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Mechanics
Mechanics is one the most important subject in physics
...

Mechanics can be defined as the behavior of the bodies under any effects
...


Mechanics

kinematics

dynamics

KINEMATICS
Kinematics is the study of classical mechanics which describes the motion of points, bodies (objects)
and systems of bodies (groups of objects) without consideration of the causes of motion
...

Types of motion
Linear motion : when a body moves either in a straight line or along a curved path, then we say that
it is executing linear motion
...
When a body moves in a straight line then the linear motion is
motion
...
g
...

2
...

e
...
, a planet revolving around its parent star
Other types of motion are:
Rotatory motion: A body is said to be in rotatory motion when it stays at one place and turns round
and round about an axis
...

Oscillatory motion: a body is said to be in oscillatory motion when it swings to and fro about a mean
position, example: the pendulum of a clock, the swing etc
...

Even a person without a background in physics has a collection of words, which can be used to
describe moving objects
...

In physics, we use these words as the language of motion
1
...
Speed and Velocity
3
...

The quantity is either a vector or scalar
...

 Vectors are quantities which are described by both a magnitude and a direction
...

It is a scalar quantity
...

It is the object's overall change in position
...

SI unit: meter (m)
Other common units: kilometer (km), centimeter
(cm)

A student walks 4 m East, 2 m South, 4 m West, and finally 2 m North
...

Total displacement = 0 m
When he is finished walking, there is no change in his position
...

Speed
Speed can be defined as “how fast something moves” or it can be explained more scientifically as
“the distance covered in a unit of time”
...
Speed does not show us the direction of the motion it just gives the
magnitude of what distance taken in a given time
...

 metric unit of speed: m/s
 English unit of speed: ft/s
We use a symbol v to show speed
...
Average speed is
a measure of the distance traveled in a given period of time; it is sometimes referred to as the
distance per time ratio
...
2 hours (12 minutes)
...
During your trip, there may
have been times that you were stopped and other times that your speedometer was reading 50
miles per hour
...

Instantaneous speed:
Instantaneous speed: is the speed at any instant
•

Use speedometer to find instantaneous speed

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•

Can be found by finding the gradient of the tangent to the displacement-time graph, at that
point in time

Constant speed
Sometimes when we are describing motion we use the terms "steady speed" or "constant speed"
...
The speedometer reads the speed of
the car at each moment in time throughout the car's journey
...
5 hours
𝑉 = 𝑠/𝑡
𝑉=

144 𝑘𝑚
1
...
83m/s (2dp)

Example3
I ran 1000 m in 3 minutes then ran another 1000 m uphill in 7 minutes
...
= 1000 m + 1000 m = 2000 m
Total Time = 3 min + 7 min = 10 min
Ave speed = total dist/total time =
2000m/10 min = 200 m/600s = 0
...


Solution
a) The total distance d covered by the object is
s = AB + BC + CB = 5 km + 4 km + 4 km = 13 km
distance
time

average speed =
Velocity

=

13km
0
...
It is calculated the same as
speed, but you must include a direction in your answer
...

Average Velocity
The average speed of an object is defined as the distance traveled divided by the time elapsed
...


Example1
If a cyclist in the Tour de France traveled southwest a distance of 12,250 meters in one hour, what
would the velocity of the cyclist be?
Solution
Given
S= 12,250m, T= 1h, V= ?
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Convert one hour in second , 1h= 3600s
𝑽=

𝒔
𝑻

𝑽=

𝟏𝟐,𝟐𝟓𝟎𝒎
=
𝟑𝟔𝟎𝟎𝒔

3
...
6 km in
1
...

Solution
𝑽=

𝒔
𝑻

𝑽=

𝟏
...
𝟒𝒉

×

𝒉
𝟑𝟔𝟎𝟎𝒔

= 50
...
He then continues
north, traveling 130 km in 2 hours
...
d1 = v1t1 = 85km/h× 12 ℎ= 49
...
The total distance traveled is 179
...
His
displacement is 179
...


𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 =

𝒕𝒐𝒕𝒂𝒍 𝒅𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕
𝒕𝒐𝒕𝒂𝒍 𝒕𝒊𝒎𝒆

Total time 15min+35min+120min=2
...
𝟔𝒌𝒎
=
𝟐
...
4km/h

Example4
The magnitude of the displacement D is equal to the hypotenuse AB as shown below

a) Find the magnitude of D?
b) Average velocity?
Solution
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Use Pythagoras’s theorem to find AB as follows
AB2 = 32 + 32 = 18
D = AB = 3√2 km
average velocity =

𝐭𝐨𝐭𝐚𝐥 𝐝𝐢𝐬𝐩𝐥𝐚𝐜𝐞𝐦𝐞𝐧𝐭
𝐭𝐨𝐭𝐚𝐥 𝐭𝐢𝐦𝐞

=

𝟑√𝟐𝐤𝐦
𝟏𝐡+𝟏𝟐𝐦𝐢𝐧

=

𝟑√𝟐𝐤𝐦
𝟏
...
5√2 km/h = 3
...

a) Find the average speed of the moving object in m/s
...


Solution:
a
...
Using the given scale,
s = 2 AB + 2 BC = 10 + 6 = 16 km
distance

16km

1600m

Average speed=
=
=
= 3200m/s
time
5s
5s
b
...

0

Average velocity = 5s = 0
Acceleration
Acceleration is defined as the rate of change of velocity
...

Notes
 If velocity is constant throughout, there is no acceleration (a= 0)
 If the velocity is increasing, the object is said to be accelerating
...
What is the skydiver’s average
acceleration?
Solution

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Example2
The car is accelerated as the following

Example3
A car is moving from rest and attained a velocity of 80 m/s
...
Plot and interpret a distance-time graph and a speed-time graph
...
Deduce from the shape of a distance-time graph when a body is:
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(a) At rest
(b) Moving with uniform speed
(c) Moving with non-uniform speed
3
...
Calculate the area under a speed-time graph to determine the distance travelled for motion with
uniform speed or uniform acceleration
...

Area under the Speed-time Graph is the distance travelled
Distance-time graph
A car has travelled past a lamp post on the road and the distance of the car from the lamp post is
measured every second
...
The following pages are the results for four possible journeys
...

Car accelerating
Speed increases, so the car travels a long distance as time increases
...

Car decelerating
Speed decreases, so the car travels a shorter distance as time increases

 The gradient of the distance-time graph gives the speed of the moving object
...

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(a) Car at rest (=0m/s)
This is so because the speed of the object is zero, as the red line shows in the graph above
...

(b) Car moving with uniform speed(=10m/s)
The speed of the object is constant
...
This also means that there is no
acceleration, as there is no increase in the speed of the object
...

Acceleration increases
Acceleration increases so speed increase more when time increases
ii
...

Example1
Using the given graph find the velocity of the object in intervals (1s – 3s) and (3s – 5s)
...

The area under a speed-time graph gives the distance travelled
...

c) The force acting in the first 4 seconds

Solutions
a) The acceleration in the first four seconds is given by the slope of the graph AB
20𝑚/𝑠−0

AB = BF/AF =
=5 m/s2
4𝑠
b) The distance covered in the first four seconds = area of Δ ABF
1
1
1
= 2bh = 2AF x BF=2x 4 x 20 = 40m
Example5
A cyclist started from rest achieved a speed of 10 m s-1 in 5 s
...
Finally he decelerate to complete his 30 s journey
...

c) Calculate the distance that he travelled during the journey
...
Simple relations exist between these quantities
...

There are three equations of motion
...
v = u+at
𝑢+𝑣
2
...
S = ut + 𝟐 at2
4
...

Derivation of Equation of Motion
First Equation of Motion
Consider a particle moving along a straight line with uniform acceleration 'a'
...

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𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚
𝑻𝒊𝒎𝒆

𝐀𝐜𝐜𝐞𝐥𝐞𝐫𝐚𝐭𝐢𝐨𝐧 =

=

𝐯−𝐮
𝒕

at = v − u
v = u+ at
...
(1)

Average Velocity can be written as
𝑢+𝑣
2

Average Velocity =

=

𝑢+𝑣
2


...
(3)
𝐬
𝒖+ 𝒗
=
𝒕
𝟐
𝐬=(

𝐮+ 𝐯
) 𝐭 … … … … … … … … … … … … … … … … … … … …
...

Substituting the value of v in equation (2) we get
s
𝑢 + 𝑣 + 𝑎𝑡
=
𝑡
2
𝐬=(

𝟐𝒖 + 𝒂𝒕
𝟐𝐮𝐭 + 𝐚𝐭 𝟐
𝟐𝐮𝐭 𝐚𝐭 𝟐
)𝐭=
=
+
𝟐
𝟐
𝟐
𝟐

𝐬 = 𝐮𝐭 +

𝟏
𝟐

𝐚𝐭 𝟐 …………………………………………………………………
...

𝑣 − 𝑢 = 𝑎𝑡
...
(2)
Average velocity =

𝑢+𝑣
…………
...
(4)

Multiplying eq (1) and eq (4) we get,
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(v - u)(v + u) = at x

2s
t

(v - u)(v + u) = 2as
[We make use of the identity a2 - b2 = (a + b) (a - b)]
v2 - u2 = 2as
...
Let it be, given a uniform
acceleration at time, t = 0 when its initial velocity is u
...
The figure
shows the velocity-time graph of the motion of the object
...

Thus, acceleration = slope = AB =

𝐵𝐶 𝑣−𝑢
=
𝐴𝐶 𝑡−0

=a =

𝑣−𝑢
𝑡

v - u = at
v = u + at
...
second equation

Eng: farah khadaad

Third Equation of Motion

Let u be the initial velocity of an object and 'a' the acceleration produced in the body
...

Distance traveled s = area of the trapezium ABDO
= area of rectangle ACDO + area of ΔABC
1

= OD x OA + 2BC x AC
1
2

= t x u + (v - u) x t
1

= ut + 2 (v - u) x t
(v = u + at I eqn of motion; v - u = at)
1

S = ut + 2at x t
1

S = ut + 2at2………………………………third eq (3)
Fourth Equation of Motion
Let 'u' be the initial velocity of an object and a be the acceleration produced in the body
...


S = area of the trapezium OABD
...
(1)

But we know that a = v−ut

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Or t = v−ua
Substituting the value of t in eq
...
Fourth Equation of Motion
How do we select the right equation?
The flow chart below can be used to help you to select the correct equation of motion to use:

Example1
A toy car accelerates from 3m/s to 5m/s in 5 s
...
The car carries on moving
during this reaction time
...
The
thinking distance increases if the reaction time increases
...

Braking distance
The braking distance is the distance taken to stop once the brakes are applied
...


Stopping distances
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When the brakes are applied, work is done by the friction force between the brakes and the wheels
...
A car accelerates uniformly from a speed of 20ms-1 to a speed of 25ms-1 in 2s
...
the average speed for this period of 2s
b
...
the acceleration
2
...

a
...
QR
c
...
a
...
What is the acceleration of the object
c
...
What is the average speed of the object during the first 15 seconds?

4
...
What does the portion of the graph between O and A indicate?
b
...
What is the deceleration of the bus between C and D?
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d
...
What is the average velocity of the bus?

5
...
A accelerates for the first 5 s, until his velocity reaches
12ms-1, after which he travels with constant velocity
...
Sketch the velocity-time graphs for the two cyclists
b
...
Who is in the lead after 10 s?
6
...
The speedometer reading after every 5 s is tabulated
below
Time/s

0

5

10

15

20

25

30

35

40

Velocity
m/s

0

10

20

30

30

30

30

15

0

a
...
Describe the motion of the car
c
...
What is the total distance travelled by the car
e
...
Find the average velocity of a car which travels 360km in 6 hours in
a
...
m/s
8
...
m/s
b
...
The graph below shows the speed-time graph for a child on a swing

a) Write down
i
...
The time at which the maximum speed occurs
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b) i
...
Mark with 'M' one point at which the acceleration is zero
c) Estimate the distance travelled by the child in 1
...
When we say that an object is being accelerated, we mean that
a
...
it is moving,
c
...
Dynamics involves the study of the
cause of motion, which is force
...

Effects of Force
A force is push or pull exerted on an object
...

The unit of force is Newton ( or kgms-2)
...
The net
force is known as the unbalanced force or the resultant force
...

Formula of Force

from Newton's Second Law, we can derived the equation
(IMPORTANT: F Must be the net force)
Newton I
Newton’s First Law states:
Every object continues in its state of rest or uniform motion in a straight line, unless it is
compelled to change that state by an external force acting on it
...
The total force is
zero
...

2) Passengers fall forward when bus suddenly stops
...


Newton II
Newton's Second Law states:
Rate of change of momentum is proportional to the total force acting on a body, and occurs in the
direction of the force
...


𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒎𝒐𝒎𝒆𝒏𝒕𝒖𝒎
∝ 𝑭
𝒕𝒊𝒎𝒆
mv−mu
∝F
t
m(v−u)
∝F
t

Now acceleration, a =

(𝑣− 𝑢)
𝑡

F  m × a
 F = k × m × a (k is a constant with no units
...

Acceleration is always caused by a total force, the vector sum of all the forces
...

Example1:
A box of mass 150kg is placed on a horizontal floor with a smooth surface; find the acceleration of
the box when a 300N force is acting on the box horizontally
...
If the velocity of the
object changes from stationary to 25
...
The mass m is
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already given in the question, but the acceleration is not give directly
...

Newton III
Newton’s Third law states that:
“For every action there is an equal and opposite reaction”
If body A exerts a force on body B, body B must exert an equal and opposite force on body A
...
This is true whether the forces are in equilibrium,
moving, stationary or accelerating
...


2) Same thing happens in the rocket propulsion
...


Momentum
Momentum is a vector quantity, given the symbol p, which measures how hard it is to stop a moving
object
...
We can therefore calculate momentum using the equation:

Momentum is something which is associated with mass of the moving body
...

The change in momentum formula is given as
Where
p = momentum of the body,
m = mass of the body and
v = velocity of the body
...
I unit for momentum is Kgms-1
...
Calculate its momentum?

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Solution

Example2
A motor bike is moving at the rate of 20 m/s having momentum of 6000 kgm/s
Calculate its mass?
Solution

Example3
A student releases a ball with mass of 2 kg from a height of 5 m from the ground
...

The final velocity = ?
From the equation
v2 = u2 + 2as
v2 = (0)2 + 2(10)(5)
v = 10ms-1
The momentum,
p = mv =(2)(10) = 20 kgms-1
Principle of Conservation of Momentum
The principle of conservation of momentum states that in a system make out of objects that react
(collide or explode), the total momentum is constant if no external force is acted upon the system
...
If car B moves forwards at 30 ms-1 by the impact, what is the velocity, v, of the
car A immediately after the crash?
Solution
m1 = 600kg
m2 = 800kg
u1 = 40 ms-1
u2 = 20 ms-1
v1 = ?
v2 = 30 ms-1
According to the principle of conservation of momentum,
m1u1 + m2u2 = m1v1 + m2v2
(600)(40) + (800)(20) = (600)v1 + (800)(30)
40000 = 600v1 + 24000
600v1 = 16000
v1 = 26
...
50kg ball traveling at 6
...
0 kg ball moving in the opposite direction
at a speed of 12
...
The 0
...
0 ms-1 after the collision
...

Solution
m1 = 0
...
0 kg
u1 = 6
...
0 ms-1
v1 = -14
...
5)(6) + (1
...
5)(-14) + (1
...

direction
...
5 kg
...

m1 = 2
...
01 kg
u1 = 0 ms-1
u2 = 0 ms-1
v1 = ?
v2 = 250 ms-1
By using the equation of conservation of momentum principle
0 = m1v1 + m2v2
0 = (2
...
01)(250)
(2
...
5v1 = -1 ms-1
Impulse
As you can see, momentum can change, and a change in momentum is known as an impulse
...

Example2
A body having 3 kg weight is traveling at 2m/s is subjected to Velocity of 10m/s
...
Impulsive force is defined as the rate of change of momentum in a reaction
...
It is a force which acts on an object for a very short interval during a collision or explosion
...
A greater force
produces a higher acceleration
...
A greater impulse yields a higher
velocity change
...
The car hits a street lamp and is stopped
in0
...
What is the impulsive force acting on the car during the crash?
Solution
m = 1000kg
u = 24 m/s
v=0
t = 0
...
05

Application of momentum and impulses
Safety Features in Vehicles
Crumble Zone
The crumple zone increases the reaction time of
collision during an accident
...

Seat Belt
Prevent the driver and passengers from being
flung forward or thrown out of the car during an
emergency break
...

Padded Dashboard
Cover with soft material
...


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=F=480,000N

Collapsible Steering Columns
The steering will swing away from driver’s chest
during collision
...


Passenger Safety Cell
The body of the car is made from strong, rigid stell
cage
...


Projectile Motion
Projectile motion is a form of motion in which an object or particle (called a projectile) is thrown
near the earth's surface, and it moves along a curved path under the action of gravity only
...

A vector quantity is a quantity which is fully described by both magnitude and direction
...

The length representing the magnitude of the vector
...

Vector Addition
Vector Addition - Triangle Method

Join the tail of the 2nd vector to the head of the 1st vector
...

Vector Addition - Parallelogram Method

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Join the tail of the 2nd vector to the tail of the 1st vector
...

Addition of 2 Perpendicular Vectors

If 2 vectors (a and b) are perpendicular to each others, the magnitude and direction of the resultant
vector can be determined by the following equation
...
What is the
magnitude of the resultant force if P and Q are acting on an object?
Solution
Magnitude of the resultant force
∣∣F∣∣=102+122 =√244=15
...
All the
forces are perpendicular to each others
...

Therefore, the magnitude of these 2 force components,
∣∣F∣∣=32+42 =√25=5N
Vector Resolution
Vector Resolution

A vector can be resolve into 2 component which is perpendicular to each others
...
If the tension of the cable is 3000N and
the friction between the log and the ground is 500N, find the horizontal force that acting on the log
...
Find the
acceleration of object P, in ms-2
...
36N
Vertical component of the forces = 25sin45° - 25sin45° = 0N
The acceleration of the object can be determined by the equation
F = ma
(35
...
68 ms-2
Inclined Plane

Weight component along the plane = Wsinθ
...

Example2

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A block of mass 2 kg is pulling along a plane by a 20N force as shown in diagram above
...

Solution

First of all, let's examine all the forces or component of forces acting along the plane
...

What is the name of this resistive force called?
It is called friction
...
So when you
rub your hands together you feel the resistive force of friction
...

3
...

Even in deep space, bits of micrometeorites will hit a moving object, causing some friction
(although it is incredibly small)
...
Static friction
the friction that exists between two surfaces that is not
moving relative to each other
...
Kinetic friction
the friction that exists between two surfaces that is
moving relative to each other
...
Sliding friction friction experienced when
two solid objects are in contact and a force is
applied to slide one object against the other,
sliding friction force resists the motion
b
...

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Effect of friction
ADVANTAGES OF FRICTIONS
Friction plays a vital role in our daily life
...

1
...
When we move on ice, it
becomes difficult to walk due to low friction of ice
...
We cannot fix nail in the wood or wall if there is no friction
...

3
...
You cannot keep a pencil in your hand
without friction
...


Driving car: Your car would not begin moving if it wasn't for the friction of the tires against
the street
...
Likewise, you could not stop without
the friction of the brakes and the tires
...
The main disadvantage of friction is that it produces heat in various parts of machines
...

2
...

3
...

4
...

5
...


METHODS OF REDUCING FRICTION
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There are a number of methods to reduce friction in which some are discussed here
...

USE OF GREASE:
Proper greasing between the sliding parts of machine reduces the friction
...


DESIGN MODIFICATION (Streamlining)
Friction can be reduced by changing the design of fast moving objects
...

Modern cars are also streamlined
...


Terminal velocity
When an object falls, it accelerates
...

Eventually, the force from the air resistance willequal the force from the weight of the object
At that point, the speed will remain constant: the object has reached its "terminal velocity" and can't
fall any faster
...


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For a free-fall parachutist, before the parachute opens, terminal velocity is around 120 miles
per hour
...

Free falling is a motion under force of gravity as the only force acting on the moving object
...

The gravitational acceleration is the acceleration of an object due to the pull of the gravitational
force
...

Gravitational acceleration does not depend on the mass of the moving object
...
80 m s2
g  10 m s2

or
or

32
...

its acceleration is equal to the gravitational acceleration, g,
which taken to be 10ms-2 in SPM
...

Case of Free Falling 2 - Launching Object Upward
If an object is launched up vertically,
the acceleration = -g (-10ms-2)
the velocity become zero when the object reaches the highest point
...

Example1
The referee tosses the coin up with an initial speed of 5
...
In
the absence if air resistance, how high does the coin go above its
point of release?
Solution
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H

A

v
0 m/s

2

?

-9
...
00 m s2
h
2 9
...
00m/s

2
v 2  vo
2a

 1
...
The Stone takes 4s to touch the water surface of
the river
...

Velocity of iron V = gt = 9
...
8 m/s2 × 3s = 29
...

The Velocity of iron is more than cotton
...

The Universal law of gravitation states that:
Every mass exerts an attractive force on every other mass
...


The gravity formula is given by
Where G is a constant equal to 6
...

The gravitational force formula is very helpful in finding larger radius, larger mass, gravity values
etc
...
Its velocity is changing not because the magnitude of the velocity is changing but because
its direction is
...
For this acceleration to happen there must be a resultant force, this
Force is called the centripetal force
...
This means that the unit for angular speed
is the radian per second (rad s-1)
...

r = is the radius of the circle in meters (m)
...

Example1
A train is travelling on a truck which part of a circle of radius 600m, at a constant speed of 5m/s,
what is the angular velocity of train?
Solution
 = v/r
= 50/600 = 0
...
It is always directed
towards the center of the circle
...
0 m radius circle
...
The centripetal force, measured in Newton (N)

Factors affecting centripetal force
The centripetal force needed to keep an object moving in a circle increases if:
the mass of the object increases
the speed of the object increases
the radius of the circle in which it is travelling decreases
Example1
A car of mass 1000 Kg moves in a circular path of radius 50 m
...
Determine the centripetal force of the car?
Solution

Work
Work done by a constant force is given by the product of the force and the distance moved in the
direction of the force
...

Work is a scalar quantity
...

Example1

Diagram above shows a 10N force is pulling a metal
...
If the distance travelled by the metal block is 2m, find
the work done by the pulling force
the work done by the frictional force
Solution
(a) The force is in the same direction of the motion
...

Solution

Example3

A force of 50 N acts on the block at the angle shown in the diagram
...
0 m
...

solution
Work done,
W = F × s × cos θ
W = 50 × 3
...
9J

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Example4

the graph above shows the force acting on a trolley of 5 kg mass over a distance of 10 m
...

Solution
In a Force-Displacement graph, work done is equal to the area below the graph
...
position graph of an object is given below
...


Solution
Area under the graph gives us work done by the force
...
5=20 joule
Work done between 5-8m:
W2=

(𝟔+𝟒)
=15
𝟐
...
𝟑
W3= 𝟐 =9 joule
Work done between 11-15m:
𝟓
...

Work is done when energy is converted from one form to another
...
E
...

𝑾𝒐𝒓𝒌 𝒅𝒐𝒏𝒆 = 𝒇𝒐𝒓𝒄𝒆 𝒙 𝒅𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕
But F = ma, and displacement = s
So Work done = 𝑚
...
as
V2

So W = m 2 Or

1

Work done = Ek = 2mu2
Gravitational Potential Energy
𝑬𝒑 = 𝑷
...

𝑻𝒉𝒆 𝒘𝒐𝒓𝒌 𝒅𝒐𝒏𝒆 𝒍𝒊𝒇𝒕𝒊𝒏𝒈 𝒕𝒉𝒆𝒎 = 𝒑𝒐𝒕𝒆𝒏𝒕𝒊𝒂𝒍 𝒆𝒏𝒆𝒓𝒈𝒚 𝒔𝒕𝒐𝒓𝒆𝒅 𝒊𝒏 𝒕𝒉𝒆𝒎
𝑾𝒐𝒓𝒌 𝒅𝒐𝒏𝒆 = 𝑭𝒐𝒓𝒄𝒆 𝒙 𝒅𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕
𝑯𝒆𝒓𝒆 𝒕𝒉𝒆 𝒇𝒐𝒓𝒄𝒆 = 𝒘𝒆𝒊𝒈𝒉𝒕 = 𝒎 𝒙 𝒈
𝑨𝒏𝒅 𝒕𝒉𝒆 𝒅𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕 = 𝒉𝒆𝒊𝒈𝒉𝒕 = 𝒉
𝑺𝒐 𝑾𝒐𝒓𝒌 𝒅𝒐𝒏𝒆 = 𝒎 𝒙 𝒈 𝒙 𝒉 = 𝑷
...
This is true for any movement near the Earth's
surface
...
It is powerfully simple, and gives us a direct relation
between net work and kinetic energy
...

Example1
What is the kinetic energy of a 2 kg ball that travels a distance of 50 meters in 5 seconds?
Solution
50m
The velocity of the ball is easily calculable: v =
= 10 m/s
...
F = am = 1000×2= 2000N
1
1
s= ut + 2at2 = 2 ×2×400= 400m
W= FS= 2000N× 400m = 800000J
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b)
...

a)
...
calculate the final kinetic energy of the car ?
c) Calculate the change in kinetic energy?
Solution
1
1
a) kE1=2mu2 = 2 (800)(20)= 160000j
1

1

b) KE2= 2 mv2= 2 (800)(30)= 360000j
c)
...
What is the work done to overcome the friction?
Solution
In this case, kinetic energy is converted into heat energy due to the friction
...

Formula:

Example1
An electric motor takes 20 s to lift a box of mass 20kg to a height of 1
...
Find the amount of work
done by the machine and hence find the power of the electric motor
...
5) = 300𝐽
Power,
w 300
P= t = 20 =15J
example2
John is having mass 60 kg runs up to 12m high in 40 seconds
...

Solution:
Given: mass m = 60 kg,
Height h = 12 m,
time taken t = 40 seconds
...

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Example3
A constant force of 2kN pulls a crate along a level floor a distance of 10 m in 50s
...
One such category
is tensile materials, which operate by resisting being pulled upon
...

Silk and collagen are both composed of proteins, while cellulose and chitin are composed of
polysaccharides (sugars)
...

Spider webs, which function in prey capture for many species, are made of silk, a well-studied
example of a tensile material
...

Hard - Can scratch or indent, and withstands being scratched
Brittle - Breaks without plastic deformation
Ductile - Can be drawn into a wire
Malleable - Can be reshaped
Elastic - Returns to its original shape after being deformed
Plastic - Does not return to its original shape after being deformed
Strong - Withstands large static loads without breaking
Tough - Withstands large dynamic loads without breaking
Stiff - Resists deforming by tension or compression
Strong materials can withstand large static loads whilst tough materials can withstand large
dynamic loads
...

Stress
Stress is "force per unit area" - the ratio of applied force F and cross section - defined as "force per
area"
...
kips))
A = area (m2, in2)
a kip is a non-SI unit of force - it equals 1,000 pounds-force
1 kip = 4448
...
4482216 kilonewtons (kN)
Example - Tensile Force acting on a Rod
A force of 10 kN is acting on a circular rod with diameter 10 mm
...
The dressed size
of the post is 5
...
5 in and the compressive stress can be calculated as
(𝟑𝟎𝟎𝟎𝟎 𝒍𝒃)

σ =((𝟓
...
(2)
where
τ = shear stress ((Pa) N/m2, psi)
Fp = parallel component force (N, lbf)
A = area (m2, in2)
Strain
Strain is defined as "deformation of a solid due to stress" and can be expressed as
𝑑𝑙
Ε=
𝑙0

= σ / E ……………………………………………
...

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Example - Stress and Change of Length
The rod in the example above is 2 m long and made of steel with Modulus of Elasticity 200 GPa
...
00127 (m)
= 1
...
Stress is proportional to
load and strain is proportional to deformation as expressed with Hooke's law
𝒔𝒕𝒓𝒆𝒔𝒔
E=
𝒔𝒕𝒓𝒂𝒊𝒏
=σ/ε
= (Fn / A) / (dl / lo) …………………………………………………
...
Tensile modulus is often used for plastics and is expressed
in terms 105 lbf/in2 or GPa
...
(5)
Where
S = shear modulus (N/m2) (lb/in2, psi)
τ = shear stress ((Pa) N/m2, psi)
γ = unit less measure of shear strain
Fp = force parallel to the faces which they act
A = area (m2, in2)
s = displacement of the faces (m, in)
d = distance between the faces displaced (m, in)
Elastic Moduli
Elastic moduli for some common materials:
Material
Young's Modulus
Shear Modulus
Bulk Modulus
10
2
6
2
10
2
6
2
10 N/m
10 lb/in
10 N/m
10 lb/in
1010 N/m2 106 lb/in2
Aluminum 7
...
4
3
...
0
10
Brass
9
...
6
5
...
1
8
...
2
6
...
5
7
...
3
3
...
7
5
...
1
13
7
...
6
2
...
56
0
...
77
1
...
4
12
16
23
Elasticity
Elasticity is the ability of a sub-stance to recover its original shape and size after distortion
...

Elastic Limit
The elastic limit of a spring is defined as the maximum force that can be applied to a spring such that
the spring will be able to be restored to its original length when the force is removed
...

It is a measure of the stiffness of a spring or elastic object
...

For example, the stiffness of spring A is greater than spring B
...
2-kg mass is placed on top of a vertical spring, the spring compresses 5
...
Find the
force constant of the spring
...
2×9
...
93 cm =0
...
0593)x
x = 2181 N/m
Elastic Strain Energy
Up to the elastic limit of a sample, all the work done in stretching it is stored potential energy, or
Elastic Strain Energy
...
If the sample obeys Hooke's Law, and is below the elastic limit, the Elastic Strain
Energy can be calculated by the formula:
E = ½kx2

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Graph of Stretching Force - Extension

Gradient = Spring constant
Area below the graph = Work done
Example1
A spring has a spring constant of 1000N/m, when it is compressed to an extension of 10cm, find
the spring tension work?
Solution
Given
K= 1000N/m x= 10cm = 0
...
01m)2
W = 5Nm= 5j

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Introduction
Wave
Wave: Is a disturbance causing energy transfer from one point to another without the actual
movement of particle, is called a wave
...

Waves can be classified in two types:
1
...
Mechanical waves
Electromagnetic wave:
The existence of medium is not essential for propagation
...

Mechanical Waves
A Mechanical wave is a periodic disturbance, which requires a material medium (solid, liquid or gas)
for its propagation
...


Example:
Light wave, ripple, radio wave

Longitudinal Wave
A longitudinal wave is a wave where the particles of the medium vibrate in a direction that is parallel
to the direction of the wave motion
...

 The point at which the displacement of the water from its normal level is highest called the
crest of the wave

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 The point at which the displacement of the water from its normal level is lowest called the
trough of the wave
...

 In compression regions of longitudinal waves, wave particles of the medium are packed
closer
...


Wave Characteristics
Wavelength

The wavelength (λ) is defined as the distance between two successive points which are at
the same phase (exactly the same point in their paths and are moving in the same direction
...


Wavelength is the distance
between two successive
compression or rarefaction
...
What is the amplitude of the wave?
solution
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Amplitude=10cm/2=5cm
Example 2:

The figure above shows the simulation of longitudinal wave by using a slinky spring
...
What is
the wavelength of the wave?
solution

Amplitude (A): This is the maximum displacement from the rest/centre position
...
It tells you the
'loudness' if it's a sound wave
...

Frequency (f): This is the number of complete wave produced per second SI unit-hertz
(Hz)
...

Period (T): This is the time taken for one point on the wave to complete one oscillation
...
The SI unit is
second (s)
...

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The speed of the wave in a given medium is always constant
...
A phase is the current position in the cycle of something that changes cyclically
...
Two vibrating particles are in the same phase if their displacement and direction of motion are
the same
...
In phase – Same phase
b
...
Anti-phase – Phase different = 180o
Wave front

 A wave front is a line or a surface that connects points that are moving at the same phase and
has the same distance from the source of the waves
...

 Characteristics of wave front:
a) Wave fronts are always perpendicular to the direction of wave propagation
...


Equation of a wave
We can calculate the speed of a wave using:
𝒗 = 𝒇 𝝀
Where:

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v = speed (m/s)
f = frequency (Hz)
λ = wavelength (m)
You need to be able to derive this equation from speed = distance/time
...
It has an amplitude of 3
...
8
cm
...

solution:
f=1/T, so T=1/f
The question had a lot of useless information to throw you off, all you have to do is use
T=1/f, so T=1/50
T=0
...
Find their speed in cm/s
...
2cm
...
2=5Hz
example3
What is the wavelength of a sound wave of frequency 100 Hz
...

Solution
v= f x λ
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λ= v / f
λ= 340 / 100 = 3
...


Phenomena of Waves
There are 4 phenomena of waves:
a
...
Refraction
c
...
Interference
Reflection
 Reflection occurs when an incident wave hits a reflector and reflected back
...

 The wavelength, frequency and speed of wave remain unchanged
...


Reflection of Straight and Circular Wave
1
...
The angle of incident is equal to the angle of reflection
b
...

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2
...


Reflection of Light Wave
1
...
Objects that do not emit
light are not seen in the dark
...
The experiment of reflection of light wave shows that reflection of light wave obeys the law
of reflection
...


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 Plane water wave strikes a plane barrier, is reflected as plane wave
...


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 Circular water wave strikes plane barrier
...


 Circular wave reflection from a convex barrier/obstacle, the reflected wave are circular

Refractions
Speed of Water Waves

1
...
wave-length becomes shorter
b
...
frequency remain unchanged
2
...


3
...


4
...

Refraction of Waves at a Boundary

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1
...

2
...

3
...

4
...


5
...


Note
There is one special case you need to know
...

Diffraction
 Diffraction is the spreading of a wave when it travels through an opening or a small obstacle
...
Wavelength does not change
...
Frequency does not change
...
Speed of diffracted does not change
...
The amplitude of the wave decreases after diffraction
...
The longer the wavelength, the greater the effect of
diffraction
Experiment 2

Bigger opening - The wave spreads to a smaller Smaller opening - The wave spreads to a wider
area
area
Conclusion:
Diffraction is affected by the size of the opening
...


Coherent Wave
Two wave sources which are coherent have same frequency or have constant phase difference
...
The effect of superposition of two coherent waves is interference
...
Interference is a phenomenon of wave caused by the superposition of 2 or more coherent waves
...
The effect of interference can be studied using a ripple tank
...

4
...

5
...

Constructive Interference and Anti-node

1
...
This is
called the constructive interference
...
A place where constructive interference occurs is called the anti-node
...
This is called the destructive interference
...

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 The same rules apply
...


Properties of electromagnetic waves







68

They are all transverse waves
...

They all show wave properties such as reflection and refraction
...

The equation [wave speed = frequency x wavelength] applies to them
...


Type

Waves

Ionizing

Gamma rays
X-rays





Ionizations can cause DNA damage in body cells
mutating effect to future generations
cause cancer

Non-ionizing

Ultraviolet
Visible light
Infra-red
Microwaves
Radio waves



heating of body surface

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Effects of absorption

Introduction
The structure of an atom
Although the word 'atom' comes from the Greek for indivisible, we now know that atoms are not the
smallest particles of matter
...
Most of the mass of atom is
contained in the nucleus
 The electrons move in orbits around the nucleus
...

 Protons and neutrons also known as nucleons
...

 A neutron is an uncharged particle of about the same mass as the proton
...
So
the net charge is zero
...

 Number of neutrons, N = A - Z
 A nuclide is an atom of a particular structure
...


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Isotopes
 Isotopes are atoms with the same proton number but different nucleon number
...
So isotopes have the same chemical properties chemical reactions involve the
electrons in an atom
...

 Some isotopes exist naturally
...

Example

Radioactivity
In general, the nucleus of the various atoms is stable
...
Often in this process, high energy gamma radiation and
other particles are emitted
...

Radioisotopes
Radioisotopes are unstable isotopes which decay and give out radioactive emissions
...
The Technetium is
combined into samples of the protein albumin,
Emit 
and this is injected into the patient
...

for detecting changes
Patients are given an intravenous injection of
in the thyroid glands
...
A detector is placed near the
Emit  and 
thyroid to read its activity or function
...
its
operated by remote control from behind thick
Emit  and 
lead and concrete walls
...

Radioactive decay
Many nuclei are radioactive
...
A chain of
decays takes place until a stable nucleus is reached
...
Atomic number decreases by 2 (2
protons lost)
...
By rearranging the
layout of their protons and neutrons, they reach a lower energy state and the excess energy is
emitted in the form of a gamma ray
...


No charge

Mass

Large

Very small

No mass

Speed

10 % of the speed of
light
...


Ionising power

Strongest

intermediate

Weakest

Penetrating power

Weak

Moderate

Strong

Range in air
Stopped by

A few cm
Human skin or a thin
piece of paper
...

Deflection is greater due
to the small mass of
electron

No deflected because 
has no charge
...


Greater deflection
because  has a very
small mass
...


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74
Background radiation
Radioactivity around us
When we use a Geiger counter, it clicks even without a radioactive source near it
...

Background radiation is:
 ionizing radiation from space (cosmic rays)
 from devices e
...
X-ray tubes
 from radioactive substances in environment-some are present due to nuclear weapons testing and
nuclear power stations, but most of it is from substances in the Earth (e
...
radon gas is radioactive
and is a product of the decay of uranium in the ground)

Detecting Nuclear Radiation
 Most methods of detecting alpha-, beta- and gamma-rays are based on the fact that these
radiations have an ionizing effect
...


Gold Leaf Electroscope

Film Badge (Dosimeter)

Table below shows the types of emission that can be detected by different detectors
Detectors
Gold Leaf Electroscope
Geiger-Muller Tube
Cloud Chamber

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Alpha

Beta

Gamma

75
Spark-Chamber Detector
Film Badge (Dosimeter)

Radioactive Half Life
Half life can be defined as the time taken for the number of nuclei in a radioactive
material to halve
...

Radioactive elements have a wide range of half life values
...
5 billion years whereas the half life of Thorium-234 is as little as 24 days
...
B
...


Graph of half life

Calculating Half Life
We know that after one half life, one half of the original radioactive nuclei remain
...


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76
We can therefore say:
1 half life
2 half lives

=
=

½ of the original radioactive nuclei remain
¼ of the original radioactive nuclei remain

This can be written as an equation as:
Or use this

N = Amount of radioisotope particles
after nth half life
...

n = number of half life

Or use

Example1
A radioactive isotope has a radioactivity measured on a Geiger-Muller tube at 10,000
Becquerel’s or 10,000 counts per second
...
Initially, there were 3
...

How much time is taken for the number of atoms of the radioisotope to fall to 4
...
6 x 1018 radioisotope atoms to 4
...
Therefore, the time
taken
t=3T12/t=3(8)=24h
Example4
You discovered a new radioactive isotope and named it boogonium (don't ask)
...
23 years
...
7 years?
Solution

Example 5

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78

The diagram shows the graph of the activity of a radioisotope, X, against time
...

From the graph we can see that the radioisotope take 6 days for the activity to become half
...
If you start with a sample of 8 kg, how
much will be left in 100 years?
Uses of radioactive
Thickness control
 A radioactive sends radiation through the sheet material as it comes off the production line
...
A radiation detector on the other side of the sheet measures the
intensity of the radiation passing through the sheet
...

 A signal is sent from the roller control to the rollers so that the pressure on the sheets can be
reduced
...

 A radioactive substance which emits beta particles is added to a fluid in a pipeline to measure the
flow rate in the pipeline and to find leaks
...

 A larger increase in the count rate will indicate that there is leak in that area
...

A radioisotope is taken in by a patient through the digestive system, by inhalation or through the
blood vessels by injection
...
Disorders can then be detected
...

This method is named as the radiocarbon dating
...


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80

Example:
A piece of wood found in a cave of an archaeology site has a carbon-14 activity 25% of the activity from
a live plant
...
[Half-life of carbon-14 = 5730 years]
Answer:
100% → 50% → 25%
Carbon-14 take 2 half-life to decay from 100% to 25%, hence the age of the wood
= 2(5730)
= 11460 years
Nuclear Energy
 In a radioactive decay, one element changes into another in a process called transmutation
...
This difference in mass is
called mass defect or mass loss
...

 Einstein's formula can be used to calculate the amount of nuclear energy released from the defect of
the mass in a radioactive decay or nuclear reaction
...
The
defected mass is then converted into energy called the nuclear energy
...
In short, nuclear energy is the energy released owing to the defect of mass in a nuclear reaction
...
Nuclear fission is the process of splitting nucleus into 2 smaller nuclei whereas nuclear fusion is
the process which 2 small nuclei combine to form a larger nucleus
...

 The number of nuclei which undergo fission multiplies rapidly
...

 At the same time, the mass of fission material must exceed a certain minimal mass known as
the critical mass
...


Nuclear Fusion
1
...


2
...


3
...

Fusion is much more difficult to achieve than fission because the hydrogen nuclei repel each
other
...

Example
The Sun get its energy from the fusion of hydrogen nuclei
...

Advantages of using nuclear fission:
 Nuclear power costs about the same as coal, so it is not expensive
 It does not produce smoke or carbon dioxide
...
It
produces less waste than fossil fuels
...

 Nuclear power stations need less fuel than stations which use fossil fuels
 Vast reserves of nuclear fuel in the world
...


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83
Disadvantages of using nuclear fission
 The initial cost to design and build a nuclear power station is very high
...
If a chain reaction goes out of control, explosion or leakage or
large amounts of radioactive substance may happen
...

 Expensive procedures are required to cool down the rods and store them
...

Nuclear Reactor
 A nuclear reactor produces tremendous amount of energy through nuclear fission
...

 As a result, steam is generated to drive turbines, which in turn drive the electrical generators
...
In some nuclear power plant, the moderator is water
...
The uranium used is often
'enriched' by increasing the proportion of the isotope uranium-235 above the natural value of
0
...

c) Control rod
The rate of the fission reaction is controlled by inserting or withdrawing these rods
...
Sometimes the rod is made of
cadmium
...
Substances with high specific heat capacity such
as 'heavy' water and carbon dioxide are used
...

f) Steam generator
Water in the generator is heated and changed into steam
...

g) Turbine
To turn the dynamo in the electrical generator to produce electricity
...

The induced current is produced only when there is relative motion between the conductor / coil
and the magnetic field lines
...


b) Moving a permanent magnet towards one end of a solenoid
...

This current is called induced current
...
m
...

This can be achieved in two ways:
I
...


a conductor can be moved in a magnetic field
a magnet can be moved in a coil of wire Induction does not happen
...


Law of Electromagnetic Induction
There are two principal laws of electromagnetic induction:

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85
 The Faraday’s law
 The Lenz’s law

Faraday's Law
Faraday's Law states
that the magnitude of the induced e
...
f is directly proportional to the rate of change of magnetic flux
through a coil or alternatively the rate of the magnetic flux being cut
...
m
...

The size of the induced voltage increases when
...

Lenz's Law obeys the principle of conservation of energy
...
This work done is converted to electric energy which manifests as an induced current
...


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87

The direction of the current can be reversed by
 Moving the magnet in the opposite direction
...

Example1
A wire 15cm long is moved upwards at a speed of 100cm/s at right angle to the magnet of strength
0
...

Find the EMF induced in the wire and illustrate its direction by a diagram?
V= 100cm/s

Solution
𝐸𝑀𝐹 = 𝐵𝑙𝑣
𝐸𝑀𝐹 = 0
...
15 × 1 = 0
...
5 × 10−3 𝑣
Using the right-hand rule we find that the induced current goes into the page along the wire
...
g
...


Tape recording
Tape recorders store the information music, speech or data, on plastic tape that is coated with iron
oxide powder
...
Warning – don't try
to do this with a tape that already has some music or data stored on it – you will ruin it!
Each grain of iron oxide acts like a tiny magnet and on a tape that has no data stored on it these gains
are arranged irregularly on the tape – the tape is unmagnetised
...
The changing flux in the coil creates an induced emf which is then
amplified and then sent to the speakers
...

 Current generator works based on electromagnetic induction and uses the Fleming’s Right hand
rule
...


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Direct Current generator

 consists of a rectangular coil of wire connected to a pair of slip rings
...
m
...
is induced
in the coil
...

 Direct current is a uniform current flowing in one fixed direction in a circuit
 Direct current (d
...

 A common example of acid-based (electrolyte) batteries is the car battery
...
Hence, the
induced current is called a direct current
...


Alternating Current Generator

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 Alternating current is an electric current in which the direction of flow of the electrons reverses
periodically

 The two ends of the coil are connected to two slip rings which rotate with the coil
...

 Alternating current changes direction 50 times every second
...


 The output current generated is an alternating current because the current changes direction in
the external circuit each time the coil passes the vertical position
...

The frequency f is defined as the number of complete cycles in 1 second
...


Effects on a bulb
Effects on a capacitor

Effects on moving coil
loudspeaker

Direct Current
The bulb lights up
Current is detected at the very
beginning and then ceased to
become zero afterward
...
c source is known as the peak voltage VP
...
c is equal to the potential difference of a alternating
current if both results in the same heating effect
...
c is known as the root mean square voltage (r
...
s) of the
a
...
and is given y the following equation:

 The root-mean-square (r
...
s) value of an alternating current is the value of the steady direct
current which produces the same power in a resistor as the mean power produced by the
alternating current
...
m
...

 The r
...
s
...
Find
the Vr
...
s
...

Solution

Example 2

The diagram above shows the wave form of an a
...
supply
...
When another coil is placed within
that magnetic field, it will induce a current flowing in
that coil
...
That is why transformers which
functioning on the principle of mutual induction has
efficiency near 99%
...

Function:
The function of a transformer is to increase or decrease the potential difference of an alternating
current supply
...
The 2 lines in between the coil denote the
core
...
A transformer consist of 3 parts, namely
1
...

3
...
The current, potential
difference and coil (winding) in the primary circuit are called the primary current (Ip), primary potential
difference (Vp) and primary coil respectively
...
The function of the core
is to transfer the changing magnetic flux from the primary coil to the secondary coil
...
The current,
potential difference and coil (winding) in the secondary circuit are called the secondary current (Is),
secondary potential difference (Vs) and secondary coil respectively
...

 When an alternating current flows in the primary coil, a changing magnetic flux is generated
around the primary coil
...

 The changing magnetic flux is cut by the secondary coil, hence induces an e
...
f
...

 The magnitude of the output voltage can be controlled by the ratio of the number of primary
coil and secondary coil
...
A changing magnetic flux is needed to induce e
...
f
...

 The induced current in secondary is also an alternating current
...

 The alternating in the secondary circuit can be converted into direct current by using a pair of
diode
...

the step up transformer
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2
...
m
...
in the secondary coil is greater than the e
...
f
...
It is used to increases the potential difference
...

 The current in the primary coil is greater than the current in the secondary coil
...
m
...
in the secondary coil is less than the
e
...
f
...
It is used to reduce the potential difference
...

 The current in the primary coil is lesser than the current in the secondary coil
...
We use following equations to find potential, current or
number of turns of any coil;

Np = number of turns in primary coil
Ns = number of turns in secondary coil
Vp = input (primary) potential difference
Vs = output (secondary) potential difference
Ip = input (primary) current
Is = output (secondary) current
Example1
A 16
...

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a) What type of transformer is it?
b) Calculate the number of turns in the primary coil
...
There are 16
...

b) Np = 100 × 16
...
What is the output voltage if the
input voltage is 500V?
Solution
Vp

/Vs = Np/Ns Therefore Vs/Vp = Ns/Np

Vs

/500 = 400/20

Vs = 500 x (400/20)
Vs= 10,000 Volts
Efficiency of transformer
Efficiency of a device is equal to the ratio of output to input
...
The heating effect of current in a coil
Power is lost as heat I2R whereby I is the current flowing through the coil and R is the resistance of
the coil
Methods to increase the efficiency
Use thick copper wires of low resistance
...


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2
...

Methods to increase the efficiency
Use a laminated iron core whereby each layer is insulated with enamel paint to prevent the flow of
eddy currents
...


3
...

The energy used in the magnetization and de-magnetization of the iron core each time current
changes its direction is known as hysterisis
...

Methods to increase the efficiency
Use a soft iron core that is easily magnetized and de-magnetized
...
Flux leakage
...
m
...

Methods to increase the efficiency
Wind tightly the secondary coil on top of the primary coil,
The iron core should form a closed loop
...

Electricity is generated on a large scale at power stations and then transmitted through a network
of cables (called the National Grid) to factories and homes
...


end
prepared : farah khadad

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