physics booklet

7/30/2019 Physics Booklet

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Presents

a sample chapter from the

Advanced Diploma Preparation CourseFundamentals of Engineering

Physics Booklet


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MOTIONMOTION -- II

ONE-DIMENSIONAL


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TopicsTopics

Equations of motion

Newtons laws of motion

Potential energy and kinetic energy

Conservation of mechanical energy


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IntroductionIntroduction

Motion Change in location of an object

as a result of applied force.

Motion in single dimension can be

described with the following quantities: Position or displacement

Speed or velocity

Acceleration Time


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IntroductionIntroduction (cont...)(cont...)

Frame of reference


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IntroductionIntroduction (cont...)(cont...) Displacement change in position (x)

Displacement does not depend on the path travelled.

Velocity rate of change of position

Instantaneous velocity and average velocity

)(mxxx initialfinal=

).( 1

= sm

t

xv


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IntroductionIntroduction (cont...)(cont...)

Acceleration the rate of change of

velocity. ).( 2

= smtva

Motion at constant acceleration


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Equations of MotionEquations of Motionatvv initialfinal +=

tvv

xfinalinitial

2

)( +=

2

2

1attvx initial +=

xavv initialfinal += 222


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NewtonNewtons Laws of Motions Laws of Motion

First law

An object will remain in a state of rest orcontinue travelling at constant velocity, unless

acted upon by an unbalanced (net) force.

Second law

Force equals mass times acceleration (F=ma). Third law

For every action there is equal and opposite

reaction.


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ProblemProblem11

What happens while the car turns?


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ProblemProblem22

Two crates, 10 kg and 15 kg respectively, are connectedwith a thick rope according to the diagram. A force of 500

N is applied. The boxes move with an acceleration of 2

ms2. One-third of the total frictional force is acting on

the 10 kg block and two-thirds on the 15 kg block.

Calculate:

The magnitude and direction of the frictional force present.

The magnitude of the tension in the rope at T.


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ProblemProblem33 A force T = 312 N is required to keep a body at rest on a

frictionless inclined plane which makes an angle of 35with the horizontal. The forces acting on the body are as

shown. Calculate the magnitudes of forces P and R.


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ProblemProblem44 Which of the following pairs of forces correctly

illustrates Newtons Third Law?


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SolutionSolution22

motion.ofdirectionthetooppositeN450isforcefrictionalThe

N450F50050F

(2)15)(10F500

maFFmaF

positive.bemotion toofdirectiontheAssume

f

f

f

fapplied

R

=

=

+=+

=+

=


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SolutionSolution22 (cont...)(cont...)

N170T20150)(T

(10)(2)FT

maF:LawSecondsNewtonapplyweIf

N150F

4503

1F

:thereforetotal,theofthirdoneisblockkg10on theforcefrictionalThe

:ropeon thetensiongCalculatin

f

R

f

f

=

=+

=+

=

=

=


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SolutionSolution33

N445.6R

31255tanR

31255tan

55tan

:ratiosrictrignometusingdeterminedbecanP

:RofmagnitudetheFinding

N544P

35.sinP312sinPT

magnitude.samethehasittherefore

and(Px)PofcomponenthorizontalthebalancesthatforcetheisT

:PofmagnitudetheFinding

=

=

=

=

=

=

=

R

T

R


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Mechanical EnergyMechanical Energy Gravitational Potential Energy

The energy of an object due to its position above thesurface of the Earth.

Kinetic Energy

The energy an object has due to its motion.

)( joulesmghPE=

)(2

1 2 joulesmvKE=


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Mechanical EnergyMechanical Energy

(cont...)(cont...) Mechanical Energy, U is the sum of Potential Energy and

Kinetic Energy.

Conservation of Energy

Energy cannot be created or destroyed, but is merely changed

from one form into another.

Conservation of Mechanical Energy

The total amount of mechanical energy in a closed systemremains constant.

KEPEU +=


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Conservation of MechanicalConservation of Mechanical

EnergyEnergy In the absence of friction, mechanical

energy is conserved.

In the presence of friction, mechanical

energy is not conserved.

AfterBefore UU =

AfterBefore UUU -=


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ProblemProblem55 During a flood, a tree trunk of mass 100 kg falls down a

waterfall. The waterfall is 5 m high. If air resistance isignored. Calculate

The potential energy of the tree trunk at the top of the waterfall

The kinetic energy of the tree trunk at the bottom of the waterfall.

The magnitude of the velocity of the tree trunk at the bottom ofthe waterfall.


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ProblemProblem66 A 2 kg metal ball is suspended from a rope. If it is

released from point A and swings down to the point B(the bottom of its arc):

Show that the velocity of the ball is independent of its mass.

Calculate the velocity of the ball at point B.


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SolutionSolution55 Potential energy at the top:

Kinetic energy at the bottom:

KE of the tree trunk at the bottom of the waterfall is equal to the

potential energy it had at the top of the waterfall.

J

mghPE

4900

58.9100

=

=

=


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SolutionSolution55 (cont...)(cont...) Velocity of the tree trunk:

1

2

2

2

.90.9

98

1002

14900

21

=

=

=

=

smv

v

v

mvKE


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SolutionSolution66 Law of Conservation of Mechanical Energy:

As there is no friction, mechanical energy is conserved.

2

21

2

2

1

2

21

2212

21

)()(

)(00

)()(

BeforeAfter

BeforeAfter

BeforeAfter

BeforeBeforeAfterAfter

BeforeBeforeAfterAfter

BeforeAfter

vghvmmgh

vmmgh

vmmghvmmgh

KEPEKEPE

UU

=

=

+=+

+=+

+=+

=


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SolutionSolution66 (cont...)(cont...) Velocity of the ball:

12

2

221

.8.9)(

)(5.08.92

)(

=

=

=

smv

v

vgh

Before

Before

BeforeAfter


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QUIZ / ASSIGNMENTQUIZ / ASSIGNMENT


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MOTIONMOTION -- IIII

TWO-DIMENSIONAL


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TopicsTopics Projectile motion

Circular motion

Rotatory motion

Periodic motion Universal gravitation


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Projectile MotionProjectile Motion


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Projectile MotionProjectile Motion Projectiles have zero velocity at their greatest height.

(a) Position vs. time graph (b) velocity vs. time graph (c) acceleration vs. time graph.


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Path of a Projectile motionPath of a Projectile motion

The parabolic trajectory of a particle that leaves the origin with a velocity of v0.

(changes with time)

Vx is the x-component of the velocity, (remains constant in time)Vy is the y-component of the velocity (0 at the peak of the trajectory,

but the acceleration is always equal to the free-fall acceleration and

acts vertically downward.

Horizontal and vertical motions are

completely independent of each other.


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Equations of Projectile MotionEquations of Projectile Motion

.cosvvwhere

x2avv

ta2

1tvx

tavv

:havewedirection,-xIn the

000x

x

2

0x

2

x

2

x0x

x0xx

=

+=

+=

+=

direction.-yin thevelocityinitialtheisv

direction-xin thevelocityinitialtheisv

angle)n(projectio

velocity)(initialvv

:0At t

0y

0x

0

0

=

=

=


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EquationsEquations (cont...)(cont...)

000y

y

20y

2

y

2

y0y

y0yy

sinvvwhere

y2avv

ta2

1tvy

tavv

:havewedirection,-yIn the

=

+=

+=

+=

2

y

2

x vvv

:asgivenisvspeedsobjectThe

+=

:bygivenisaxis-xwith themakesvectorvelocitythat theangleThe

)v

v(tan

x

y1-=


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ProblemProblem11 A ball is thrown upwards with an initial

velocity of 10 ms1. Determine the maximum height reached

above the throwers hand.

Determine the time it takes the ball to reach itsmaximum height.


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SolutionSolution11Given:Initial velocity vi = 10 ms

1

Acceleration due to gravity g = 9.8ms2.

At the maximum height the velocity of the ball is 0 ms1

Therefore,

vi = 10ms1 (it is negative because we chose upwards as positive)

vf= 0ms1

g = +9.8ms2

We can use: v2 f= v2i + 2gx

Substituting the values and solving forx we get:

x = 5.102m = height


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SolutionSolution11 (cont...)(cont...)The appropriate equation to determine the time

vf= vi + gt

Substitute the values and find time t:

vf= vi + gt

0 = 10 + 9.8t

10 = 9.8t

t = 1.02s


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Circular MotionCircular Motion


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Circular MotionCircular Motion Circular motion is rotation along a circle.

Centripetal force is a force that makes a body follow acurved path

A force directed perpendicular to the motion and towards the

centre of curvature of the path.


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Circular MotionCircular Motion (cont...)(cont...) The centripetal force is given by:

v

Fc

R

vmmaF cc

2

==

Rv =

22

mRR

vmmaF cc ===


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Circular MotionCircular Motion (cont...)(cont...) Centrifugal force

The force directed outwards, away from the centre ofrotation due to the effect of inertia.

This is called a fictitious force.

Uniform circular motion The motion of a body traversing a circular path at

constant speed.

The change in velocity is only in terms of change in

direction.


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Circular MotionCircular Motion (cont...)(cont...) Uniform circular motion in a horizontal plane

Example:

An object tied to a string is rotated in horizontal plane by virtue of the

tension in the string.

Ideally we cannot obtain uniform circular motion due to

gravitational pull.

In order to obtain, the string should be slanted such that thetension as applied to the object forms an angle with the

horizontal plane.

Horizontal component of the tension provides the needed centripetal

force Vertical component balances the weight of the object.


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Circular MotionCircular Motion (cont...)(cont...)

Uniform circular motion in a horizontal plane

Note: String is not in the plane of circular motion.

Taking ratio we get,


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Rotatory MotionRotatory Motion


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Rotatory MotionRotatory Motion Central concepts of rotatory motion are:

Angular velocity Angular acceleration

Angular momentum

Torque


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TorqueTorque Force causes acceleration, and torque causes angular

acceleration.

The magnitude of the torque exerted by a force is given

by:

An object remains in a state of uniform rotational motionunless acted on by a net torque.

(N.m)rF =F is magnitude of the force acting on an object,

r is the length of the position vector

A birds-eye view of a

door hinged at O, with a force

applied perpendicular to the door.


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Condition of EquilibriumCondition of Equilibrium An object in mechanical equilibrium must

satisfy the following two conditions: The net external force must be zero: F = 0

Translational equilibrium: The sum of all forces

acting on the object must be zero The net external torque must be zero: = 0

Rotational equilibrium: The sum of all torques on

the object must be zero


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Angular VelocityAngular Velocity The angular velocity is a pseudo-vector quantity that

specifies the angular speed of an object and the axis

about which the object is rotating.

The direction of the angular velocity vector is

perpendicular to the plane of rotation.

A l M tA l M t


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Angular MomentumAngular Momentum A vector quantity that is useful in describing the rotational

state of a physical system.

Angular momentum L of a particle with respect to somepoint of origin is:

The magnitude L of the angular momentum of a particle

is

r is the particle's position from the origin

p = mv is its linear momentum, and denotes the cross product.

Where I is moment of inertia,

is the angular velocity


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Angular Momentum and TorqueAngular Momentum and Torque An object of mass m rotates in a circular path of radius r,

acted on by a net force Fnet.

Resulting net torque on the object increases its angular

speed from the value 0 to the value in a time interval

t.

L = I Where L is the angular momentum

t

L

intervaltime

momentumangularinchange

==


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Principle of MomentsPrinciple of Moments For equilibrium:

The sum of the clockwise moments about apoint = sum of the anticlockwise moments

about that point.

Example:

Stable Unstable and NeutralStable Unstable and Neutral


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Stable, Unstable and NeutralStable, Unstable and Neutral

EquilibriumEquilibrium Stable equilibrium:

If displaced, the object returns back to its formerposition.

Unstable equilibrium:

The body if disturbed does not tend to return to its

former position, but tends to move further away from

it.

Neutral equilibrium:

If displaced from its position, it again stays in

equilibrium but in its new position.


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Periodic MotionPeriodic Motion


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Periodic MotionPeriodic Motion Any motion that repeats itself in equal intervals of

time along the same path is called Periodicmotion.

Periodic motion can always be expressed in

terms of sine and cosine functions of time.Hence it is also knows as harmonic motion.

Simple harmonic motion:

A period motion in which a body moves to and froabout a fixed mean position.


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Simple Harmonic Motion (SHM)Simple Harmonic Motion (SHM) A body should obey the following conditions to

execute SHM: Motion should be periodic

The object must move to and fro about mean position.

Acceleration must be directly proportional to the

displacement from the mean position

Acceleration must always be directed toward the

mean position.

Acceleration and displacement must always beopposite to each other.


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Simple PendulumSimple PendulumAccording to Hookes law:

From the figure, the restoring force is

Ft= - ks

Ft= mg sin

Where Ft is the force acting in a direction

tangent to the circular arc.

Substituting = s/L, we obtain: s)L

mg(-Ft =

The angular frequency is given by m

kf2 ==

Substituting k we get:L

g=

g

L2TTherefore =


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OscillationsOscillations Damped oscillations:

Oscillations tend to decay (become damped)with time unless there is some net source of

energy into the system.

Driven oscillations An oscillating system may be subject to some

external force the oscillation is said to

be driven.


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Universal GravitationUniversal Gravitation


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Universal GravitationUniversal Gravitation Newtons law of universal gravitation

Every point mass attracts every other point mass by a force directed

along the line connecting the two. This force is proportional to the product of the masses and inversely

proportional to the square of the distance between them.

Magnitude of the attractive gravitational force between the two point

masses, F is given by:

2

21

r

mmGF =

masses.pointtwoebetween thdistancetheisrandmasspointsecondtheofmasstheism

mass,pointfirsttheofmasstheism

kg..mN106.67constantnalgravitatiotheisG

2

1

-22-11


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KeplerKeplers Lawss Laws All planets move in elliptical orbits with the Sun at one of

the focal points.

A line drawn from the Sun to any planet sweeps out

equal areas in equal time intervals.

The square of the orbital period of any planet is

proportional to the cube of the average distance from theplanet to the Sun.

32rKT s=

planettheofradiustheis

/102.97theisKplanettheofperiodtheisT

3219

s

r

ms


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Escape VelocityEscape Velocity Escape velocity

The speed at which the kinetic energy of an object isequal to its gravitational potential energy.

The escape velocity does not depend on the mass of

the body.

RgVe 2=

forcenalgravitatiotheisg

planettheofradiustheisR


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Orbital VelocityOrbital Velocity The speed at which it orbits around the barycenter of a

system, usually around a more massive body.

:isvelocityorbitalearth,thenearer tosatelliteaofcaseIn

gRvo =


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ProblemProblem22 Calculate the force of attraction

If a man of mass 80 kg stands 10 m from awoman with a mass of 65 kg.

If the man and woman move closer to each

other, until they are 1 m apart.


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ProblemProblem33 On Earth a man has a mass of 70 kg. The planet

Zirgon is the same size as the Earth but has

twice the mass of the Earth. What would the man

weigh on Zirgon if the gravitational acceleration

on Earth is 9.8 ms2?


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SolutionSolution22

N103.47

)(10)

(80)(65))(10(6.67

r

mmGF

9-

211-

2

21

=

=

=

Attractive gravitational force between them:

If the man and woman move to 1 m apart, then:

N103.47

)(1)

(80)(65)

)(10(6.67

r

mmGF

7-

2

11-

2

21

=

=

=


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SolutionSolution33the mass of the man on Earth = mmass of the planet Zirgon (mZ) in terms of the mass of the Earth (mE); mZ = 2mE

the radius of the planet Zirgon (rZ) in terms of the radius of the Earth (rE); rZ = rE

the mans weight on Zirgon (wZ)?

2

21

r

mmGmgw ==

On Earth:

686N

).skg)(9.8m(70

r

mmGmgw

-.2

2

E

EEE

=

=

==


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SolutionSolution33 (cont...)(cont...)On Zirgon:Substitute the values for mZ and rZ, in terms of the values for the Earth.

372N1

2(686N)

2wr

.mm2(G)

r

.m2mG

rmmGmgw

E

2

E

E

2

E

E

2

Z

ZZZ

=

=

=

==

==


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HEATING ANDHEATING ANDCOOLINGCOOLING

TopicsTopics


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pp

Pressure, volume and density

Heat and internal energy

Kinetic theory of gases

Specific heat

Calorimetry

Latent heat

Transfer of heat energy

Laws of thermodynamics Entropy

Pressure, Volume & DensityPressure, Volume & Density


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, y, y

Pressure, P

Pressure is an effect which occurs when a force is

applied on a surface.

It is the amount of force acting on a unit area.

P=F/A

Pressure is a tensor quantity, and has SI units of

Pascal; 1 Pa = 1 N/m2

9Q: What is the pressure exerted by a 10 kg

backpack put onto a rectangular table of area 0.5m2?


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Pressure, Volume & DensityPressure, Volume & Density Density, D

It is the mass per unit volume of a substance.

SI unit is kilogram/meter3 (kg/m3)

9Q: A piece of an unknown material has a

mass of 5.854 g and a volume of 7.57cm3. What is the density of the material?

Pressure, Volume & DensityPressure, Volume & Density


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(cont(cont)) Volume

The amount of 3-dimensional space occupied by an

object.

Mercury has a density of 13.5 g/cm3. 50.0 g of

mercury would occupy a space of ..

V=m/D V=(50g)/(13.5 g/cm3 )3.7cm3

9Q: Iron has a known density of 7.87 g/cm3. Find

the volume of this piece of iron having mass

of 20 kg.

Solutions


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SolutionsSolutions

Pressure:

The force acting on the table is the weight of thebackpack, which is equal to its mass times the

acceleration of gravity.

Pressure = (mass)*g/(area),

where g is the acceleration of gravity.

P=(10 Kg x 9.8 m/s2 )/0.5m2

P=196 N/m2

Solutions (cont)


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SolutionsSolutions

(cont(cont

))

Density:

D=m/v = 5.854g/7.57 cm3D=0.73 g/cm3

Volume:

Volume of iron =m/D

V=(20000g) / (7.87 g/cm3 )= 2541.3 cm3

Heat and Internal Energy


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Heat and Internal Energygy

Heat

The transfer of internal energy between a system and

its environment due to a temperature difference

between them.

Q, amount of energy transferred.

Internal energy Includes kinetic and potential energy with the random

translational, rotational, and vibrational motion of the

particles that make up the system.

Heat and Internal EnergyHeat and Internal Energy


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(cont(cont)) Calorie

Amount of energy necessary to raise thetemperature of 1 g of water from 14.5C to

15.5C.

The mechanical equivalent of heat:1 cal 4.186 J

In food energy, 1 Calorie = 1 kcal

Kinetic Theory of Gases


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Kinetic Theory of Gasesy

Assumptions of kinetic theory for an ideal gas

The number of molecules in the gas is large, and the

average separation between them is large compared

with their dimensions.

The molecules obey Newtons laws of motion, but as a

whole they move randomly. The molecules interact only through short-range

forces during elastic collisions.

The molecules make elastic collisions with the walls.

All molecules in the gas are identical.

Kinetic Theory of GasesKinetic Theory of Gases


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(cont(cont)) The pressure of N molecules of an ideal

gas contained in a volume V is given by

where is the average kinetic energy

per molecule.

= 2

2

1

3

2mv

V

Np

2

2

1mv

Tkmv B23

21 2 =

Kinetic Theory of GasesKinetic Theory of Gases


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The internal energy of n moles of a monatomic

ideal gas is

The root-mean-square (rms) speed of the

molecules of a gas is

nRTU 2

3=

m

RT

m

Tkv Brms

33==

(cont(cont))

Specific HeatSpecific Heat


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p

Specific heat ,c of a substance is

where Q is the quantity of energy transferred to a

substance of mass m, changing its temperature byT = Tf-Ti

Tf=final temperature, Ti =initial temperature

SI unit: Joule per kilogram-degree Celsius ( J/kg C)

TmQc

Specific HeatSpecific Heat (cont(cont))


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p

From the definition of specific heat,

Q = mcT

What is the energy required to raise the

temperature of 0.500 kg of water by 3C?

SolutionSolution


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Q = (0.500 kg)(4 186 J/kg .C)(3.00C)

=6.28 103 J. When the temperature increases, T and

Q are positive, corresponding to energy

flowing into the system. When the temperature decreases, T and

Q are negative, and energy flows out of

the system.

CalorimetryCalorimetry


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Experimental technique used

to determine heat loss or

gain

Calorimeter

A device used to measure the

specific heat of a material or

determine its energy content.

Must be a container that is well

insulated so that energydoesnt leave the system.

CalorimetryCalorimetry (cont(cont))


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The heat gained by the calorimeter cup

and the water = the heat loss of theunknown material.

Qcold= - Qhot , Q = 0

Based on the conservation of energy andthermal equilibrium.

Latent HeatLatent Heat


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Any phase change involves a change in the

internal energy, but no change in the

temperature.

For pure substance, energy Q needed to change

the phase is

Q= mL

where L, the latent heat of the substance,

depends on the nature of the phase change aswell as on the substance.

Latent HeatLatent Heat (cont(cont))U it j l kil ( J/k )


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Units : joule per kilogram ( J/kg).

At atmospheric pressure the

Latent heat of fusion for water is 3.33105J/kg

Latent heat of vaporization for water is 2.26106J/kg.

A plot of temperature versus energy added when 1.00 g of ice,

initially at 30.0C, is converted to steam at 120C.

Energy TransferEnergy Transfer


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Three mechanisms of thermal energy

transfer: Conduction

Convection

Radiation

Heat is always the transfer of internal

energy from one body to another.

Energy TransferEnergy Transfer


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Conduction

Exchange of kinetic energy between colliding

molecules or electrons.

Occurs only if there is a difference in temperature

between two parts of the conducting medium.

The energy transfer rate by conduction through a slabof area A and thickness L is

( )L

TT

kAp

ch =

Energy TransferEnergy Transfer (cont(cont))


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Convection

The transfer of energy by the

movement of a substance is

called convection.

Natural convection: When the

movement results fromdifferences in density, as with

air around a fire.

Forced convection

Warming a hand by

convection.



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Convection Applications

Cooling automobile engines Algal blooms in ponds and

lakes

Radiator raises thetemperature of a room

Convection currents are set

up in a room warmed by a

radiator.



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Radiation

All objects emit radiation from their surfaces in the form of

electromagnetic waves at a net rate of

Where T is the temperature of the object and T0 is the temperature

of the surroundings. An object that is hotter than its surroundings radiates more

energy than it absorbs.

A body that is cooler than its surroundings absorbs more energy

than it radiates.

)( 404 TTAepnet =



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Blackbody

The perfect absorber and

emitter of EM radiation.

Radiation Applications

Thermography

Radiation thermometers for

measuring body temperature

Light-colored summer

clothing A radiation thermometer measures a patientstemperature by monitoring the intensity ofinfrared radiation leaving the ear.

Laws of ThermodynamicsLaws of Thermodynamics


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Zeroth law of thermodynamics

If objects A and B are separately in thermal

equilibrium with a third object C, then A and B are inthermal equilibrium with each other.

The zeroth law of thermodynamics


(cont(cont ))


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(cont(cont)) First Law of Thermodynamics

When a system undergoes a change from one state to

another, the change in its internal energy U is

U=Uf-Ui =Q+W

Q energy transferred into the system by heat

W work done on the system.

For an ideal gas

U =nCvT where Cv is the molar specific heat at

constant volume.


(cont(cont ))


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(cont(cont)) In isobaric process,

The work done on the system is -P V

Thermal energy transferred by heat is

Q=ncp T

In adiabatic process, U=W

In isovolumetric process, U=Q

In isothermal process,

Work done by an ideal gas on environment is

=

i

fenv

VVnRTW ln


(cont(cont ))


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(cont(cont)) Energy flow of heat engine

Heat QH is supplied to the engine by the hot reservoir .

Heat QC is rejected from the engine into the cold

reservoir in the exhaust.

The portion of the heat supplied by the engine

converts to mechanical work (W) Q=W=QH+QC=|QH|-|QC|

Thermal efficiency,

H

C

H Q

Q

Q

We == 1


(cont(cont ))


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(cont(cont)) Second law of thermodynamics

No heat engine operating in a cycle canabsorb energy from a reservoir and use it

entirely for the performance of an equal

amount of work.

The conversion of work to heat is irreversible

process.

The heat flow from hot to cold across a finitetemperature gradient is irreversible process.



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The Carnot cycle

No real engine operating between two

energy reservoirs can be more efficient

than a Carnot engine operatingbetween the same two reservoirs.

EntropyEntropy


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A state variable called the entropy, S is related to

the second law of thermodynamics.

The change in entropy during any constant

temperature process connecting the two

equilibrium states is defined as

SI unit: joules/ Kelvin ( J/K)

T

QS r=

EntropyEntropy (cont...)(cont...)


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When all systems taking part in a process

are included, the entropy either remains

constant or increases.

No process is possible in which the total

entropy decreases, when all systemstaking part in the process are included.

S 0


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LIGHT AND OPTICSLIGHT AND OPTICS

TopicsTopics


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Reflection and refraction

Hyugens principle Diffraction of light

Optic lens

Optical centre, Principal axis, principal focus,

and focal length

Lenz formula positive and negative Optical fibres

LightLight


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Light is a transverse, electromagnetic

wave.

It travels in straight lines.

It can travel through a vacuum.

It has dual nature.

ReflectionReflection


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Part of the light encountering the second

medium bounces off that medium.

Law of reflection states that:

The angles of incidence and reflection are

always equal and The reflected ray always lies in the plane of

incidence

ReflectionReflection (cont...)(cont...)

i =


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According to the law of reflection

Reflection made with laser light

ri

Types of ReflectionTypes of Reflection


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Reflection depends on the texture of the

reflecting surface.

Types of reflection

RefractionRefraction


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Light passing into the second medium

bends through an angle with respect to the

normal to the boundary.

RefractionRefraction (cont...)(cont...)


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Refractive IndexRefractive Index

Th d f b di f h li h


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The degree of bending of the light

depends on the refractive index of material

through which the light passes.

)(m.smediumgivenainlightofspeedv

)m.s108~(3.00vacuumainlightofspeedc

unit)(noindexrefractiven

1-

1-

=

=

=

v

c=n

SnellSnells Laws Law

Th l f i id d f ti


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The angles of incidence and refraction

when light travels from one medium to

another can becalculated using Snells

Law.2211 sinsin nn =

incidenceofanglesand

2materialofindexRefractive1materialofindexRefractive

21

2

1

=

=

=

nn

HuygensHuygens PrinciplePrinciple

H d th t li ht i f f


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Huygens assumed that light is a form of

wave motion rather than a stream of

particles.

Huygens constructions for(a) a plane wave propagating to the

right and (b) a spherical wave.

HuygensHuygens PrinciplePrinciple

E h i t th f t i id d


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Each point on the wave front is considered

a point source.

If the propagating wave has a frequency, f,

and is transmitted through the medium at a

speed, v, then the secondary wavelets willhave the same frequency and speed.

Huygens principle proves the laws of

reflection and refraction.

DiffractionDiffraction

The ability of a wave to spread out in wave


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The ability of a wave to spread out in wave

fronts as the wave passes through a small

aperture or around a sharp edge.

Increases with increasing wavelength and

decreases with decreasing wavelength. When the wavelength of the waves are

smaller than the obstacle, no noticeable

diffraction occurs.

Optic LensOptic Lens

A piece of transparent material with its

id d t h i l f


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sides ground to spherical form.

Spherical surfaces: Concave

Convex

Biconcave

Biconvex

Plano concave

Plano convex

Optic LensOptic Lens (cont...)(cont...) Optical centre

The geometric centre of the lens

P i i l i


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Principal axis

Line joining the centres of curvature of the two

surfaces of a lens

A lens has one principal focus on either side of it.

Principal focus

A point on the principal axis where light comes to a

focus (for a converging lens) or appears to be

diverging from (for a diverging lens).

Optic LensOptic Lens (cont...)(cont...)

Focal length


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Focal length

The distance between the optical centre and

principal focus.

formulaLens111 = vuf


A lens is usually ground to some specific focal


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A lens is usually ground to some specific focal

length using glass material of known refractive

index (n). Lens makers formula:

.vertices)surfacetwoebetween thaxislensthealongdistance(thelenstheofthicknesstheis

andsource,lightthefromfarthestsurfacelenstheofcurvatureofradiustheis

source,lighttheclosest tosurfacelenstheofcurvatureofradiustheis

material,lenstheofindexrefractivetheis

lens,theoflengthfocaltheis

2

1

d

R

R

n

f

( )( )

+= 2121

111

1

1

RnR

dn

RRnf


For a thin lens: 111


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For a thin lens:

Iffis negative then the lens is diverging and if

it is positive then the lens is converging. Simple lenses are subject to the optical

aberrations

Spherical aberration

Chromatic aberration

Coma

( )

21

111

1

RRn

f

AberrationsAberrations


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Compound LensCompound Lens

Previously mentioned aberrations can becompensated for by using a combination of


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simple lenses with complementary aberrations.

Compound lens A collection of simple lenses of different shapes and

made of materials of different refractive indices,

arranged one after the other with a common axis.

If the lenses of focal lengths f1 and f2 are thin, the

combined focal length fof the lenses is given by

Critical AngleCritical Angle

The angle of incidence where the angle of


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The angle of incidence where the angle of

reflection is 90. The light must travel from

a dense to a less-dense medium.

Total Internal ReflectionTotal Internal Reflection

If then refracted ray will not emerge fromthe medium, but will be reflected back into the

ci >


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the medium, but will be reflected back into the

medium.

Total internal reflection takes place when:

Light shines from an optically denser medium to an

optically less dense medium.

The angle of incidence is greater than the criticalangle.

2materialtheofindexrefractivetheis1materialtheofindexrefractivetheis

Where

2

1

nn

=

1

21

sin n

nc

Fibre OpticsFibre Optics

One of the most common applications of total


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pp

internal reflection is fibre optics.

Optical fibre is a thin, transparent fibre, usuallymade of glass or plastic, for transmitting light.

Structure of single optical fibre

Overall diameter of the fibre is about 125 m

Diameter of the core is just about 10 m

Fibre OpticsFibre Optics (cont...)(cont...)

Applications:


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pp

Telecommunications, etc.

Medicine Endoscopes


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ELASTICITYELASTICITY

TopicsTopics

Hookes law


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Elastic potential energy

Strain energy

Poissons ratio

IntroductionIntroduction

Rigid body


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A body which does not undergo any change in its

shape or size under the action of any external force. Deforming force

The force which changes or tries to change the shape

or size of a body without moving it as whole. Restoring force

The force acting in the body, which opposes changes

in the shape and dimensions of the body.

ElasticityElasticity

The property of the body to resist change


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and regain its dimensions or shape when

the deforming forces are removed.

Examples:

Steel Glass

Rubber

It is the molecular property of matter

ElasticityElasticity Elastic body

A body that exhibits elasticityElastic bodyregains its shape


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y y

Inelastic or plastic body

A body that does not regain its original shape when

subjected to deforming forces

Examples:

Putty

Lead solder

Wax

Elastic limit Every body acts as an elastic body within this limit

Inelastic body remainsstretched

ElasticityElasticity (cont...)(cont...)

For perfectly elastic bodies the elastic limit


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is very high

For perfectly inelastic or plastic bodies the

elastic limit is very low

Elastic Potential EnergyElastic Potential Energy

In order to stretch a rubber-band we have to do work on

it


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it.

This means we transfer our energy to the rubber-bandand it gains potential energy.

Once released, the rubber-band begins to move and

elastic potential energy is transferred into kinetic energy.

extensiontheis

constantelastictheiswhere

2

1energypotentialElastic 2

x

k

kx=

Elastic Potential EnergyElastic Potential Energy

(cont...)(cont...)


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StressStress

When a body is subjected to an external force,

the force per unit area is called


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the force per unit area is called Stress.

Types of stress:

Longitudinal

Volume or bulk

Shearing and tangential

( ) pascalorNmarea

forceStress 2-=

StrainStrain

The fractional deformation produced in a body

when it is subjected to a set of deforming forces


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when it is subjected to a set of deforming forces.

Strain being a ratio has no units

Types of strain:

l

e

lengthoriginal

lengthinchangeStrainalLongitudin ==

VV-

volumeoriginal(decrease)in volumechangeStrainBulk ==

layerstwo

betweendistancelarperpendicutheisZ

surfaceupperofthentdisplacemetheisXWhere

Z

X)(StrainShearing

=

Stress vs. StrainStress vs. Strain


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A = Proportionality limitB = Elastic limit

C = Yielding point

D = Breaking point

Sb = Ultimate tensile strength

Behaviour of a wire under graduallyincreasing load.

Strain EnergyStrain Energy

Strain energy is a form of potential energy.


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External work done on an elastic member

in causing it to distort from its unstressed

state is transformed into strain energy

HookeHookess LawLaw

Within the proportional limit, the strain produced

in a body is directly proportional to the applied


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in a body is directly proportional to the applied

stress.

( )

bodytheofmaterialtheof

elasticityofmodulusthecalledconstantaisEwhere

pascalorNmstrainstressE

stress1strain

stressstrain

2-

E

=

=

HookeHookess LawLaw


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Moduli of ElasticityModuli of Elasticity

Youngs modulus (Y)

YstressalLongitudin

=


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Bulk modulus (K)

( )( ) eA

Fl

le

AFY

Y

.

strainalLongitudin

==

=

( )( ) VPV

VV

AF

K

K

==

=straincVolumeteri

stressVolumetric

Longitudinal stress on a wire

which produces strain

Moduli of ElasticityModuli of Elasticity (cont...)(cont...)

Rigidity modulus()stressTangential


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( )

XA

FZ

Z

X

A

F

A

FAF

=

=

=

==

=

.

ZXsmall,isWhen

strainShearing

g

Tangential stress or shearing

stress and shearing strain

PoissonPoissons Ratio (s Ratio ())

Ratio between lateral strain and the longitudinal

strain of the body


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strain of the body.

( )ed

dl

le

dd

.

strainalLongitudinstrainLateral

==

=

(a)Poissons ratio in a rubber cord.(b)Poissons ratio in a wire


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ELECTRICITYELECTRICITY

TopicsTopics

Introduction Ohm's law


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Series and parallel circuits Alternating current and applications

Electromagnetism Right hand grip rule Current flowing through a long straight wire, a short

coil and a solenoid

Force on a conductor in magnetic field

TopicsTopics (cont(cont))

Forces effecting current carrying conductors


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Electromagnetic induction Electric motor operation

Transformer

OhmOhms Laws Law

Definition

The amount of electric current through a metal


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The amount of electric current through a metal

conductor, at a constant temperature, in acircuit is proportional to the voltage across the

conductor.

Mathematically, V = R I

Here R is a constant called the resistance of

the conductor.Simple Representation of

Ohm's Law

OhmOhms Laws Law (cont(cont))


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OhmOhms Laws Law (cont(cont))

Using Ohms law

Consider the circuit, calculate the current flowing


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through the resistor.Ohms law is:

Rearranging,

What is the voltage across a 10 resistor when a

current of 1.5 A flows though it?

AV

R

VI 1

5

5=

==

IRV =

Series CircuitSeries Circuit

In a series circuit,

The charge has a single path from the battery,


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returning to the battery. The amount of current is the same through any

component in the circuit.

Equivalent resistance in a series circuit,

Rs =R1+R2+R3

Voltage across the battery is equal to

the sum of the voltages in the circuit.

Parallel CircuitParallel Circuit

In a parallel circuit

The charge has multiple paths from the battery,

returning to the battery.


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The voltage is equal across all components in thecircuit.

All currents through each component must add up to

the total current in the circuit. I = I1

+ I2+ I

3 Equivalent resistance in a

parallel circuit,

++= 321

1111

RRRRp

SeriesSeries--Parallel NetworkParallel Network

213132

321

1 RRRRRR

RRR

Rp ++=


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421

RRRR pps ++=

KirchhoffKirchhoffss LawsLaws

Complex circuits can be analyzed by two simple

rules called Kirchhoffs rules.


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Junction Rule At any junction of several circuit elements, the sum of

currents entering the junction must equal the sum of

currents leaving it.

Based on the conservation of charge

i1 + i4 = i2 + i3

KirchhoffKirchhoffss LawsLaws (cont(cont))

Loop rule

The directed sum of the electrical potential differences


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around any closed circuit must be zero. . Based on the conservation of energy

v1 + v2 + v3 + v4 = 0

Alternating CurrentAlternating Current

In alternating current (AC), The movement (or flow) of electric charge periodically

reverses direction.


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An electric charge would for instance move forward,then backward, over and over again.

The horizontal axis measures time; the

vertical, current or voltage

Alternating CurrentAlternating Current (cont(cont))

Figure a:

A Sine wave representing the

variation of current.


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The value of current at any instantsay t seconds is i=i0 sint

Figure b:

The variation of emf over a period

of time T.

The instantaneous emf is e=e0sint

A.C current and voltage

(a)

(b)


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ElectromagnetismElectromagnetism

RightRight--Hand Grip RuleHand Grip Rule

Determines the direction of a

magnetic field from the


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current direction in aconducting wire.

The right hand grips the wire

so that the thumb points thesame way as the current.

The fingers curl the same

way as the field lines.

Magnetic FieldMagnetic Field

Magnetic field on a long straight wire

The magnetic field lines form circles around the wire.


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Magnetic field due to a long, straight wire is

where 0 is permeability of free space0 4 10

-7 T.m/A

r

IB

2

0=

Magnetic FieldMagnetic Field(cont(cont))

Circular loop

Magnetic lines resemble those of a bar magnet.


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The magnitude of the magnetic field at the center of acircular loop carrying current I is

Magnetic field lines for a currentcarrying loop

rIB

2

0=

Magnetic FieldMagnetic Field(cont(cont))

Magnetic field on a solenoid

A solenoid is a long, straight wire bent into a


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coil of several closely spaced loops Also called an electromagnet

The magnetic field inside a

solenoid is B =0nI

Magnetic field lines of aloosely wound solenoid

Magnetic ForceMagnetic Force

Magnetic force on a current-

carrying conductor


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If a straight conductor of length carries current I, the magnetic force

on that conductor when it is placed in

a uniform external magnetic field is

F= BI sin

Where is the angle between the

direction of the current and the

direction of the magnetic field.

Magnetic ForceMagnetic Force (cont(cont))

The size of the force on a current in a magnetic field

depends on the size of the current.

The direction of the force depends on the direction of the


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current and the direction of the magnetic field.

The direction of the force is at right angles to the current

and to the magnetic field. (Flemings left-hand rule.)

Aluminium foil placed in the magnetic field of a large

permanent magnet and connected to the power supply.

Factors Affecting the ForceFactors Affecting the Force

Force F on the conductor is proportional to

The length of wire in the field, L


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The current I

Strength of the field, B and the angle factor

Combining these, we get F = BIL

Electromagnetic


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ElectromagneticInductionInduction

MotorsMotors

An electromechanical device that converts

electrical energy to mechanical energy.

A t i t i


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A motor is a generator run in reverse.

The mechanical energy can be used to

perform work such as Rotating a pump impeller, fan, blower, driving

a compressor, lifting materials etc

MotorsMotors (cont(cont))


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MotorsMotors (cont(cont))

Motorloads

Description Examples

Constant

t

Output power

i b t t

Conveyors, rotary

kil t t


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torqueloads varies but torqueis constant kilns, constant-displacementpumps

Variable

torqueloads

Torque varies

with square ofoperation speed

Centrifugal pumps,

fans

Constant

powerloads

Torque changes

inversely withspeed

Machine tools

MotorsMotorsClassificationClassification


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Types of AC MotorsTypes of AC Motors

Electrical current reverses direction

Two parts: stator and rotor

St t t ti l t i l t


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Stator: stationary electrical component

Rotor: rotates the motor shaft

Two types Synchronous motor

Induction motor

Synchronous motor

Induction MotorInduction Motor


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TransformerTransformer

A device that transfers energy from one

AC circuit to other by means of

electromagnetic induction


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electromagnetic induction Primary and secondary windings (insulated

from each other electrically) are mounted

on opposite sides of a ferromagnetic core.

Used to raise voltage (step-up transformer)

or lower voltage (step-down transformer)

TransformerTransformer (cont(cont))


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TransformerTransformer (cont(cont))

Voltage is raised when the primary winding

has fewer turns than the secondary

winding


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winding. Voltage is lowered when the primary

winding has more turns than the

secondary winding

Step-up transformer:V2 / V1 = N2 / N1



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SOUNDSOUND


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SOUNDSOUND

TopicsTopics

Properties of sound

Relation between velocity, wavelength and

frequency


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frequency Solve problems: t=1/f; v=f()

Reflection and refraction

Beats - Doppler effect

Nodes and anti-nodes

Resonance

SoundSound

Sound waves are pressure fluctuations, createdby a vibrating source.

Sound is a longitudinal wave produced by thei d f ti f ti l i


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Sound is a longitudinal wave, produced by thecompression and rare fraction of particles in amedium.

Compressions and rarefactions on a longitudinal wave

Properties of SoundProperties of Sound

Amplitude

It is the maximum displacement of the

vibrating particle from the mean position


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vibrating particle from the mean position. Expressed in meters in S.I. system.

The amplitude of a sound determines its

loudness or volume. Larger amplitude implies louder sound, and

vice versa.

Properties of SoundProperties of Sound (cont(cont))

Phase

A state or conditions with regard to position anddirection of motion with reference to its mean position.

Expressed in radians or degrees


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Expressed in radians or degrees

Time period, T

Time taken by a particle to complete one vibration(cycle).

Expressed in seconds.


Frequency, f

Number of vibrations made by a vibrating particle in one second.

f= 1/T Hertz (vibrations per second)

Frequency of sound is heard as pitch.


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A higher frequency sound has a higher pitch, and vice versa.

The human ear can hear frequencies from 20 to 20 kHz.

Infrasound waves have frequencies 20 kHz.


Wavelength, The distance between two successive particles of the

medium which are in the same phase.

There is a phase difference of 2 radians betweenparticles separated by one wavelength


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pparticles separated by one wavelength.

Acoustic

Longitudinal Wave


The speed of a longitudinal wave isv= /t or v=f . ms-1

Speed of sound

Depends on the medium the sound is travelling in.


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p g

The speed of sound in air, at sea level, at atemperature of 21C and under normal atmospheric

conditions, is 344 ms-1

.


Intensity

It is the energy transmitted over a unit of area eachsecond.

WattsJoulespowerenergy


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Threshold of hearing is 1012 W m2.

Threshold of pain is 1.0 W m2

22.

....m

Watts

ms

Joules

area

power

areatime

energyIntensity ==

=

CalculateCalculate

9The musical note A is a sound wave. Ithas a frequency of 440 Hz and a

wavelength of 0,784 m. Calculate thed f th i l t


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g ,speed of the musical note.

9The wavelengths of audible sounds are

17m to 0.017m. Find the range of audiblefrequencies assuming velocity of sound inair is 340 ms-1

SolutionsSolutions

1.Solution:

f = 440 Hz

= 0.784 m


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v = f

= (440 Hz)(0.784m)

= 345m s1

2.Solution:

Range of audible frequencies is 20 Hz to 20 kHz.

ReflectionReflection

Sound can bounce off of objects. The angle of incidence is equal

to the angle of reflection.

Sound reflection gives rises toechoes.


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The study of sound properties(especially reflections) is called

acoustics.Sound reflection from a wall.

RefractionRefraction

The change of speed in differentmedia can bend a sound wave ifit hits the different medium at an

angle other than 90.Th b d t d


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The wave bends toward aslower medium or away from afaster medium.

Ultrasound imaging, bats, anddolphins all use reflection andrefraction.

Refraction of a sound

BeatsBeats

An interference effect that occurs whentwo waves with slightly different

frequencies combine at a fixed point inspace


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space.

Beat frequency, fb=|f2-f1|

Beats

Doppler EffectDoppler Effect

Definition

The apparent change infrequency of the source ofsound due to relative

ti b t th


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motion between theobserver and the source

of sound.

+=

s

oso

vv

vvff

Doppler EffectDoppler Effect (cont(cont))

Doppler effect is applicable when vs


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Accurate navigation of aircraft.

Velocities of stars are determined, relative

to earth.

Used for tracking artificial satellites.

Nodes and AntinodesNodes and Antinodes

Node A node is a point on a wave where no displacement

takes place.

In a standing wave, a node is a place where the twowaves cancel out completely as two waves


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destructively interfere in the same place.

Anti-node

An anti-node is a point on a wave where maximumdisplacement takes place.

In a standing wave, an anti-node is a place where the

two waves constructively interfere.

Nodes and AntinodesNodes and Antinodes (cont(cont))


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ResonanceResonance

The tendency of a system to vibrate at amaximum amplitude at the natural frequency ofthe system.

A special case of forced vibrations.


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p

Resonance



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NUCLEAR PHYSICSNUCLEAR PHYSICS


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UC S CSUC S CS

TopicsTopics

Mass defect and binding energy Isotopes

Radioactivity

Nature and properties of radiation

H lf lif


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Half-life

Fusion and fission

Chain reaction

Nuclear reactor

Applications

Atomic StructureAtomic Structure

J.J.Thomsons model of the atom

J.J.Thomson (18561940)

Positive charge distributed throughout the

atom.

Electrons embedded throughout the volumeof the atom like seed in watermelon.


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Rutherfords Planetary model

Ernest Rutherford (18711937)

Positive charge concentrated at the centre

of the atom, known as the nucleus.

Electrons move in orbits about the positively

charged nucleus in the same way thatplanets orbit the Sun.

Atomic StructureAtomic Structure (cont...)(cont...)

Niels Bohr (18851962)

Bohr model is a quantum physics-based

modification of the Rutherford model.

Bohr model is a primitive model of thehydrogen atom.

Electrons can only travel in special orbits: at


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Rutherford-Bohr atomic model

Electrons can only travel in special orbits: at

a certain discrete set of distances from the

nucleus with specific energies.

The electrons can only gain and lose energyby jumping from one allowed orbit to another.

Absorbing or emitting electromagnetic

radiation with a frequency according to

thePlanck relation

: hvEEE == 12

Composition of NucleusComposition of Nucleus

The nucleus is spherical in shape and has a

diameter in the order of

The entire mass of the atom and positive chargeis concentrated inside the nucleus.

m1410


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Atomic nucleus is composed of protons and

neutrons. Proton has +ve charge whose magnitude is

equal to the charge of an electron but heavier

than electron.


(cont...)(cont...) The neutron is electrically neutral and has a

mass slightly greater than that of a proton.

Protons and neutrons collectively are callednucleons. += NZA


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neutronsofnumbernumberneutrontheN,

protonsofnumbernumberatomictheZ,

nucleonsofnumbernumbermasstheA,

==

=


(cont...)(cont...) The symbol to represent a nuclei is as follows:

XA

Z

numberatomictheisZ

numbermasstheisA


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The nuclei of all atoms of a particular element must

contain same Z.

For a nucleus to be stable, N = Z for lighter nuclei and N

> Z for heavy nuclei.

elementtheofsymbolchemicaltheisX

IsotopesIsotopes

Isotopes of an element have same Z value but

different N and A values.

For example are fourisotopes of carbon.

CCCC14

6

13

6

12

6

11

6

and,,

C12

6

C13


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The natural abundance of is 98.9%, whereas

isotope is only about 1.1%. Some isotopes dont occur naturally but can be

produced in laboratories.

C13

6

Mass Defect and BindingMass Defect and Binding

EnergyEnergy Mass defect

The actual mass of a nucleus is always found to be

less than the sum of the masses of the nucleons

present in it. This difference is called Mass defect and is denoted

b


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by m.

Binding energy The energy equivalent of the mass defect is bindingenergy of the nucleus.

It is also defined as the minimum energy required to

split the nucleus into its constituent nucleons.

Mass Defect and BindingMass Defect and Binding

EnergyEnergy According to the Einsteins mass energy

relation, Binding energy is expressed as

follows:Kginmeasuredisdefectmasswhen the

joulemcB.E 2=


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If the mass defect is measured in amu

then:

Kg.inmeasuredisdefectmasswhen the

Mev931.5mB.E =

RadioactivityRadioactivity

In 1896, Becquerel accidentally discovered that

uranium salt crystals emit an invisible radiation.

After several such observations, under controlledconditions he concluded that the radiation did not

require external stimulation


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require external stimulation.

This spontaneous emission of radiation is calledRadioactivity.

RadioactivityRadioactivity (cont...)(cont...)

Radiation is of three types:

Alpha

Beta

Gamma From the experiments it is found that:

Al h h li l i


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Alpha rays are helium nuclei

Beta rays are electrons

Gamma rays are high-energy photons

These three radiations have different penetrating powers.

Decay ConstantDecay Constant

Decay constant:

If a radioactive sample contains Nradioactive nuclei at some

instant, then the number of nuclei N, that decay in time interval

t is proportional to N.

NN


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Isotopes with a large value decay rapidly; those with smalldecay slowly.

constantdecaytheiswhere

tNN

Nt

=

Half LifeHalf Life

The half-life T1/2of a radioactive substance is the time it

takes for half of a given number of radioactive nuclei to

decay.

h

eq.AeNN t-0 =


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constantsEuler'is2.718,e

0,tat timepresentnucleieradioactivofnumbertheisNt,at timepresentnucleieradioactivofnumbertheisN

where

0

=

=

Half LifeHalf Life (cont...)(cont...)

Eq. A can be written as follows:

eq.B2

1NN

n

0

=

lives-halfofnumbertheisnWhere,


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n is related to time t and the half-life T1/2 by

21T

tn =

Half LifeHalf Life (cont...)(cont...)

Substitute the value ofnand solving eq.B, we get the

final expression for T1/2 as follows:

693.0

21 =T


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General decay curve of a radioactive sample

Nuclear ReactionsNuclear Reactions

Radioactivity can be of two types:

Natural radioactivity

Artificial radioactivity

Nuclear reactions It is possible to change the structure of nuclei by bombarding

them with energetic particles


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them with energetic particles

FissionFission

Nuclear fission occurs when a heavy nucleus, such as235U, splits, or fissions, into two smaller nuclei.

In such a reaction, the total mass of the products is less

than the original mass of the heavy nucleus. The fission of235U by slow (low-energy) neutrons can be

represented by the sequence of events


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represented by the sequence of events

About 200 MeV of energy is released in each fission event

nKrBaUn 109236141562359210 3+++

FusionFusion

When two light nuclei combine to form a heavier nucleus,

the process is called nuclear fusion.

There is a loss of mass, accompanied by a release of

energy. All stars generate their energy through fusion processes.

P t t l


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Protonproton cycle

4 protons combine to form an alpha particle and 2 positrons, withthe release of 25 MeV of energy release.

FusionFusion (cont...)(cont...)

HeHH

and

eDHH

3

2

1

1

1

1

21

11

11

++

+++ + v

Where D stands for Deuterium


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( )H2HeHeHeor

eHeHeH

1

1

4

2

3

2

3

2

4

2

3

2

1

1

++

+++

+v

Energy liberated is carried primarily by gamma rays, positrons, and neutrinos.

Chain ReactionChain Reaction As discussed in previous slides neutrons are are emitted

when 235U undergoes fission. These neutrons can in turn trigger other nuclei to

undergo fission known as the chain reaction.


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Nuclear ReactorNuclear Reactor

A nuclear reactor is a system designed to maintain what

is called a self-sustained chain reaction.

Uncontrolled chain reaction will proceed too rapidly and possibly

result in the sudden release of an enormous amount of energy(an explosion)

Reproduction constant K, defined as the average number

f t f h fi i t th t ill


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of neutrons from each fission event that will cause

another event. Neutron leakage

If the fraction leakage is large then the reactor will not

operate.

Nuclear ReactorNuclear Reactor (cont...)(cont...)

Moderator

In order for the chain reaction to continue, therefore, the neutrons

must be slowed down.

This is accomplished by surrounding the fuel with moderator. Most modern reactors use heavy water (D2O) as the moderator

Control rods


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To control the power level, control rods are inserted into the

reactor core These rods are made of materials such as cadmium that are

highly efficient in absorbing neutrons.

Nuclear ReactorNuclear Reactor (cont...)(cont...)


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Main components of a pressurized-water nuclear reactor.

ApplicationsApplications

Nuclear power

Medical Imaging CAT scans and MRI

Industrial applications - Oil and Gas Exploration

Radioactive dating

Commercial applications

T iti i d ith h h i ifl i ht t i i ht ti


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Tritium is used with phosphor in rifle sights to increase night time

firing accuracy Luminescent exit signs use the same technology

Food processing and agriculture

Food irradiation



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physics booklet

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