Department : Physics
Cairo Governorate
Nozha Directorate of Education
Nozha Language Schools
Ismailia Road
Form
:2nd sec.
Revision Sheet
Unit one
Chapter one
Definitions:
Amplitude: is the maximum displacement.
Frequency: the no. of complete cycle done in one second.
Periodic time: the time taken to make one complete vibration.
Wave length: is the distance between two points having same phase.
Or: the distance between 2 successive crests or two successive troughs.
Or: the distance between centers of two successive compressions or two
successive rarefactions.
5- Wave: disturbance happened in the medium to transfer energy.
1234-
Comparison:
Mechanical wave
Electromagnetic wave.
Need medium to propagate.
Its velocity depends on the
medium.
Transverse and longitudinal
wave.
Sound, water wave.
Doesn’t need medium to propagate.
It’s speed is 3 x 108 m/s
Transverse only.
Light wave.
Transverse wave .
It is normal to the direction of
propagation.
Consists of crests and troughs.
Wave length: is the distance
between 2 successive crest or two
successive trough.
1
Longitudinal wave.
It is parallel to the direction of
propagation.
Consists of compression and
rarefaction.
Wave length: the distance between
centers of two successive
compressions or two successive
rarefactions.
Rules:
1- =
2- T =
=
=
=
= = .
3- Vel. = / T = = m/sec.
4- = =m
. --------------------------------------------------------------------------Sheet one
Q1: what’s meant by:
1- The wave length of longitudinal wave = 30 cm?
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2- The distance between two pints at which the velocity of them
vanishes = 4 cm?
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3- The no. of complete vibration in 3 seconds = 1500?
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4- The distance between the 1st trough and 5th crest = 35 m?
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Q2: compare between:
1- Mechanical and electromagnetic wave.
2- Transverse and longitudinal wave.
Q3: Give reason for:
1- We can see the sunlight but cannot hear the explosion on the sun?
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2- Light is an electromagnetic wave?
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3- Sound is longitudinal wave in air?
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4- When the velocity of same source increases as the wave length increases?
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2
Q4: this graph shows the relation between velocity and wave length of different
sources which of them has higher frequency (A) or (B)?
v
A
B
Q5: Problems:
1- If the velocity of water wave at certain point 1.5 m/s if the no. of waves is
24 wave in distance 120 cm , calculate the frequency of this waves?
2- Wireless sta(on emits a wave of speed 3 x 108 m/s towards a satellite after
0.03 sec. the same sta(on receives the wave using a radar, calculate the
distance between the station and satellite.
3- Two waves whose frequencies are 256 Hz and 512 Hz propagate in same
medium find the ration between their wavelengths and their velocities.
4- A simple pendulum makes 1200 complete vibra(on in a minute, in each
complete vibra(on it covers a distance of 20 m, calculate
a) The amplitude.
b) The frequency.
c) The periodic time.
5- The following table shows the relation between the wave length (
) and its
frequency (
) in certain medium:
in meter 0.5
1
1.5
2.5
3
4
in Hz
600
300
200
A
100
75
Draw a graphical relation between the frequency on y- axis and on x- axis
and from it find:
a) The value of (A)
b) The wave velocity.
3
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4
Sheet two
Q1: What's meant by each of the following:
1-
2-
3-
4-
5-
The echo?
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The wave length of standing wave = 20 cm?
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The length of segment =10 cm?
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The beat?
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A string makes 1200 vibrations each 3 sec. making 3 segments?
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Q2: Give reason for:
1-
2-
3-
4-
5-
6-
The person diving under the surface of water can't hear the sound
above the water surface?
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The least frequency produced from the string during the
fundamental tone?
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Thin vibrating string gives higher frequency than the thicker one?
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To have echo, the distance between the sound the reflector must
be > 17 m?
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We can hear a person speaking in another room?
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Astronauts on moon surface can't hear their direct voices?
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5
Q3: Mention the condition required:
Echo?
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2- Constructive interference?
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1-
Q4: Problems:
1- A person stands between two high buildings, at 50 m from one of them
and 200 m from the other, when he fired a pistol he heard two echoes,
if the velocity of sound in air is 300 m/s find the time interval between
two echoes.
2- Two strings A and B are from the same material and are equal in
length, knowing that the diameter of A is half the diameter of B and
are stretched by tension force 20 kg.wt. Calculate the tension force of
B to produce the same fundamental tone of A.
3- A string of length 100 cm and it is stretched by force of 16 N emits its
fundamental tone of frequency 256 Hz, explain how we can increase its
frequency to 512 Hz by:
a. Changing its length only.
b. changing the tension force only
c. What did you deduce?
4- A string from steel of length 1m vibrates in the form of segments, it
produces a frequency of 150 Hz, if the mass per unit length of the
string is 0.01 kg/m, the string is stretched by tension force 10 kg.wt,
what is the number of segment in which the string is divided during its
vibration given that g= 10 m/s2 , calculate the speed of propagation
wave in the string , then draw the formed harmonics?
5- A transverse wave propagates in a string its length is 2m, and its mass
is 0.02 kg in the shape of two parts when the tension equals 104 N
calculate the speed of wave propagation in the string and if the wave
length in air is 65 cm, calculate the speed of sound in air?
6- The following table shows the relation between the inverse of length of
a uniform string and the frequency of the fundamental tone when it
vibrates, the tension is kept constant.
1/L (m-1)
1
x
2
3
4
5
6
υ ( Hz)
150
210
300
450
600
y
900
Draw the graph between (1/L) on x- axis and (υ) on y axis find:
i. x and y
ii. the velocity of the wave
iii. If the mass per unit length is 0.01 kg/m find the tension force.
6
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7
Chapter 3
Light
1- Electromagnetic wave: doesn’t need medium to propagate.
2- Transverse wave: consists of electric and magnetic field perpendicular to each
other and perpendicular to the direction of propagation.
3- Has constant velocity c = 3 x 108 m/s
Properties of light:
1- Travel in straight line.
2- Reflect.
3- Refraction of light: bending of light due to changing of medium.
φ: angle of incidence.
Θ: angle of refraction.
φ
θ
Absolute refractive index
ratio between the velocity of light in
air to the velocity of light in medium
(n) = >1
Snell’s law:
Relative refractive index
ratio between the velocity of light in medium
to the velocity of light in other medium
; may be >1
1 n2 =
n1 sin φ = n2 sin θ
4- Interference of light: (young’s double slit exp.:
∆! =
"#
$
∆y: distance between two bright or dark fringes
R: distance between double slit and screen.
d: distance between double slits.
λ: wave length of monochromatic (coherent) light.
5- Diffraction of light: α
"
%&$'(
Total internal reflection
reflection
Φ1
Φ2
ΦC
Φ3 Φ\3
From Snell’s law:
n1 sin φ = n2 sin θ
n denser sin φ c = n less sin 90
n denser sin φ c = n less
sin φ c = - ./00
if n less = n air = 1
4
1/20/3
Sin Φ c = 8
(one wave length)
Applications:
1- Optical fiber.
It made of double layer, which has high refractive index to get small Φ c.
Used in medicine to transfer light by total internal reflection when the light
enter to the fiber it suffer from multiple reflection bec the angle of
incidence greater than the critical angle.
2- Reflecting prism:
It preferred than mirror in reflection bec. Mirror may lose some of its
luster and mirror may absorb some light intensity before reflection.
Used in binocular in fields.
And in periscope in submarine.
3- Mirage.
When the light falls from upper layer (denser) to the lower layer (less
dense) of the air it refracts away from the normal from layer to another till
it suffer from total internal reflection so you can see the reflection of any
object as in mirror.
Angle of deviation in a prism:
A + Q = 180
Θ1 + φ2 + Q = 180
∴ A = Θ1 + φ2
α = α1 + α2
Φ1 = θ1 + α1 ⇒ α1 = Φ1 - θ1
Θ2 = Φ2 + α2 ⇒ α2 = θ2 – Φ2
α = Φ1 - θ1 + θ2 – Φ2
α = Φ1 + θ2 – (θ1 + Φ2)
α = Φ1 + θ2 – A
at minimum deviation:
Φ1 = θ2 = Φ o
Θ1 + φ2 = Θ o
A = 2Θo
⇒
Θ8 =
α = 2 Φ o– A
sin ?@
>=
sin A@
n=
φ1
9
:
⇒Φ 8
=
<=9
:
α
EFG
)
G
BC- ( )
BC- (
9
Thin prism A < 10o
sin φ = φ
n=
EFG
)
G
BC- ( )
BC- (
=
(
EFG
)
G
( )
=
I=J
J
An = K + M
K = An - A
α = A(n-1)
α r = A(nr-1)
α b = A(nb-1)
α y= A(ny-1)
Angular size = α b – α r = A ( n b – nr)
α = α3
αy= O
:
nP + nQ
ny=
2
Average deviation: α y= A(ny-1) or
Dispersive power: S
A ( n b – nr)
A(ny−1)
=
=
TUVWTX Y&Z[
T\[XTU[ $[\&T'&@
n b – nr
ny−1
10
=
αb–αr
αy
=
Sheet three
Q1: what is meant by:
1- The absolute refractive index of glass = 1.5.
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2- The relative refractive index between glass and water = 8/9.
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3- The critical angle of glass = 42o.
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4- The minimum angle of deviation in a triangular prism = 30.
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5- The angular size in a thin prism = 3o.
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6- The dispersive power of a thin prism = 0.3.
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Q2: give reason for:
1- The absolute refractive index is usually greater than one.
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2- The relative refractive index is may be greater than one.
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3- Using optical fiber to transfer light.
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4- Totally reflecting prisms are preferred to mirrors.
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5- The occurrence of mirage.
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6- At minimum deviation position of triangular prism the blue color is deviated
more than the red color.
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7- The prism at min. deviation position it disperse white light into seven colors.
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Q3: mention the condition:
1- The angle of incidence = the angle of emergence.
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2- The dispersion of white light.
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3- Total internal reflection.
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4- Diffraction of light.
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5- Constructive interference.
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Q4: mention one use:
1- Double slit in double slit experiment.
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2- Double slit exp.
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3- Optical fiber.
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4- Periscope.
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5- Binocular.
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6- Reflecting prisms.
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Q5: write the mathematical formula and what does the slope
mean:
α
n
α
1
1
n-1
α
n
-A
Q6: problems:
1- A light beam is incident from air on a liquid surface making angle 30o with its
surface, the ray is deviated from its path by 20o. find the refractive index of
liquid. (1.347)
2- If the speed of light in the 1st medium is 1.2 x 108 m/s, and the speed of light in
the 2nd medium is 1.92 x108m/s. find n1 , n2 , n1-2 , n2-1 , if the velocity of light
in air is 3 x 108m/s.
3- If the critical angle of water is 47o and that of glass is 40o, find the critical
angle of glass relative to water?
(61.5o)
12
4- In young’s double slit exp. A green light falls its wave length is 5500 A o the
distance between the slit and screen is 20 cm and the distance between lighted
fringe and successive dark fringe is 0.0024 cm, calculate the distance between
two slits.
5- a ray falls on a triangular prism whose angle is 72o, it is refracted by an angle
30o and emerges tangentially to the other side, find:
a- the critical angle between glass and air.
b- The refractive index of the prism material.
c- Sin φ1.
( 42o ,1.49, 0.745)
6- A ray light falls perpendicular on one side of glass triangular prism it emerges
as a tangent on the other side, if the refractive angle of the prism 45o, calculate
the speed of light in glass.
(2.1 x
8
10 m/s)
7- A prism of angle 60o, it has two incident angles 60o, 40o at which for these
angles deviation occurs, calculate the angle of minimum deviation and its
refractive index.
(40o. 1.5)
8- The following table shows the relation between the refracted angles of light
falls on a side of a triangular prism (θ1) and the second incidence angles of this
ray (φ1) draw the relation.
Θ1
55
40
35
A
20
15
0
Φ1
5
20
25
30
40
45
B
Draw the relation (Θ1) on x- axis and (Φ1) on y axis. Find:
a- The value of A and B
b- The refractive index of the prism if α = 37.2o.
9- Trace the light: if ( n g = 1.5)
60
60
30
30
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14
Unit two
Chapter four
Density
ρ=
Mass per unit volume.
b
@W
=
cU
de
Relative density: ratio between the densities of substance to water.
OR: The ratio between the mass of substance to the mass of water at constant volume and
temp.
fg
R.d =
Factors:
fh
=
bg
bh
1- Kind of material.
2- Temperature.
Applications:
1- Identify the electrolytic solution of ca battery:
If it has low density so it is out of charge and if it has high density so the battery is
recharge.
2- In medicine:
a- If the density of blood is low indicates anemia.
b- If the urine has high density indicates of salts in urine.
Pressure:
Pressure:
i
j
k
P= J = d = de = kg .m-1 .s-2 = Pascal.
It is the normal force acting per unit area.
Pressure at a point inside liquid:
i
%[&U('
J
J
P= =
=
bU
J
=
f\U
J
=
fJ(U
J
=ρgh
1- All points have same level have same pressure.
2- The dam has thick wall at the base to compensate the pressure.
Applications:
1-
systolic
Diastolic
Increase in pressure.
120 mm Hg
Heart muscles contract
Decrease in pressure.
80 mm Hg
Heart muscles relax
2- Pressure gauge.
Atmospheric pressure: the weight of air column above sea level per unit area
is 1.013x 105 N
15
Or: equivalent to the weight of mercury column per unit area of height 76cm.
To measure the height if building:
ρ air h building = ρ Hg (H bottom – H top)
P
P
h
h
Closed container
Open container
U shaped tube
ρ1 h1 = ρ2 h2
R.d =
fl
fh
=
(h
(l
Pascal principle
Pressure applied to a liquid enclosed in a container is transmitted to every
portion of the liquid and walls of the container.
P large = P small
E large = E small
16
Sheet four (1
(1 )
Q1: what is meant by:
1- The density of mercury = 13600kg/m3?
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2- The specific weight of oil = 0.8?
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3- The normal force acting per 3 cm2 = 150N?
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4- The atmospheric pressure at sea level = 76 cm Hg?
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5- The reading of mercury manometer = - 10 cm Hg?
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6- The mechanical advantage of hydraulic press = 400?
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7- The efficiency of hydraulic press is 80%?
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Q2: Give reason for:
1- Pascal principle applied for gases?
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2- The efficiency of hydraulic press is less than 100%?
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3- Mercury is preferred to water for barometer?
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4- The mercury of height in the barometer doesn't depend on tube area?
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5- The thickness of the dam base is higher than the thickness of its top?
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6- The needle has pointed end?
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7- The relative density of water = 1?
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17
Q3: mention the factors affecting on:
1- Density of material.
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2- Pressure at a point inside liquid?
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Q4: the given graph show the relation between pressure (P)
inside two liquids A and B and the depth (h) in different
containers:
P
a- Which container is closed?
b- Which liquid is denser? Why?
A
B
h
Q5: compare between barometer and manometer?
Q6: problem:
1- A block of stone of dimensions (2x2x1) m3, it has a mass of 8000Kg, if
g=10m/sec2. Calc. its density?
2- A submarine is designed to withstand a maximum pressure of 1.03 x 106N/m2,
if ρ sea = 1030Kg/m3 g =10 m/s2 find:
a- The maximum depth.
b- The force acting on the door.
3- Cylindrical container, the area of its base of its base is 2 m2, contains amount
of water to height 0.8m, oil is poured until its height becomes 2m from the
base. Calculate the pressure on its bottom and the total force if the relative
density of oil is 0.8 and ρ w = 1000 kg/m3 g = 9.8m/s2.
4- A u-shaped tube of a uniform cross-sectional area contains water, oil of
density 600 kg/m3 is poured in one side, so that the level of water surface in
this side is lowered by 3cm, if ρ w=1000kg/m3 , find the height of oil column.
5- A u shaped tube containing some mercury, a water column 50cm long is
poured in one branch, then oil column 50cm long is poured above water, if ρ
3
3
3
Hg = 13600kg/m , ρw= 1000kg/m , ρ oil = 800kg/m , find:
a- The height of mercury column above interference between mercury and
water.
b- The height of water column which is poured in the other side above
mercury makes mercury surface in the two sides to be the same horizontal
level.
6- U shaped tube of cross sectional area 2cm2 has amount of water, if 9cm3 of
kerosene has been poured in one side so the height difference of water in the
two sides is 3.6cm, find the volume of benzene poured in the other side till the
level of water becomes the same in the two sides where the density of water is
1000Kg/m3 and the density of benzene is 900Kg/m3.
7- What will be the reading of mercury barometer at the top of building of height
100m, if it reads 76cm Hg at the ground floor, if ρ Hg =13600kg/m3, ρair
=10m/s2.
18
8- In a mercuric manometer is connected to a gas supply, the mercury level in the
free side is higher than the other side by 39 cm Hg if Pa = 75 cm Hg ρ Hg =
13600kg/m3 , g = 9.8 m/s2, find the gas pressure in units:
a- Torr.
b- Pascal.
C- Bar.
9- A mercury manometer is connected to a gas supply, if the difference between
the level in the two branches is +25cm. calculate the difference in pressure and
also the absolute pressure of the trapped air in N/m2, if ρHg =13600kg/m3, g=
9.8 m/s2 , Pa = 1.013 x105 N/m2?
10- The area of the small piston in hydraulic press is 4 x 10-4 m2 and the area of
large piston is 1200 cm2, if a force of 100N acts upon the small piston,
g=9.8m/s2 calculate:
a- The maximum mass can be lifted by the large piston.
b- The mechanical advantage of the press.
c- The ratio between the pressure acts on the two pistons.
11- In a hydraulic car lift, the radius of the small piston is 1.2 cm and that of the
large piston of mass 350kg is 15 cm , what is the value of the input force
needed to support a 1720kg car when:
a- The two pistons are in the same horizontal level.
b- The large piston is lower than the small one by 1m, knowing that the
relative density of oil = 0.8.
12- When hydraulic press is used the following results are obtained:
f
10
20
35
50
F
160
320
560
800
Plot (F) on ordinate and (f) on abscissa. Find from the graph:
a- η mech.
b- (F) if (f) = 40N.
c- If (R) = 100cm find (r).
19
80
1280
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20
Chapter four
Part two
Archimedes' principle
'"When a body is wholly or partially immersed in a fluid, it experiences an up
thrust force equal to the weight of the liquid displaced by the immersed part by
the body"
Proof:
Horizontal forces:
It is equal and opposite in direction so the resultant force is zero.
Vertical forces:
1- Down ward force (Fg) = M g = ρL g vL
2- Up ward force (Fb) due to difference in pressure
(Fb) = ∆P . A
(Fb) = (P2 – P1) .A
(Fb) = (ρL g h1 – ρL g h2) .A
(Fb) = ρL g A (h2 – h1)
(Fb) = ρL g A hc
(Fb) = ρL g vL
∴ (Fb) = (Fg)
1) Floating: Fb > Fg (ρL > ρs)
Fnet = Fb – Fg (+ve)
2) Suspended: Fb = Fg (ρL = ρs)
Fnet = Fb – Fg (zero)
Fb < Fg (ρL < ρs)
3) Sinking:
Fnet = Fb – Fg (-ve)
Factors affecting on Fb:
Fb α ρL
im
im
Fb α Vim
=
im
im
f
f
=
no
no
Applications on buoyancy (Fb):
1234-
Hydrotherapy.
Weightless experiment.
Submarine floats.
A diver breath.
21
Apparent weight:
Fg/ = Fg – Fb
1- Floating (Fg/ = -ve)
2- Suspend (Fg/ =0)
3- Sink (Fg/ = +ve)
-----------------------------------------------------------------------------------------------
Sheet four (2
(2 )
Q1: What is meant by:
1- Law of floating.
…………………………………………………………………………………..
2- Archimedes' principle.
…………………………………………………………………………………
3- The up thrust force acting on floating body = 12N.
…………………………………………………………………………………..
4- The apparent weight of a balloon = -500N.
…………………………………………………………………………………
Q2: give reason for:
1- An iron nail sinks while the ship floats on water.
…………………………………………………………………………………..
2- The weight of an immersed body in a liquid is less than in air.
…………………………………………………………………………………..
3- When a ship sails from river to the sea it floats higher.
…………………………………………………………………………………
4- Bodies which has same volume but has different densities affected by same up
thrust force in same liquid.
…………………………………………………………………………………
5- Balloon filled with helium has the same up thrust force when it filled with
hydrogen.
………………………………………………………………………………..
Q3: prove that the buoyancy of a liquid on a body equal the weight of the displaced
liquid by immersed part of body.
Q4: problems:
1- A wooden cube of length 15cm floats on water, if the immersed depth is
10.5cm, find the density of wood if ρw = 103kg/m3.
2- A submarine of volume 1000m3, floats in fresh water ρ = 103kg/m3 to be
completely immersed, then transferred to sea water ρ = 1030kg/m3. If
g=10m/s2 find:
a- The buoyant force in the two cases.
b- The appearing volume in 2nd case.
22
3- A metallic cube of side 10cm and its relative density is 2.7, hang with thread,
calculate the tension in the thread in the following cases:
a- The cube hanged in air.
b- Its half volume immersed in water.
c- It is completely immersed in water. (ρw = 103kg/m3, g=10m/s2)
4- A body has volume 0.01m3 and ρs = 600kg/m3 it is fixed by a string in the
bottom of a container filled with water such that it is wholly immersed. If ρw =
103kg/m3 g=10m/s2, calculate:
a- The up thrust force.
b- The tension in the string.
c- If the body is released, calculate the up thrust force and the appeared part
of the volume.
5- A wooden cube carries 0.2kg and immersed completely under the surface of
water, when the mass is removed, the cube rises up 0.02m. find its volume and
its side length.
6- A light boat has mass 10kg, 4% of its volume is immersed when it floats on
water surface. Calculate the maximum number of men the boat can carry
without sinking if ρw = 1000kg/m3 and the mass of each man = 62.5kg.
7- A piece of metal weight in air is 0.5N in air and 0.35N in water calculate the
relative density and the appeared weight In a liquid of density 800kg/m3 if
ρw=103kg/m3.
8- A piece of metal is immersed in water; its weight in water is less than its
weight in air by 2N, while its weight in benzene is less than its weight in air by
1.8N. Calculate the density of benzene if ρw = 1000kg/m3, g = 9.8m/s2.
9- A balloon of volume 0.5m3 and the mass of it attachment is 0.45kg is filled
with hydrogen with ρH = 0.1kg/m3. Calculate the lifting force of the balloon if
g=9.8m/s2 and ρair =1.3kg/m3.
23
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24
Chapter five
Steady flow:
"The fluid flows in steady layers and the layer moves in slide, smooth and soft
that is means that the transfer of the fluid from point to another point
continuously (stream lines)"
Stream lines:
It is the imaginary lines showing the path of a liquid particle during its flow.
The turbulent flow:
When the velocity of the flow exceed certain limit.
Mention the conditions and properties of steady flow?
Conditions:
1234-
The liquid fills the tube.
The rate of flow of liquid is constant along its path.
The velocity of liquid at any point is constant.
There is no force of friction.
Properties of stream lines:
1- Don't intersect.
2- The tangent at any point of the stream line gives the direction of the
velocity.
3- The stream lines close to each other in small area and away in large
area.
The rate of volume flow:
It is the volume of liquid flow though a certain area per unit time.
Qv=
@W
p
=
J .q
p
= M rst.
(uv /x)
The rate of mass flow:
It is the mass of liquid flow though a certain area per unit time.
Qv=
b
p
=
f .@W
p
=
fJ .q
p
= yM rst. = yz\ ({|/x)
Continuity equation:
The velocity at any point in the tube is inversely proportional to the area of the
tube at this point.
Qv (in) = Qv (out)
A 1 v1 = A 2 v2
25
Viscosity
It is a property of fluids due to the friction force between its layer which resist
sliding of them one over the other and resist the motion of bodies inside fluids.
Coefficient of viscosity:
FK
J \[W
$
F = const.
F=
J \[W
$
} J .\[W
$
~=
i .$
J .\[W
kg m-1 s-1 (Pascal . sec)
It is the tangential force acting on unit area to produce a unit change in velocity
between two liquid layers separated by a unit distance.
Factors affecting on η vis:
1- Kind.
2- temperature.
Applications:
1- Lubrication. (by high viscous liquid to protect machines from erosion)
2- Moving vehicles. ( after critical velocity Rof air αv2)
Dec. the consumption of fuels by dec. the velocity of car.
3- In medicine. (by sedimentation rate, and detect anemia)
Solved example:
in the following figure:
C
rA = 25cm, rB = 15cm, rc =10cm, rD = 8cm
calculate:
A
1- Qv at A if the velocity = 2m/s.
2- VB and vD if vc = 4m/s.
B
D
Sol.
1- Qv = Aa va = π r2va = 3.14x (0.25)2 x 2=0.3925m3/s.
2- Aa va = AB vB
0.3925 = 3.14 x (0.15)2x vB
Vb = 5.55m/s.
Qa = Qc + QD
Av=Av+Av
0.3925 = 3.14x (0.1)2x4 + 3.14x (0.08)2x vc
Vd = 13.28m/s
26
Sheet five
Q1: what is meant by :
1- The rate of liquid flow = 3x106kg/s.
…………………………………………………………………………
2- The coefficient of viscosity of liquid =0.3kg/m.s.
…………………………………………………………………………
3- The rate of flow = 8liter/s.
……………………………………………………………………….
Q2: give reason for:
1- The blood flow through the capillaries slower than the major artery.
…………………………………………………………………………….
2- It is necessary to lubricate the machines from time to time.
……………………………………………………………………………….
3- Water is not used for lubrication.
………………………………………………………………………………
4- During decrease the velocity of a car the consumption of fuel decreases.
…………………………………………………………………………………
5- When solid object flow through a liquid it loss some energy.
.........................................................................................................................
Q3: choose:
1- The unit of coefficient of viscosity. (kg.m-1.s-2 , kg.m-1.s-1 , kg.m-2.s)
2- In the steady flow the rate of flow in small area is (smaller, greater , equal) the
rate of flow in large area.
3- When the tangential force between two liquid layers increases then the
coefficient of viscosity (increase, decrease. Remain constant)
4- The ratio between the diameters of two different pistons is 2:3, then the ratio
between their velocities of steady flow (2:3 , 3:2 , 9:4 , 4:9)
Q4: problems:
1- A liquid flow in a pipe of radius 2cm, with velocity 8m/s, calculate the radius
of the tube that makes water passes with velocity 32m/s.
2- In normal adults the average speeds of blood through aorta of radius 0.7cm. is
0.33m/s from the aorta the blood goes through 30 arteries each of radius
0.35cm, calculate the speed of blood in each artery.
3- If kerosene flow across a pipe by rate 60liter/min. with velocity 40m/s,
calculate the cross sectional area of the pipe?
4- A metallic flat plate of surface area 0.01m2 is separated from another large
plate by a liquid layer by a liquid 2mm height. If a force of 2.5N acts on the
first plate which moves by velocity of 12.5cm/sec. calculate the coefficient of
viscosity and find the pressure acts on it.
27
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28
Unit three
Chapter six
Brownian motion:
That gas moves in all directions.
Boyles' law:
Pressure is inversely proportional to the volume of certain mass of gas at
constant temperature.
P1 = Pa
V = V1
P1 = Pa + h
V = V1
P3 = Pa - h
V = V2
Procedure:
1234-
Bring apparatus like in the fig.
Record the volume and the pressure of the gas.
Repeat the steps by changing the position of the tube as in the fig.
Record the volume and the pressure of the closed gas.
5- Find that P α .
6- P1V1 = P2V2 = P3 V3
The relation between volume and temp.:
The volume expansion coefficient (αv):
It is the increase in volume at constant pressure per unit volume at 0oc for 1oc rise in
temperature.
∝\ =
∆
1
=
{ …4
@ . ∆‚ 273
Charles' law:
4
At constant pressure the volume of certain mass of gas increase by :†v of its volume
at 0oc for each degree rise in temp.
Or: at constant pressure the volume of certain mass of gas is directly proportional to
its temperature on Kevin scale.
29
Procedure:
1- Put crashed ice till reach the temperature to 0oc, record the reading of
Volume at this temp. Vo.
2- Insert a steam at 100oc then record the volume of the gas V100.
3- Repeat the same steps with different temp.
4- Plot a graph between these readings.
5- Absolute zero: it is the temperature at which the volume of certain mass of
V
gas theoretically vanishes.
‡
‡
=
p
p
On Kelvin scale.
Vo
The relation between pressure and temp.:
to c
-273
The pressure expansion coefficient (βp):
It is the increase in pressure at constant volume per unit pressure at 0oc for 1oc rise of
temp.
ˆ‰ ∆Š
1
{ …4
Š@ . ∆‚ 273
Pressure' law:
At constant volume the pressure of certain mass of gas increases
increase by
pressure at 0oc for each one degree rise in temp.
4
:†v
of its
Or: at constant volume the pressure of a certain mass of gas is directly proportional
to its temperature on Kelvin scale.
Procedure:
1- Bring apparatus as in the fig.
2- Fill the container with crashed ice and move the free branch
branch till the level of
mercury return back to its level.
3- Record the reading of pressure (po) at 0oc.
4- Repeat the steps with different temperature till 100oc.
5- And record the reading of pressure.
6- Plot graph between (P) and (toc).
7- Absolute zero: it is the temperature at which the pressure
of certain mass of gas theoretically vanishes.
‹
‹
p
p
p On Kelvin scale.
po
to c
-273
The general gas law:
Œ‡

>Ž
Universal gas constant (R): the energy requires increasing the temperature of 1 mole
1ok.
30
Sheet six
Q1: what is meant by:
1- The coefficient of volume expansion = 1/273k-1.
…………………………………………………………………………………
2- The coefficient of pressure expansion = 1/273k-1.
………………………………………………………………………………….
3- The absolute zero.
………………………………………………………………………………….
4- General gas constant =8.31 J/k.
………………………………………………………………………………
Q2: give reason for:
1- A drop of H2SO4 is preferred than mercury in Charles' experiment.
…………………………………………………………………………………
2- In jolly's apparatus 1/7 of the bulb is filled with mercury.
…………………………………………………………………………………..
Q3: choose:
1- If the volume of certain mass of gas at 0oc is vo and at 100oc is vt (at constant
pressure). So
 … 
‘
4
4“
4““
equals: [:†v , :†v , :†v ]
2- If the pressure of certain mass of gas at equal 2Pa at 0oc if th temp. becomes
273oc at constant volume, its pressure equal [1/2Pa , Pa , 2Pa , 4Pa]
3- If we have three moles of gas, so the quantity
”
p
for this gas is approximate
equal [22.4 , 25 ,8.31 ,1.38x10-23]
Q4: problems:
1- A nitrogen gas for 15 liters under pressure of 12cm.Hg. and oxygen gas of
volume 10 liter under pressure of 50cm.Hg the two gases are mixed in a vessel
of volume 5 liter, find the pressure of the mixture at same temperature.
2- A quantity of gas at 17oc, the temp. Increases by 100oc, while the pressure is
constant, so the volume increases by 2.5cm3. Find the volume before heating?
3- The pressure of a gas at 26oc is 59.8cm.Hg; find the pressure at 130oc
assuming that the volume is constant.
31
Chapter seven
Postulates of kinetic theory:
1- A gas composed of elastic molecules obeys Newton's law.
2- The intermolecular space is relatively large.
3- The intermolecular force is very weak due to the large intermolecular space.
4- Gas molecules are random in motion due to the random collision between its
molecules.
5- The collisions between the gas molecules are perfectly elastic collision so the
kinetic energy is the same.
6- The gas is in thermal equilibrium state with the wall of the container.
At (STP) standard temp. and pressure
12345-
P of gas = Pa = 1.013 x 105 N/m2
Vol. = 22.4liter.
n (no. of moles ) = 1mole
N (no. of molecules) = Na = 6.023x1023 molecule
R (general gas constant) = 8.31 J/k
32
Test (1)
Question (1) :
[A] Choose the correct answer :
1. Two waves of frequency 400 Hz and 200 Hz respectively propagates in
same medium the ratio between their wave lengths is …………..
[2:1 , 1:2 , 3:1 , 1:1]
2. The angle of incident in a medium is 60° and the angle of refraction in
the other medium is 30° , the refraction index from the 1st to the 2nd
medium is ……………..
[ √3 , 1–2 , √2 , 2 ]
3. If the tension force of a string is increased 4 times and its length is
doubled , then its fundamental tone frequency .
[ remains constant , increase 2 times , increase 4 times ]
4. One of the following waves doesn't travel in vacuum .
[ sound , radio , x-ray , ultraviolet ]
[B] Compare between each of the following :
1. Mechanical and electromagnetic wave .
2. Constructive and distractive interference .
[C] Find the value of :
1) The wave length
2) The velocity of the wave .
cm
90 m
0.12 Time
0.02
0.04
0.06
0.08
(sec)
0.1
Question (2) :
[A] Give reason for each of the following :
1. The least frequency produced from a vibrating string is the
fundamental .
2. The absolute refractive index of medium is greater than one .
3. You can hear a person speaking in another room .
4. Fiber optics can be used in medical endoscope .
[B] Write the mathematical formula and what does the slope mean :
V
∆y
—˜
33
[C] In young's double slite exp. The separating distance between the two
slits was 0.2 mm, and the distance between the two slits and the screen on
which the frings are formed was 120 cm . if the distance between two
successive illuminated frings is 3 mm , calculate the wavelength of the
used monochromatic light in angstrom .
Question (3) :
[A] Mention the factors affecting on :
1. Total internal reflection .
2. Distractive interference .
3. Frequancy of fundamental tone .
[B] Trace the light :
ng = 1.5
45
60
45
60
60
[C] The following table shows the relation between frequency of
fundamental tone and reciprocal of a stretched string length ( 1–L)
š (Hz)
–
›
(m-1)
150
210
300
450
600
Y
900
1
X
2
3
4
5
6
Draw the graph with ( ) on ordinate and
the graph :
– on
›
abscissa , then find from
1. The value of X and Y .
2. Velocity of the wave in the string .
3. Calculate the tension force if the mass per unit length of string is
0.01 kg/m .
34
Test (2)
Question (1) : A) Choose the correct answer :
1- If the angle of incidence in a medium is 60° and the angle of refraction in
the second medium is 30° , the relative refractive index from the first to
the second is ………….
4
a) 2
b)
c) √2
d) √3
:
2- If the ratio between large and small piston diameters of water piston is
9 : 2 , the ratio between two forces on the two pistons are …………..
a) 2 : 9
b) 4 : 18
c) 81 : 4
d) 4 : 81
3- All the following waves travel in space except …………….
a) X-ray
b) radio
c) sound
d) light
4- All the following values represent the atmospheric pressure except ……
a) 76 cm of mercury
b) 10.33 cm of fresh water
c) 760 mm of Hg
d) 1.013 bar
B) Give reason for :
4
1- In Jolly's apparatus of the bulb is filled with mercury .
†
2- When a ship sails from fresh water into the sea , it raise a little .
C) Half a liter of hydrogen is heated from 20 °C to 313 °C . Find the
volume assuming that the pressure is constant .
Question (2) : A) Write the scientific term :
1- The path taken by a particle of a liquid inside a tube .
2- The temperature at which the volume and the pressure of an ideal gas
vanish .
B) Write the mathematical equation that relate the following physical
quantities and find the slope . P
m
Pa
(1)
h
Vo1
(2)
C) The following table illustrates different wave lengths of waves
formed in air and their corresponding reciprocal of frequency .
(m)
0.16
–
œ
0.5 × 103
0.32
1 × 10
0.64
-3
2 × 10
1- Draw a graph between () and –œ .
3- Calculate the velocity of the wave .
35
1.28
-3
a
2.56
8 × 10
5.12
-3
16 × 103
2- Find the value (a) .
Question (3) : A) Correct the underlined words :
1- Two moles of oxygen gas at standard temperature and pressure occupies
11.2 liters .
2- The angle of deviation in the thin prism is given by K = (∅ + žŸ ) – A
3- Temperature of boiling water on the Kelvin scale equals 37°K .
4- Antinode is the position where the amplitude of the vibrating string is
zero.
B) Compare between :
1- Refraction and diffraction .
( with respect the wave length )
2- Manometer and Barometer .
C) A string of length 1m is stretched by a force of 4 kg.wt where it's
mass per unit length
is 1×10-3kg/m .Calculate the frequency of its fundamental tone .
( giving that g = 10 m/sec2).
Question (4) :
A) Light ray is incident perpendicular to one side of a triangular prism
of refractive index 1.5 as shown in figure . Trace the path of the light
ray inside the prism and then find the angle of emergence .
٦٠
٣٠
B) What is meant by :
1- Coefficient of viscosity = 0.04 kg.m-1.sec-1 .
2- Pressure expansion coefficient of a gas =
4
:†v
°C-1
3- The distance between the first crest and the fourth crest = 30 cm.
4- Pressure at a point = 4 bar .
C) The average velocity of blood in aorta ( radius 0.7 am ) for an adult
is 0.33 m/sec.
from the aorta , blood is distributed to main arteries ( each radius
0.35 cm ) . if we
have 30 main arteries , calculate the velocity of blood in each .
Question (5) : A) Mention the scientific idea and one use for each of
the following :
1- Periscope
2- Jolly's apparatus
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B) What happens when :
1- Compressing the gas to double its pressure at the constant of temperature
2- Sound ray passes from cold air to hot air .
C) A wooden piece when place in water –¡ of its volume is immersed
and when placed in oil ¢–¡ of its volume is immersed . (knowing that the
density of water is 1000 kg/m3) . Find the density of oil and the density
of wood .
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