26 class 10 semester 2 physics

7/31/2019 26 Class 10 Semester 2 Physics

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MACHINES

INTRODUCTION

Machines have been used for centuries, not only to make work easy but also to make it

efficient and safe. The constructions of simple machines are not complicated. They are used

in our day-to-day lives. Simple machines do not convert energy from one form into another.

Complicated machines such as bicycles and sewing machines are made by combining two

or more simple machines.

Def. A machine is a device by which we can either overcome a large resistive force at

some point by applying a small force at a convenient point and in a desired direction or by

which we can obtain a gain in speed.

CLASSIFICATION OF MACHINES

There are certain common terms used for almost every simple machine. Let us understand

these terms first.

Input Energy It isthework done on a machine or the energy supplied to amachine.

Output Energy It is the work done by a machine or the energy obtained from amachine.

Principle of Machine In an ideal machine, the output energy is equal to the inputenergy. Therefore, mathematically we can express it as .This is called

the principle of machine.

Velocity Ratio- The ratio of velocity of effort to the velocity of load is called velocityratio of the machine.

Velocity Ratio=


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Efficiency=

=

MA=

and VR=

Or, M.A. = V.R.

LEVER

A lever is a simple machine. It consists of a rigid bar that is capable of turning around a

pivot (also called the fulcrum). Generally, we use a rod, which rotates freely about thefulcrum.

For a lever, apart from the general terms used for all machines, we usually use two more

terms.

Load Arm It is the distance between the fulcrum and the point where the load isapplied.

Effort Arm It is the distance between the fulcrum and the point where the effortis applied.

The working of all levers is based on a common principle. This is called the principle of

lever.

Principle of Lever

Load Load arm = Effort Effort arm

If we rearrange the equation, we obtain

Therefore, the mechanical advantage of a lever is nothing but the ratio of the length of itseffort arm to that of its load arm.


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Different types of Lever

Levers are classified into three types depending upon the positions of load, fulcrum and

effort.

Lever of the first order

When the fulcrum is situated between the load and effort, we call it a lever of the first

order. For example, beam balance, crowbar, seesaw, etc.

Crowbar Beam BalanceSeesaw

Mechanical advantage of a lever of the first order

In the case of levers of the first order, we try to keep the load arm smaller than the effort

arm, i.e., effort arm > load arm. Therefore, a big load can be shifted by using a small effort

with the help of a lever of the first order. As the load arm is smaller than the effort arm,

Lever of the second order

When the fulcrum and effort are situated at the opposite ends of the lever, and a load is

placed in between them, we call it a lever of the second order. For example, nutcracker,wheel-barrow, etc.


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Wheel-Barrow

Nutcracker

Mechanical advantage of a lever of the second order

In the case of levers of the second order, the load arm is always smaller than the effort arm,

i.e., effort arm > load arm. Therefore, a big load can be shifted by using a small effort with

the help of a lever of the second order.As the load arm is smaller than the effort arm,

Lever of the third order

When the fulcrum and load are situated at the opposite ends of the lever, and an effort is

applied somewhere between them, we call it a lever of the third order. For example, pair of

tongs, fishing rod, etc.


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Fishing Rod

Tongs

Mechanical advantage of a lever of the third order

In case of levers of the third order, the effort arm is always smaller than the load arm, i.e.,load arm > effort arm. As the load arm is larger than the effort arm,

Although we do not obtain mechanical advantage from a lever of the third order, we use it

for several reasons.

We use levers of the third order where other two kinds of levers cannot be used. In the case of levers of the third order, we always obtain a bigger displacement of

load by a minimum displacement of the applied force. This is why we use a lever ofthe third order in a fishing rod.

EXAMPLES IN HUMAN BODY

Class 1 lever nod your head

The pivot is the place where your skull meets the top of your spine. Your skull is the lever armand the neck muscles at the back of the skull provide the force (effort) to lift your head upagainst the weight of the head (load). When the neck muscles relax, your head nods forward.

For this lever, the pivot lies between the effort and load. A see saw in a playground is another

example of a Class 1 lever where the effort balances the load.

Class 2 lever stand on tip toes

The pivot is at your toe joints and your foot acts as a lever arm. Your calf muscles and Achillestendon provide the effort when the calfmuscle contracts. The load is your body weight and is

lifted by the effort (muscle contraction).
http://www.sciencelearn.org.nz/About-this-site/Glossary/tendonhttp://www.sciencelearn.org.nz/About-this-site/Glossary/musclehttp://www.sciencelearn.org.nz/About-this-site/Glossary/contractionhttp://www.sciencelearn.org.nz/About-this-site/Glossary/contractionhttp://www.sciencelearn.org.nz/About-this-site/Glossary/musclehttp://www.sciencelearn.org.nz/About-this-site/Glossary/tendon


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The load is between the pivot and the effort (like a wheelbarrow). The effort force needed is less

than the load force, so there is a mechanical advantage. This muscular movement at the back ofyour legs allows you to move your whole body a small distance.

Class 3 lever bend your arm

The pivot is at the elbow and the forearm acts as the lever arm. The biceps muscle provides theeffort (force) and bends the forearm against the weight of the forearm and any weight that the

hand might be holding.

The load is further away from the pivot than the effort. There is no mechanical advantagebecause the effort is greater than the load. However this disadvantage is compensated with a

larger movementa small contraction of the biceps produces a large movement of the forearm.

This type of lever system also gives us the advantage of a much greater speed of movement.

Many muscle and bone combinations in our bodies are of the Class 3 lever type.

INCLINED PLANE

An inclined plane is a sloping surface that behaves like a simple machine whose

mechanical advantage is always greater than 1.

If the inclined plane is frictionless, then in equilibrium,

Lcos = R and Lsin = E

Now, Mechanical Advantage (M.A.) of an inclined plane=

=

=

=


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V.R. =

=

GEARS

A gear is a wheel with teeth around its rim.

The of a pair of gears is defined as the ratio of the number of rotations per

unit time of the driving (or input) gear to the no. of rotations per unit time of the driven (or

output) gear .

V.R. =

=

Thus, number of teeth, radii and speed of rotation are related as

=

=

The ratio of the number of teeth in the driving wheel to the number of wheel in the driven

wheel is called the .

Gear Ratio=

A gear system is used both for gain in speed as for the gain in turning effect or torque.

PULLEYS

Generally, a single pulley or a combination of pulleys fixed in a frame, is called a block, while a

string that winds around the pulleys in different blocks is known as tackle.

When the axis of rotation of a pulley is kept fixed, it is called a fixed pulley and if the axis of

rotation is not fixed, it is called a movable pulley.

SINGLE FIXED PULLEY


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A pulley which has its axis of rotation fixed is called a fixed pulley.

M.A. , V.R. and of a single fixed pulley:

Neglecting (i) the mass of the string (ii) friction b/w the string and surface of the rim of the

pulley and (iii) the friction at the axle or in the pulley bearings, in the balanced position of theload, we have

L=T and E=T

Mechanical advantage=

=

= 1

Velocity Ratio =

= 1

Hence, efficiency =

=1

USES:

1. It is used to change the direction of the force applied to a more convinient one.

2. To raise a load directly upwards.

SINGLE MOVABLE PULLEY

A pulley whose axis of rotation is not fixed in position, is called a movable pulley.

M.A. , V.R. and of a single movable pulley:

L = T + T =2T and E=T

M.A. =

= 2

V.R. =

= 2

Efficiency =

=

=1

It is used as a force multiplier.

Diff B/W SINGLE FIXED & SINGLE MOVABLE PULLEY


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Single Fixed Pulley Single Movable Pulley

1. It is fixed to a rigid support2. Its M.A is 1.3. Its V.R is 1.4. The weight of the pulley itself

does not affect its mechanicaladvantage.

5. It is used to change the directionof effort

1. It is not fixed to a rigid support.2. Its M.A. is 2.3. Its V.R. is 2.4. The weight of the pulley itself reduces

its mechanical advantage.

5. It is used as force multiplier


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REFRACTION OF LIGHT

SECTION I

When a light beam strikes the boundary between two transparent media(having different

optical densities), a certain part of it is reflected but a much greater part of it passes

through to the second media with a sudden change in direction. This phenomenon is called

refraction.

The bending of the ray of light passing from one medium to the other medium is called

refraction.

When light travels from rarer medium to denser medium, the ray bends towards the

normal and when it travels from denser medium to rarer medium, the ray bends away from

the normal.

The refraction of light occurs because light travels with different speeds in different media.

When a ray of light passes from one medium to another, its direction(except for


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(i) The incident ray, the refracted ray and the normal to the refracting surface at the

point of incidence all lie in the same plane.

(ii) The ratio of the sines of the angle of incidence (i) and of the angle of refraction (r) is

i.e. a constant quantity for two given media, and the color of light used (frequency

of the light wave) which is called the refractive index of the second medium with

respect to the first.

Where

are the speeds of light in media 1 and 2 respectively and

are the

refractive indices of media 1 and 2 respectively

Note: For vacuum, the refractive index equals 1. For air also, it is very close to 1 and taken

to be 1 only.

Example: On a glass plate a light wave is incident at an angle of 60o. If the reflected and the

refracted waves are mutually perpendicular, the refractive index of material is

(a)2

3(b) 3 (c)

2

3(d)

3

1

Solution:From figure or 30

330sin

60sin

sin

sin

o

o

r

i

(i) When light travels from air to any transparent

medium then R.I. of medium w.r.t. air is called its absolute R.I. i.e.

v

cmediumair

(i) When light travels from medium (1) to medium (2)

then R.I. of medium (2) w.r.t.medium (1) is called its relative R.I. i.e.

2

1

1

221

v

v

(where v1 and v2 are the speed of light in medium

1 and 2 respectively).

(i)Nature of the media of incidence and refraction.

(ii) Colour of light or wavelength of light.

60

60

90

r


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Refraction Through a Glass Slab

(1)

The refracting surfaces of a glass slab are parallel to each other. When a light ray passesthrough a glass slab it is refracted twice at the two parallel faces and finally

emerges out parallel to it's incident direction i.e. the ray undergoes no

deviation = 0. The angle of emergence (e) is equal to the angle of

incidence (i)

The Lateral shift of the ray is the perpendicular distance between the

incident and the emergent ray, and it is given by

Normal shift txOO

11'

Or the object appears to be shifted towards the slab by the distance x

TOTAL INTERNAL REFLECTION

When light travels from denser medium to rarer medium the angle of incidence for which

the angle of refraction is that angle is called the critical angle. When the angle of

incidence is more than the critical angle then the light is fully reflected back in the first

(denser) medium. This is called Total internal reflection.

Generally, critical angle of a medium is quoted for light going from the medium to the air. In

this case and writing , we get

From

Where C is the critical angle

i

r N

M

t

O O'

t

Glassx


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Total internal reflection can be observed while swimming, if one opens one's eyes just

under the water's surface. If the water is calm, its surface appears mirror-like.

C

C

cosec

sin

1 ; where DenserRerer

When a light ray travels from denser to rarer medium, then deviation of the ray is

max.2 when C min.

i.e. ;)2(max C C critical angle

(i) Colour of light (or wavelength of light) : Critical angle depends upon wavelength as

Csin1

(a) VRVR CC

(b) Sin CR

D

R

D

D

R

DR v

v

1(for two media) (c) For TIR from boundary of two

mediaD

Ri

1sin

(ii) Nature of the pair of media : Greater the refractive index lesser will be the critical angle.

(a) For (glass- air) pair oC 42glass (b) For (water-air) pairoC 49water

(c) For (diamond-air) pair oC 24amonddi

(iii) Temperature : With temperature rise refractive index of the material decreases therefore

critical angle increases.

i= C

90o

>C TIR

i

rRarer

Denser


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(i is an optical illusion, which occurs usually in deserts on hot summer days. On

such a day, temperature of air near the earth is maximum and hence is rarer or lighter. The

upper layers of air, which are relatively cool, are denser. A ray of light from the top of a tree

travels from denser to rarer and bend away from the normal. At a particular layer, if the

angle of incidence is greater than 'C', total internal reflection occurs. To far away observer,

this ray i.e., AE appears to be coming from I i.e., mirror image of O. Thus inverted image of

tree creates an optical illusion of reflection from a pond of water.

(ii) Due to repeated internal reflections diamond sparkles.

(iii) Optical fibres consist of many long high quality composite glass/quartz

fibres. Each fibre consists of a core and cladding. The refractive index of the material of the core

(1) is higher than that of the cladding (2).

When the light is incident on one end of the fibre at a small angle, the light passes inside,

undergoes repeated total internal reflections along the fibre and finally comes out. The angle ofincidence is always larger than the critical angle of the core material with respect to its cladding.

Even if the fibre is bent, the light can easily travel through

along the fibre

A bundle of optical fibres can be used as a 'light pipe' in

medical and optical examination. It can also be used for optical

signal transmission. Optical fibres have also been used for

transmitting and receiving electrical signals which are

converted to light by suitable transducers.

(iv) A right angled isosceles prism, which is used in periscopes or binoculars. It is

used to deviate light rays through o90 and o180 and also to erect the image.

Cladding

Core

2

1

Looming : An optical illusion in cold countries

Earth

Desner

Rarer

Sky

i>CO

I

Mirage : An optical illusion in deserts

Denser

Rarer

Earth

I

Oi>C

45o

45o

45o90o 45o 45o

90o

A

BA

B

45o

45o 45o

45o

90o


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PRISM

Prism is a transparent medium bounded by refracting surfaces, such that the incident

surface (on which light ray is incidenting) and emergent surface (from which light rays

emerges) are plane and non parallel.

Commonly used prism :

21 rrA and Aei

For surface1sin

sinriAC ;

For surface ABe

r

sin

sin 2

For thin prism A)1( . Also deviation is different for different colour lighte.g. VR

so VR .

CrownFlint so CF

Equilateral prism Right angle prism Right angled isosceles

A

A

B

i r1 r2

C

e

i Angle of incidence, e Angle

of emergence,

A Angle of prism or refracting

angle of prism,

r1 and r2 Angle of refraction,

Angle of deviation


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In this condition of maximum deviation

,90oi ,1 Cr CAr 2 and from Snells

law on emergent surface

C

CAe

sin

)sin(sin

1

It is observed if ei and

rrr 21

then :

(i) Refracted ray inside the prism is

parallel

to the base of the prism

(ii)2

Ar and

2

mAi

(3)

If light ray incident normally on any surface of prism as shown

In any of the above case useA

i

sin

sin and Ai

(4)

When a light ray falls on one surface of prism, it is not necessary that it will exit out from the

prism. It may or may not be exit out as shown below

ei r r

m

i

e

r1 = Cr2i= 90o

max

er2

i= 0or1 = 0o

i r1

e= 0o

r2 = 0o orand


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A = angle of prism and C= Critical angle for the material of the

prism

When light rays are incident on a prism at an angle of 45o, the minimum

deviation is obtained. If refractive index of the material of prism is 2 , thenthe angle of prism will be

(a) 30o (b) 40o (c) 50o (d) 60o

Solution:(d)

2sin

sin

A

i

2sin

45sin2

A

2

1

2

2

1

2sin

A oo AA

60302

If object and observer are situated in different medium then due to refraction, object appears to bedisplaced from its real position. There are two possible conditions.

(1) When object is in denser medium and observer is in rarer

medium

(1) Object is in rarer medium and observer is in denser medium.

(2)'depthApparent

depthRealhh

Real depth >Apparent depth that's why a coin at the bottom of

bucket (full of water) appears to be raised)

(2)h

h '

Real depth < Apparent depth that's why high flying aeroplane

appears to be higher than it's actual height.

(3) Shift hhhd

11

'

(3) hd )1(

Ray 3: TIR

A>Cand

>cosecA

Ray 2: Grazing emergence

A = Cand

= cosec A

Ray 1 : General emergence

Acosec (A/2)

Ray 2: Grazing emergenceA = 2Cand

= cosec (A/2)

Ray 1 : General emergence

A< 2Cand


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(4) For water43

4 hd

For glass32

3 hd

(4) Shift for water3

hdw

Shift for glass2

hdg

A coin is kept at bottom of an empty beaker. A travelling microscope is

focussed on the coin from top, now water is poured in beaker up to a height

of 10 cm. By what distance and in which direction should the microscope be

moved to bring the coin again in focus

(a) 10 cmup ward (b) 10 cmdown ward (c)2.5cmup wards

(d) 2.5 cmdown wards

Solution:(c) When water is poured in the beaker. Coin appears to shift by a distance

cmh

d 5.24

10

4

Hence to bring the coil again in focus, the microscope should be moved by 2.5

cmin upward direction.

LENS AND ITS PROPERTIES

Lens is a transparent medium bounded by two refracting surfaces, such that at least one

surface is spherical.

Double convex Plano convex Concavoconvex

Double concave Plane concave Convexoconcave

Thick at middle Thin at middle

It forms real and virtual images both It forms only virtual images


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(Light ray passes undeviated through optical centre).

(ii)

(i) A point for a given lens through which light ray passes undeviated

(Light ray passes undeviated through optical centre).(ii)

First principle focus

Note : Second principle focus is the principle focus of the lens.

When medium on two sides of lens is same then |||| 21 FF .

If medium on two sides of lens are not same then the ratio of two focal

lengths2

1

2

1

f

f

(iii) Distance of second principle focus from optical centre is called focal

lengthconvexf positive, concavef negative, planef

(iv) Effective diameter of light transmitting area is called aperture.

2(Aperture)imageofIntensity

(v) Means the ability of a lens to converge the light rays. Unit of power is

Dioptre (D).

C1, C2 Centre of curvature,

R1, R2 Radii of curvatureOptical axis

Principle

axis

C2

+R1R2

C1

O

C1

+R2R1

C2

O

F1 F1F2 F2


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)(

100

)(

1

cmfmfP ; positive,convex P negative,concave P zeroplane P .

For a lens immersed in a medium of refractive index

Note : Thick lens Thin lens

P f R P f R

Real Image Virtual Image

1. A real image is formed due to actual

intersection of reflected or refracted

rays.

2. A real image can be obtained on a

screen.

3. A real image is inverted with respect to

an object.

Example-The image of a distant object

formed by a convex lens.

1. A virtual image is formed when the

refracted or reflected rays meet if they

are produced backwards.

2. A virtual image cannot be obtained on a

screen.

3. A virtual image is erect with respect to

the object.

Example-The image of an object formed by a

concave lens.

Convex At infinity

i.e. u

At focus i.e. fv 1m diminished

Real Inverted

Away from 2f

i.e. )2( fu

Between f and2fi.e. fvf 2

1m diminished

Real Inverted

At 2f or)2( fu

At 2fi.e. )2( fv 1m same size

Real Inverted

2f f f 2f


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Between fand 2f

i.e. fuf 2 Away from 2fi.e.

)2( fv 1m

magnified

Real Inverted

At focus i.e. fu At infinity i.e. v m magnified

Real Inverted

Between

optical centre

and focus,

fu

At a distance

greater than that

of object uv

1m magnified

Virtual Erect

Concave At infinity i.e.

u

At focus i.e. v= f 1m diminished

Virtual Erect

Anywhere

between

infinity and

optical centre

Between optical

centre and focus

1m

diminished

Virtual Erect

Note : Minimum distance between an object and its real image formed by a convex

lens is 4f.

Maximum image distance for concave lens is its focal length

The splitting of white light into its constituent colours is called dispersion of light.

Newton had shown that light rays that we obtain from the sun consist of seven different

colours red, orange, yellow, green, blue, indigo and violet. When rays of the sun are made

to pass through a glass prism, we will see the seven different colours.

V

Y

R

Screen

Incident

white li ht


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The rainbow : A rainbow is seen when the sun appears in the sky after the rains. The moisture in theatmosphere behaves like tiny prisms, dispersing the suns rays into seven colours (Vibgyor). The redcolour appears on the top of the rainbow and the violet colour appears at the bottom.

It can be achieved by placing an inverted prism in front of the first prism.

The electromagnetic spectrum is a continuum of all electromagnetic waves

arranged according to frequency and wavelength. The sun, earth, and other

bodies radiate electromagnetic energy of varying wavelengths.

To remember try:RabbitsMateInVeryUnusualeXpensiveGardens

meaning:RadioMicrowaves increasingInfra-Red frequencyVisible light andUltra-violet decreasingX-rays wavelengthGamma rays

Wave Uses Dangers

Radio Radio None


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Waves transmitters Radar Television

Microwaves

MicrowaveovensCommunication system

Internal heating of body tissue

Infra-red

Thermalimaging Remotecontrols

Burns skin

Light Optic fibres Seeing!

Strong light causes damage to vision.

Ultra-violet

Washing

powder (whiterthan white) Securitymarking

Skin cancer and blindness

X raysTaking imagesof the skeleton

Mutations in cells and severe burns to the skin.

GammaRays

CancertreatmentSterilisation ofequipment

Cancers and cell mutation

26 class 10 semester 2 physics

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