second (s)
4) Electric current intensity (I) Ampere (A)
5) Absolute temperature (T) Kelvin (K)
6) Amount of matter (n) Mole (mol)
7) Luminosity (Iv)
Units has been added
8) Angle measure 2D
9) Solid angle measure 3D
Candela (cd)
Radian
Steradian
Standard Units:
It is the measuring Units internationally agreed and used in the International system
units.
The standard meter:
 Is calibrated by the distance between the two marks engraved at both end of rod
of the alloy platinum – Iridium kept at zero °C.
The standard kilogram:
 Is calibrated by equal to the mass of the alloy Cylinder platinum- Iridium with
finite dimensional reserved at zero °C.
The standard second:
 Is equal to
1
86400
of the average solar day
GR: Platinum and iridium is used in making standard meter?
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The Importance of using atomic clocks
1. Characterized accuracy infinite.
2. Study of a large number of important matters such as
 To determine the day length.
 Reviews to improve the ground and air navigation.
 Checking spaceship trips schedule to discover the universe.
Dimensional equation (formula)
 It is the formula that expresses the derived physical quantities in terms of the
fundamental physical quantities-Mass, Length and Time each has a certain
exponent.
 Any derived physical quantity A can be expressed (represented) in terms of the
fundamental physical quantities
a) Mass “M”
b) Length “L”
c) Time “T”
[A]= M
±a
L
±b
T
±c
Ex:
Length L its unit meter
Area A= Length x Width = L x L = L2
its unit = m x m = m2
(meter2
)
Volume V= Length x Width x height = L x L x L= L3
Its unit = m x m x m = m3
(meter3
)
Find the dimensional and the unit of measuring Density?
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Units’ conversion:
Power of the number (10)
 It used to express large or small quantities in the simplest from
 From bigger to smaller (times), from smaller to bigger (divide)
1-To add or subtract two physical quantities, they must:
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2-If two quantities have different units, one unit should be converted into the other unit.
3-Dimensional formula cannot be add or subtracted but it can be multiplied or divided.
The importance of the Dimensional formula:
It can be used to verify the validity of a physical relation.
𝑥 10−2
Centi c
𝑥 103
Kilo K
10−3
Milli m
10−6
Micro μ
10−9
Nano n
106
Mega M
109
Giga G
Pico
10−12

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Types of measurements
Direct measurements Indirect measurements
No. of measuring
tools
One measuring tool is used More than one measuring tool is
used
No. of measuring
processes
one
Ex: measuring volume
using graduated cylinder
More than one
Ex: measuring volume using
ruler by multiplying
Length x width x height
No. of
measurements error
One Three
Measurements error
Measurement process cannot be accurately 100%
But there could be even a simple percentage of error
Reasons of measurement error:
1. Choosing unsuitable measuring tool.
2. A defect in the measurement tool.
3. Using wrong procedure in measuring.
4. Environmental factors (Temperature, humidity and air currents)
Types of error
Absolute error (ΔX) Relative error (r)
It is the difference between the real (χ0)
value and the measured value (χ)
Δx = │χ0 – χ│
It is the ratio between the absolute error
(Δx) to the real value (χ0)
r =
Δx
χ0
**Mark scale ││ indicates that the product is
always positive
even if it were real quantity less than the
measured quantity
because what is important is to know how error
whether it
increase or decreases or decreases for instance,
│d – 9d│= 8
***
The relative error of more significance in the
accuracy
of the measurement than the absolute error, and
be more
accurate measurement whenever the relative
error is small

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Ex: One of the students measured the length of a pencil and found it equals (9.9cm)
and the real value of a pencil length is equal to (10cm), while classmate measured the
length of the class room he found it equals (9.13m), while the real value of the length
of classroom (9.11m) Calculate the absolute error and relative error in each case:
- Calculation the absolute error Calculation the absolute error:
Δx= │x0 - x│= │10 – 9.9│ = 0.1cm
Length of a pencil = (10± 0.1) cm
Δx=│x0- x│= │9.11 – 9.13│ = │-0.02│ = 0.02 cm
Length of a pencil = (9.11 ± 0.02) m
- Calculation the relative error Calculation the relative error
r =
Δx
χ0
=
0.1
10
= 0.01 = 1%
r =
Δx
χ0
=
0.02
9.11
= 0.0022 = 0.22%
Calculation error in the indirect measurement
 The method of calculating the error in the case of indirect measurement
depending on the mathematical relationship during the calculation process
Mathematical relationship Example How to calculate the error
Add Measure the volume of two
quantities of liquid
Absolute error = absolute error
in the first measurement +
absolute error in the second
measurement
Δχ = Δχ1 +Δχ2
Subtract Measuring the volume of a
coin subtracting the volume of
water before you put them in a
graduated cylinder the volume
of the water after placed in the
cylinder
Times Measure the area of a
rectangle measuring the length
and width and finding (L×W)
Relative error = relative
error in first measurement
+ relative error in second
measurement
r = r1 + r2
Divide Measure the density of the
liquid, measure mass and
volume then find
mass ÷ volume

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• In physics, a physical quantity is any physical property that can be quantified,
that is, can be measured using numbers.
• Examples of physical quantities are :
Mass, amount of substance, length, time, temperature, electric current, light
intensity, force, velocity, density, and many others
All physical quantities are classified into 2 types
Scalar quantities Vector quantities
A SCALAR is ANY quantity in physics
that has MAGNITUDE only, but NOT a
direction associated with it
A VECTOR is ANY quantity in physics
that has BOTH MAGNITUDE and
DIRECTION.
Examples:
Mass
Distance
Time
…
Force
Displacement
Acceleration
…

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Vector quantity
A vector is represented by an arrow. Its length determines its magnitude and the tip
determines its direction.
Vectors
Vectors quantities are defined by magnitude and direction.
Resultant of Vectors
1. If they are in the same direction or in opposite direction
5 + 5 = 10
5 + 5 = 0
5 + 10
2. If the vectors are not in the same direction, we move them so they start from the
same place and complete the parallelogram. If they are perpendicular, we can
add them using the Pythagorean theorem:
6 + 8 =

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Distance & Displacement
Distance Displacement
A SCALAR quantity in
physics can be defined by
MAGNITUDE only,
A VECTOR is ANY quantity in
physics that has BOTH
MAGNITUDE and
DIRECTION.
It is the length of the path
moved by an object from a
position to another.
It is the length of the straight line
in a given direction between
starting point and the end point
Its unit
cm, m, km cm, m, km
**** Distance equal displacement when the motion in straight line.
Vector multiplication:
1. Scalar (dot) product
Vector A .Vector B = AB cos θ
2. Vector (cross) product
Vector A x Vector B= AB sin θ n
Where n represent the direction
****

A ˄ B ≠ B ˄ A A ˄ B = - B ˄ A

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Right hand rule
By moving the fingers of the right hand of the first vector towards the second vector
across the small angle between them, shall be thumb points for the result of vector
product
It is used to define the direction of the vector product of the two vectors A
& B

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Motion:
 The change in the position of an object relative to a fixed point as time
passes.
Objects around us can be classified into:
Static object Moving object
The object that doesn’t change its position
relative to a given (fixed) point with time.
The object that changes its position
relative to a given (fixed) point with time.
Types of Motion
 A motion which has a starting and end
points
* Motion in a straight line (as train)
* Projectiles
 The motion that repeats itself over
equal intervals of time
* Vibrational motion. (As pendulum.)
* Motion of the moon around the
earth.
* Motion in a circle.
translation
Motion Periodic
Motion

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Speed & Velocity
Velocity
It is the rate of change of displacement.
Or, the displacement of an object in one second.
Types of velocity
What is the difference between uniform velocity and non-uniform velocity?
Uniform Velocity: An object with uniform velocity covers equal distances in equal
intervals of time in a specified direction e.g., an object moving with speed of 40 km h-
1
towards west has uniform velocity.
Non-uniform Velocity: When an object covers unequal distances in equal intervals of
time in a specified direction, or if the direction of motion changes, it is said to be
moving with a non-uniform or variable velocity. e.g., revolving fan at a constant speed
has variable velocity.

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For Non-uniform velocity we can fined
1. The instantaneous velocity: 𝑣=
∆𝑑
∆𝑡
The velocity of the object at a given instant.
2. The average velocity: ⊽ =
𝑑
𝑡
It is given by dividing the total displacement of the object from the starting
point to the end point by the total time of motion.
**** Instantaneous velocity and average velocity are equal, if the object moves
at a uniform velocity.

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Acceleration:
It is the change of the object velocity per unit time.
Or
It is the rate of change of velocity.
Accelerated Motion:
It is the motion in which velocity change with time.
Types of Acceleration
Uniform acceleration Non-uniform acceleration
The object changes velocity with equal
amount in equal intervals time.
The object changes velocity with unequal
amounts in equal intervals of time.
Acceleration may be:
1) +ve acceleration (increasing velocity)
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2) –ve acceleration or deceleration (decreasing velocity)
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3) Zero acceleration (uniform velocity)
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Guidelines to solve problems,
1-when the object starts motion from rest Vi= zero.
2-when the object will stop (comes to rest) Vf = zero.
3-If the object moves at uniform velocity it’s (a)= zero
4- If (V) and (a) have the same signs (+ve or –ve) then the acceleration is positive.
{Acceleration motion}
5- If (V) and (a) have different signs then the acceleration is negative. {Deceleration
motion}

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Equations of motion
***That expresses motion of objects at uniform acceleration
First equation: the equation of (velocity-Time)
Proof:
a =
∆𝑣
∆𝑡
=
𝑣𝑓−𝑣𝑖
𝑡
⸫ vf - vi =at ⸫ vf = vi +at
Second equation: the equation of (displacement-Time)
Proof:
⊽ =
𝑑
𝑡
=
𝑣𝑓+𝑣𝑖
2
⸫
𝑑
𝑡
=
(𝐯𝐢 +𝐚𝐭)+vi
𝑡
= vi +
1
2
𝑎𝑡 multiplying both sides by (t)
⸫ d = vi t+
𝟏
𝟐
𝒂𝒕 𝟐
Third equation: the equation of (displacement-velocity)
Proof:
d=⊽ 𝐭
⊽=
𝑣𝑓+𝑣𝑖
2
And t =
𝑣𝑓−𝑣𝑖
𝑎
substituting in equation (1)
⸫ d= ⊽ 𝐭 =
𝑣𝑓+𝑣𝑖
2
x
𝑣𝑓−𝑣𝑖
𝑎
⸫ d=
𝑣𝑓2−𝑣𝑖2
2𝑎
d
tv
3 2
1
2
1

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2ad=𝑣𝑓2
− 𝑣𝑖2
⸫ 𝑣𝑓2
= 𝑣𝑖2
+ 2𝑎𝑑
Application of Motion with Uniform Acceleration
Free fall
Free fall acceleration
It is the acceleration by which objects moves during free fall towards
ground.
Force:
It is an external influence that affects the object to change its state of motion
or direction.
*It’s measured using the spring balance in newton (N)
3

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Newton’s Law of Motion
Newton’s First Law of Motion
A static object keeps its state of rest, and a moving object keeps its state of
motion at a uniform velocity in a straight line unless acted upon by a
resultant force
The mathematical formula Σ F = zero
Newton’s first law is known as the law of inertia
Inertia
It is the tendency of an object to keep either its state of rest or state of
motion at its original velocity uniformly in a straight line.
Or
It is the property of objects to resist the change of its static or dynamic state.

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Momentum (P)
It is the dot product of (velocity) and (mass).
Linear momentum is a vector physical quantity.
* Law = M.V *Measuring unit (kg.m/sec).
*Dimensional formula M.L.T-1
Newton’s second law
When a resultant force affects an object
 The object acquires an acceleration which is directly proportional to
the resultant force and inversely proportional to the object mass.
 Equals to the rate of change in the object’s momentum (motion
amount).
The mathematical formula: Σ F ≠ zero
Σ F = m a
Proof:
F=
∆𝑝
∆𝑡
=
∆𝑚𝑣
∆𝑡
=
∆𝑚𝑣𝑓−⧍𝑚𝑣𝑖
∆𝑡
F=m
(𝑣𝑓−𝑣𝑖)
∆𝑡
=m
∆𝑣
∆𝑡
= ma
⸫ F= ma –> a=
𝐹
𝑚
**In case of more than one forces acts on the body, then
Σ F= F (moving) =f1 + f2 + f3 +…, Where the forces acting in opposite
direction such as friction force take negative sign.

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 What is meant by: Newton?
It is the force that when acts on an object of mass 1 kg accelerates it at 1
m/sec2
in the same direction.
Newton’s third law
For every action there is a reaction equal in magnitude and opposite in
direction.
The mathematical formula F1 = -F2
Applications of Newton’s Third Law
1) When a man jumps from a boat to the reef (action) the boat shifts
backwards (reaction)
2) When a bullet is fired (action) the rifle recoils backwards (reaction).
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