Upload
tapas-kundu
View
225
Download
0
Embed Size (px)
Citation preview
7/31/2019 26 Class 10 Semester 2 Physics
1/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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=
7/31/2019 26 Class 10 Semester 2 Physics
2/25
7/31/2019 26 Class 10 Semester 2 Physics
3/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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.
7/31/2019 26 Class 10 Semester 2 Physics
4/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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.
7/31/2019 26 Class 10 Semester 2 Physics
5/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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.
7/31/2019 26 Class 10 Semester 2 Physics
6/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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/tendon7/31/2019 26 Class 10 Semester 2 Physics
7/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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=
=
=
=
7/31/2019 26 Class 10 Semester 2 Physics
8/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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
7/31/2019 26 Class 10 Semester 2 Physics
9/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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
7/31/2019 26 Class 10 Semester 2 Physics
10/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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
7/31/2019 26 Class 10 Semester 2 Physics
11/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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
7/31/2019 26 Class 10 Semester 2 Physics
12/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
(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
7/31/2019 26 Class 10 Semester 2 Physics
13/25
7/31/2019 26 Class 10 Semester 2 Physics
14/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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
7/31/2019 26 Class 10 Semester 2 Physics
15/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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
7/31/2019 26 Class 10 Semester 2 Physics
16/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
(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
7/31/2019 26 Class 10 Semester 2 Physics
17/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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
7/31/2019 26 Class 10 Semester 2 Physics
18/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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
7/31/2019 26 Class 10 Semester 2 Physics
19/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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
7/31/2019 26 Class 10 Semester 2 Physics
20/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
(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
7/31/2019 26 Class 10 Semester 2 Physics
21/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
(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
7/31/2019 26 Class 10 Semester 2 Physics
22/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
)(
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
7/31/2019 26 Class 10 Semester 2 Physics
23/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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
7/31/2019 26 Class 10 Semester 2 Physics
24/25
1B Panditya Road, Kolkata 29 www.edudigm.in 40034819
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
7/31/2019 26 Class 10 Semester 2 Physics
25/25
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