1

Unit ONE Chapter one

A. What is meant by? 1. The wavelength of a transverse wave is 15cm. 2. The displacement of a vibrating body at a certain instant = 7cm. 3. A body makes 300 vibrations in 5sec. 4. The periodic time of a vibration body = 0.1S. 5. The wavelength of a wave = 30cm. 6. The frequency of a wave = 1000 Hertz

B. Compare between: 1. Transverse and longitudinal wave. 2. Mechanical and electromagnetic wave.

C. Give reason: 1. Sound waves propagate in air as longitudinal waves. 2. Electromagnetic waves propagate through space.

D. What are the conditions necessary to produce mechanical Waves?

Problems 1- From the figure. Find:

i. The wavelength. ii. Amplitude of oscillation.

iii. The periodic time. iv. The frequency. v. The velocity of propagation.

2. If the wave velocity equals 1.5m/s. find the number of waves in a distance 60cm, if you know that the frequency is 30Hz. (12 waves)

3. A stone is thrown in a pool, (40) waves are produced in 4sec and the diameter of the first wave is 3.2meter. Calculate: (a) The frequency. (b) Periodic time. (c) Wave length. (d) Speed of wave. (10, 0.1, 0.04, 0.4)

4. A piano emits frequencies that range from a low of about 28 Hz to a high of

about 4200 Hz. Find the range of wavelengths in air attained by this instrument

when the speed of sound in air is 340 m/s. (12.14 m - 0.08 m)

5. The speed of all electromagnetic waves in empty space is 3x 108 m/s.

Calculate the wavelength of electromagnetic waves emitted at the following

frequencies:

a) Radio waves at 88.0 MHz (3.49 m)

b) Visible light at 6.0 x 108 MHz , X rays at 3.0 x 10

12 MHz (5 x 10

-7 m ,1 x 10

-10m)

6. The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and

travels at 3.00 x 108 m/s. Find the frequency of the laser light. (4.74Hz)

7. A tuning fork produces a sound with a frequency of 256 Hz and a wavelength

in air of 1.35 m.

2

a. What value does this give for the speed of sound in air? (345.6 m/s)

c) b. What would be the wavelength of this same sound in water in which sound

travels at 1500 m/s? (5.859 m)

8. Transverse wave propagates through a string with velocity 600 m / s. If the

distance between two successive crests is 3 m. Find the frequency of such wave.

9. Wireless station emits waves of velocity 3 x108 m / s towards a satellite.

After 3 second the same station receive the waves using radar. Calculate the

distance between the station and satellite.

10. An oscillating body of frequency 960 Hz. Find the number of waves formed

until the oscillations reach a person standing at a distance 100 meters from the

source (velocity of sound 320 m / s).

11.A tuning fork of frequency 320 Hz. Vibrates near an air column of length 12

m if the first wave formed at the beginning of the column reaches its end when

the fork starts to produce the 13th

wave. Calculate the velocity of sound in air.

12. A train emits sound of wavelength 0.6 m and frequency 550 Hz. Calculate

the sound wave velocity in the air. (330 m/s)

13. The number of water waves passing a certain point in one second is 12

waves, each of wavelength 0.1 m. Calculate the wave velocity in water. (1.2 m/s)

14. The light wave velocity in space is 300000 km/s Given that the wavelength

of light is 5000 Angstrom. Find the frequency of light wavelength of light.

(6x1014

Hz)

15. If the wave velocity equals 1.5 m/s find the number of waves in a distance

60 cm. if you know that the frequency is 30 Hz. (12 waves)

16. A tuning fork vibrates 640 Hz. and is heard at 15 m. calculate the number of waves

between the fork and the man given that the velocity of sound in air is 320 m/s .

(30)

17. Given that the frequency of transverse wave is 15 c/s. Calculate the velocity of the

wave if the distance between successive crest & trough is 1.5 m. (45 m/s)

18. From the graph shown find:

1- The amplitude.

2- The periodic time.

3- The frequency.

4- The wave length.

5- The wave velocity.

6- The number of waves done through a distance 1.6 km.

19. A source of waves produces 16 waves in 4 seconds. Calculate the periodic

time. (4

1 sec.)

3

20. The given figure shows a relation

between the displacement in cm and

time in seconds a transverse wave.

From the figure find.

1- The wave length.

2- The frequency:

3- The amplitude.

4- The wave velocity.

21. Given that the velocity of sound in air is 320 m/s. Calculate the number of waves

produce by a tuning fork until it is heard at a distance 45 m. from it knowing that the

frequency is 320 Hz. (45 waves) 22. A wave traveling with a velocity 1000 m/s. & has a wave length 5 cm. what is the time of one complete cycle ? (5 x 10

-5 sec.)

23. A simple pendulum makes 1200 complete vibrations in a minute. In each complete vibration it cuts a distance of 20 Cm Calculate

a) The amplitude of the vibration of the pendulum.

b) Frequency. c) Periodic time. (5cm, 20 Hz- 0.05 sec)

24. If the mean wavelength of the visible light is about 5000 Angstroms

(1Angstrom = 10- 10

meters) and the velocity of light in air 300000 Km/sec

Calculate the mean frequency of the visible light (6 x 1014

Hz)

25. A toning fork of frequency 256 Hz, calculate the wavelength of the sound

waves produce when the fork vibrates. Knowing that the velocity of sound in air

340 m/sec (1.328m)

26. If the time passed between the passage of the trough of the first wave and the

crest of the seventh wave with a certain point along the paths of a transverse

wave is 0.11 sec. calculate the frequency of the wave (50 Hz)

27. If the velocity of sound in air is 340 in/sec and two different waves of

Frequencies 660,220 Hertz propagate in air. Calculate the ratio between their

wavelengths and also the ratio between their periodic times

1

3,

3

1

28. The figure shows two wave

motions (A & B) Find for each of

them:

a) The wavelength.

b) Periodic time.

c) Frequency.

d) Velocity of propagation

e) The distances cd & ef and what

do they mean?

f) The amplitude.

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Unit ONE

Chapter Two I- What is meant by?

1- Echo.

2- The velocity of sound in air 340m/s.

3- The wavelength of standing waves = 50cm.

4- Interference.

5- Destructive interference.

6- Fundamental tone.

7- The wavelength of a sound wave = 0.6 meter.

8- The distance between the 1st node end the 3

rd antinode of a stationary

wave = 18 cm.

9- The distance between two successive antinodes for standing wave = 10

cm.

10- The distance between successive node and antinode of a standing wave

=10 cm.

11- The node in the standing waves,

12- The wavelength of a standing wave in a stretched string = 10 cm.

13- The third harmonic frequency of a string is 600 Hz.

14- The frequency of the 2nd

harmonic tone of a vibrating string = 450 Hz.

II- Give Reason:

1- Formation of Echo.

2- Sound waves are mechanical waves while light waves are

electromagnetic waves.

3- Sound waves are longitudinal waves while the vibrating string produces

a transverse waves.

4- Sound refracts when transmitted from one medium to another of

different density.

5- Sound refracts towards the normal when passes from air to CO2

6- Astronauts use wireless instruments for their communication on moon‟s

surface.

7- The sound in air cannot be hared by a person in water.

8- You can hear a person speaking in another room.

9- The transverse wave propagates through the stretched string in the form of a standing wave.

10- The velocity of propagation of transverse waves along a stretched wire increases with increasing its tension.

11- The pitch of the sound produced by a stretched string with the increase of its tension also with the thin string.

5

1,, vvv

12- The frequency of the third harmonic tone of a vibrating string is 1.5 times that of its second harmonic

13- The frequency of the forth harmonic tone of a vibrating string is 3

11

times that of its third harmonic. 14- A person swimming under the surface of water can't hear clearly the

sound in air. 15- Sound refracts when traveling between two different media. 16- When the sound transfers from the air to the water the angle of

refraction > the angle of incidence, 17- The vibration of string is transverse vibration 18- The fundamental frequency of vibrating string is the lowest frequency

produced. 19- As the thickness of the stretched string (of constant tension) decreases

the pitch of the tone increases,

III- A vibrating string emits a tone related to the relation:

(a) What tone this string emits.

(b) Find the wavelength of the propagated wave.

(c) If the tension is increased 4 times its value and the length of the string is

decreased to the half.

Find the frequency of the emitted tone.

IV- What happen to the frequency of a string when its length is reduced to half

and its tension force is reduced to the quarter?

V- Compare between constructive and destructive interference.

VI- Deduce the law used to calculate the frequency of standing wave in a

stretched string, what are the factors affecting the fundamental frequency.

VII- Write down the relation between the frequencies of the fundamental tone

and their harmonics in a String.

VIII- Choose The Correct Answer:

(1) If the distance between two successive points having the same phase and

direction equals 50 cm, then the wavelength for such wave equals.(25 cm, 50 cm,

100 cm)

(2) The relation between the frequency, wavelength and the propagation velocity of

the wave is:

(3) When the velocity of sound in air is 328 m/s and the distance between the

mountain and the source of sound is 164 m, the echo is heard after (½, 1,2) seconds.

(4) You are listening to sound of a certain frequency. Which one of the following

statements about the sound wave that is traveling through the air is correct if the

frequency of the sound is increased? (The wavelength of the sound wave increases -

The wavelength of the sound wave remains the same - The wavelength of the sound

m

F

L

T

2

3

6

wave decreases. - The speed of the sound wave increases. “The speed of the sound

wave decreases)

(5) The. Standing waves are produced due to the superposition of two wave motion

having: (The same frequency, amplitude and propagate in the opposite direction -

The same amplitude and propagate in the same direction. - The same frequency,

amplitude, and propagate in the same direction. - The same amplitude and

propagate in opposite direction.)

(6) In standing waves the distance between successive node and antinode equal

(1/2--1/4)

(7) When a string of length (L) vibrates and is divided into (n) segments, then the

wave length of its tone () equals......

(8) If v is the speed of the wave propagation through a vibrating string of length L,

the slope of the line representing the relation between the frequency υ of the

fundamental tone (vertical axis)and 1/L (horizontal axis) is (4v -2v - v - v/2). If you

double the length of this string and you increase by 4 times its tension, the

frequency of the fundamental tone becomes (half - the same -- double -

undetermined) with respect to that of the initial one. If the string vibrates such as 4

segments are Produced; we obtain (4 nodes - 5 antinodes - = L/2 - the 4th

harmonic tone).

(9) When a string of length 150 cm vibrates producing 3 segments (loops), the

wavelength is (150 -100 - 50) cm.

(10) The third harmonic of a vibrating string is produced when it vibrates in the

form of (three-four- five) segments

(11) Consider waves traveling along a tightrope. If the tension in the rope is

increased by a factor of 9, how does the speed of the waves change? (The speed

remains the same-The speed is reduced by a factor of 3-The speed is reduced by a

factor of 9 - The speed is increased by a factor of 3-The speed is increased by a

factor of 9)

(12) The string emits its third harmonic when it vibrates in the form of...........

(Three segments -four segments - five segments).

(13) Increasing the length of a vibrating string will: (decrease its resonance

frequency - decrease its amplitude - increase its amplitude - increase its resonance

frequency)

(14) When the string is vibrating to produce the forth harmonic tone, then the

number of standing waves is (2 waves, 4 waves, 3 waves, 5 waves). IX- What happens in each of the following cases, explaining why?

(1) A sound wave of frequency 1600 Hz and speed 336 m/s is incident on an

opening of dimension 0.3 m.

(2) A sound wave having a speed of 336 m/s and a frequency of 800 Hz is incident

on an opening of diameter 0.75 meter,

(4) Increasing the tension on a stretched string to 4 times its value (with respect to

the velocity of propagation of the transverse waves through it).

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Problems 1- The frequency of the fundamental tone of a string is 150/L. Find:

a- The velocity of the transverse wave in the string if its length 50cm and its

mass 5Kg. (300m/s)

b- The frequency of the fundamental tone. (300Hz)

c- The velocity of sound in air. (300m/s)

d- The tension force. (900000N)

2- The length of a string one meter and its mass 40gm, stretched with a force

equals 196N. Calculate the frequency of the fundamental tone, then deduce

how to increase the value of frequency to 70Hz through:

a- Change the length only.

b- Change the tension only.

3- The following table shows the relation between the inverse of the length of a

uniform string and the frequency of the fundamental tone when it vibrates. The

tension is kept constant.

Reciprocal of the length (1/L) 1 X 2 3 4 5 6

The fundament frequency ( ) Hz 150 210 300 450 600 Y 900

Draw a graphical relation between the Reciprocal of the length on the x-axis and

the fundament frequency on the y-axis from the graph find:

a- The frequency (Y). (750Hz)

b- The length of the string that emits its fundamental tone with frequency

(210Hz). (0.714m)

c- The velocity of the transverse wave propagating in the string.

d- If the mass per unit length of the string wire is 0.01Kg/m, find the tension

acting on the string.

4- The following table illustrates the relation between the lengths of a uniform

string producing its fundamental tone

Length (m) 0.1 0.2 0.25 0.4 0.5 0.6 0.8 Y

Frequency of fundamental tone (Hz) 500 250 200 125 100 X 62.5 50

Represent the relation (1/L) on the x-axis and frequency on the y-axis, and then

find: 1-The velocity of the propagation of the transverse wave in the string.

2-The value of (X) and (Y). 6-A string of length 1 meter and the mass per unit length of its wire is 0.001 Kg/m

stretched by a tension of 90 Newton. Find a- The frequency of the fundamental tone produced [150 Hz]. b- The velocity of the wave through the string. [300 m/s]. c- The frequency of the fourth harmonic tone [600 Hz].

7. Standing at the edge of a lake you shout and listen as the echo returns from a large cliff at the other side of the lake 4.2 seconds later. How wide is the lake? Use the speed, of sound in air as 340 m/s 8. A ship is moving towards a mountain along a beach at a uniform velocity. When it becomes at a distance 1 Km from the mountain, the echo of its whistle is heard after 5

8

sec. If the velocity of sound in air = 340 m/s, calculate the velocity of the ship. (60 m /sec.) 9. Vibration of strings gives the fundamental according to the relation: υ = 200/L. Calculate:

a) The speed of waves in the string, b) If the length of the string = 80 cm and its mass = 4 gm find the tension of the string (400 m/s, 800 N)

10. A string of mass 2 gm and length 1m is fixed at one end and attached at the other end to an oscillator of variable frequency. The string is under a tension of 5 1 N. Find the three lowest oscillator frequencies for which standing waves will be formed. (80,160,240 Hz) 11. A string is stretched by a force of 30 kg weight. If the length of the string is 50 cm, the mass of each cm is 0.0006 gm., calculate the frequency of the second harmonic emitted by the string, knowing that acceleration due to Earth's gravity =9.8 m/s

2. (6640.8 Hz)

12. A metallic weight is used to stretch a vibrating string that emits a fundamental tone of frequency 320 Hz. If this weight is immersed in water, what is the new frequency of the string? (ρ metal = 25000/9 kg/m

3 and ρ water = 1000 kg/m

3) (256 Hz)

13. In Meld's experiment the length of the thread is 2.5 meter, if the wave length is 0.5 meter, how many nodes and antinodes are formed 14. In Meld's experiment a tuning fork of frequency 280 Hz is used, standing waves are formed in string of length 2 m, if the mass per unit length is 0.0015 kg/m, find the number of nodes in the string when a mass of 3 kg is fixed at the end of the string. 15. If the tension force acting on a string stretched on a son meter is changed from 6.4 kg.wt,

to 8.1 kg.wt knowing that it produces its fundamental tone in each case, find the ratio between the two frequencies keeping its length constant. (8: 9)

16. An elastic string of length 2 m. produces its fundamental tone of frequency 400 c/s knowing that the wave length of the resulting wave is 80 cm. Find

1- The velocity of sound in air. 2- The velocity of the transverse wave in the string. (320 m/s, 1600m/s)

17. Two strings A & B are from the same material and are equal in length, knowing that

the diameter of (A) is half that of (B) and is stretched by a tension force 20 kg.wt.

Calculate the tension force of (B) to produce the same fundamental tone of (A).

(80 kg.wt)

18. The speed of a wave on a string is 160 m/s when the tension force in the string is 100 N. to

increase the speed to 200 m/s. to what value the tension must be increased (156.25 N).

19. The lengths of the two wires A & B of the same material are in the ratio of 2 :1 and their

diameters are as 1: 2 if the tension in (A) is 5 kg.wt. What must be the tension of (B) to emit

the same tone of A. (5 kg.wt.)

9

LIGHTAS A WAVE MOTION

(1) Give Reasons:

1. The absolute refractive index of a medium is always greater than one.

2. As the light ray passes through a narrow double slit, there are interference

fringes (bright and dark) on a white screen placed at a suitable distance.

3. In Young's double slit experiment the interference fringes become clearer as

the distance between the 2 slits decrease.

4. The optical fibers may be used in the transport of light.

5. The reflecting prism is preferred to metallic mirror in some optical

equipment.

6. The faces of the reflecting prism are covered with a thin layer of cryolite.

7. When white light is dispersed by a prism the red colour has the minimum

deviation while the violet light has maximum deviation.

8. When white light falls on a triangular prism, adjusted at the minimum

deviation position, the emerged ray is deviated into different colored rays

known as spectrum.

(2) What Is Meant by Each Of The Following?

1. The absolute refractive index of a medium 1.4

2. The refractive index of light between glass and water is 0.6.

3. The critical angle between water and air = 45°.

4. The critical angle of glass with respect to air = 42°.

5. The critical angle between diamond and air = 24.6°.

6. The minimum angle of deviation of a triangular prism is 3°.

7. The angle of deviation in triangular prism 30°

8. Angular dispersion in thin prism = 0.6.

9. Chromatic dispersive power of a thin prim 0.03.

3) Essay questions 1) Explain why light is considered to be a wave motion.

2) Describe an experiment to demonstrate the interference of light.

3) Explain how mirage is formed.

4) Define a) The relative refractive index between two media.

b) The absolute refractive index for a medium.

c) The critical angle.

d) The angle of deviation.

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5) Mention one use (The Function) for each of the following: (a) Double slit in Young' experiment,

(b) Optical fibers,

(c) The totally reflecting prism,

(d) Cryolite layer in the reflecting prism

6) Explain the scientific base (idea) (the operation principle) on which the function of

the following depends:

(a) Young's experiment (b) The optical fibers

7) EXPLAIN With drawing what happens to light ray incident on a right angles

prism with the two sides of the right angle equal, in the following cases (the critical

angle between the prism and air = 42o).

(i) The angle of incidence of the light ray on one of the sides of the right angle equals

zero.

(ii) The incident ray normal to the side corresponding to the right angle follows the

ray until it emerges from the prism.

8) Define each of the following: (i) The coherent sources in light,

(ii) The chromatic depressive power of a prism, find the relation which can be used to

calculate it

9) Mention the factors on which the following depends:

(i) The angle of deviation in thin prism.

(ii) The distance between any two successive similar fringes in Young's experiment.

(Mention One Factor)

10) Compare between refraction & diffraction regarding the indicated points of view:

conditions - change of speed.

11) Explain what happens in each of the following cases and why?

(i) Increasing the distance between the two narrow slits in Young's experiment.

(ii) The decreasing of the distance between the two slits in Young‟s double slit

experiment.

(iii) We use a plane mirror instead of a reflecting prism.

12) You have an equilateral glass triangular prism. Explain with drawing an

experiment to trace the path of a ray through the prism. Indicate on the drawing the

angle of the prism, the angle of incidence, the angle of emergence and the angle of

deviation of the ray. Write down one relation between these angles.

13) Deduce for a thin prism the relation between the angle of deviation (α), its angle

(A) and the refractive index (n) of its material.

14) Complete

a) The distance between two successive bright fringes is given by

……………..

b) Snell's law states that:……………. c) The angle of deviation in a thin prism is given from relation :……………..

d) The dispersive power is: ………………..

11

15) Choose the right answer 1) When light reflects

a) The angle of incidence is less than the angle of reflection.

b) The angle of incidence is greater than the angle of reflection.

c) The angle of incidence is equal to the angle of reflection.

d) There is no right answer above.

2) When light refracts, the ratio

sin

sin where the angle of incidence and Ө is the

angel of refraction is:

a) Constant for the two media.

b) Variable for the two media.

c) Constant, greater than one.

d) Constant, less than one.

3) The ratio between the sine of the angle of incidence in the first medium to the sine

of the (angle of refraction in the second medium is known as :

a) The absolute refractive index for the first medium.

b) The absolute refractive index for the second medium.

c) The relative refractive index from the second medium to the first medium.

d) The relative refractive index from the first medium to the second medium.

4) An incident ray at an angle 48.5° on one of the faces of a glass rectangular block (n

=1.5), the angle of refraction is :

a)20° b)30° c) 35° d) 40

5) In an experiment it was found that the minimum angle of deviation is 48.2° Given

that the angle of the prism is 58.8°, the refractive index of the material of the prism is:

a) 1.5 b) 1.63 c) 1.85 d) 1/1.85

6) A thin prism has an angle of 5°. Its refractive index is 1.6. It produces a minimum

angle of deviation equal to:

a) 5° b) 6° c) 8° d) 3°

7) A ray of light falls on a thin prism at an angle of deviation 4° and its apex angle 8°

refractive index is : a) 1.5 b) 1.4 c) 1.33 d) 1.6

PROBLEMS 1. What is length of green light wave in the water, given that its wave length in

vacuum equals 5600A° and refractive index of water 4/3. (4200)

2. If the speed of light in the air 3 x 108 m/sec and in the glass 2 x 10

8 m/sec.

Calculate the refractive index (absolute) in the glass. (3/2)

3. The absolute refractive index of glass= 1.5 and that of water = 1.32 if the

velocity of light in air = 3 x 108

m/s, calculate:

a- The relative refractive index from water to glass.

b- Sine the critical angle from glass-to air.

c- The velocity of propagation of light in glass.

12

4. A ray of light passes from a solid with refractive index I.5 to water with

refractive, index 1.3 the angle of incidence of the ray is 35°. What is the angle

of refraction?

5. If the refractive index of water 4/3 and of alcohol 3/2. Calculate the relative

refractive index from the water to the alcohol. (9/8)

6. An incident light ray falls on a surface of glass rectangular block its refractive

index 1.5 by an incident angle equal 60°, Calculate the refractive angle.

(35.2°)

7. An incident ray falls on the surface of water by an incident angle 60°, a part of

the incident ray is reflected and other part is refracted and the reflecting and

refracting rays are perpendicular to each other. Calculate the refractive index in

water. (1.73)

8. An incident ray (in the air)) falls on face of a glass rectangular block, its

refractive index 2 it is emerged with an angle 45. Calculate the angle of

incidence and the angle of refraction. (30°, 45°)

9. A glass rectangular block is placed on the reflecting surface of a plane mirror

and the absolute refractive index of glass equals 3 if an incident ray falls on

the face of the block with an angle =30° and refracts then reflects then emerged

from a point at a distance 2 cm from the incidence point, determine the

thickness of the rectangle block.

10. If the absolute refractive index of benzene equals 2. Calculate the critical angle

between benzene and air. (45)

11. An electric torch is immersed in a liquid its absolute refractive index 5/3 at a

depth equals (8) cm. Calculate the radius of the smallest disc can prevent the

light of this torch to emerge in air. (6 cm)

12. A swimming pool filled with water to its edge, the depth of water is (2) meter

an electric bulb is placed at a distance equals (8) meters from the edge of the

pool over a column its height (6) meter. Calculate the length of non-apparent

part from the pool bottom which the light doesn‟t reach to it, given that the

refractive index of water is 4/3. (1.5 m)

13. In double slit experiment (young) the distance between the midpoint of the two

holes equals 10-4

meter, and the distance between the slit and the screen (which

receives the fringes) is (80)cm. Calculate the distance between two successive

fringes, given that the wave length of falling light is 5000 A°. (4 mm)

14. In double slit experiment (young) the distance between two successive fringes

is 2 mm. and the distance between the two rectangular slits 0.0006 m., the

distance between the screen (which receives fringes) and the slits 2 meters.

Calculate the wave length of falling light. (6000 AO)

15. In Young's double slit experiment using monochromatic light if the

distance separating the two slits is 1 mm, the distance between the double

slits and the screen is 1 m, and the distance between two successive

illuminated fringes is 0.5 mm. Calculate the wavelength of the light used.

13

16. In double slit experiment the separating distance between the two slit was

0.2 mm, and the distance between the slits and screen on which the

fringes are formed was 120 cm. If the distance between two successive

illuminated fringes is 3 mm, calculate the wavelength of the used

monochromatic light in Angstrom (1 Angstrom = 10-10

meter)

17. In Young's double-slit experiment, the space between the interference

fringe, when using the yellow light is 0.275 mm, where the wavelength of

the yellow light is 500 nanometer when a crimson light is used of wavelength

400 nanometer in violet case and 600 nanometer in red case, another

interference fringes are produced.

a) The distance between the interference fringes of violet light.

b) The distance between the interference fringes of red light.

18. A green light falls on the double slit, its wave length is 5500 A°, the distance

between the slit and the screen is 20 cm, and the distance between the lighted

flings and dark fringes is 0.0024 cm. Calculate the distance between two slits.

(2.3 mm.)

19. A glass triangular prism, its refractive angle 60°, a light ray falls on one of its

sides with an angle 45°, if the refractive index of the prism is 2 calculate the...

a- Emergent angle.

b- Angle of deviation. (45°. 30°) 20. A light ray falls perpendicularly on one side of a triangular prism; its angle is

30° and its refractive index 1.5 Calculate the angle of emergence from the other side. (48.6°)

21. A ray of light falls on one side of a triangular prism, its angle is (40°) and its refractive index is 1.3, the ray emerged perpendicularly on the other side. Determine the angle of incidence. (56.6°)

22. A ray of light falls perpendicularly on one side of a glass triangular prism it

emerged as a tangent on the other side, if the refractive angle of the prism 45°. Calculate the speed of light in the glass. (2.1x10

8 m/sec.)

23. A light ray falls perpendicularly on one side of a triangular prism; it emerged as a tangent on the other side. If the refractive Index of this prism is 2. Determine the refractive angle of this prism. (45°)

24. An equilateral triangular prism its refractive index is 1.6. Determine. a- The smallest angle of min. deviation of a light ray which can pass through this prism. b-The smallest angle of deviation when the prism is immersed in alcohol (its refractive index 1.2) (46.26, 23.6)

25. A triangular prism its angle is 75° and its refractive index 2 Determine The smallest incident angle of light ray on one of its sides so that it allows the ray to pass from the other side. (45°)

14

26. A glass triangular prism its refractive index (1.5), it is immersed in benzene it

refractive index (1.2), if the refractive angle of this prism is , (6O°).Determine the angle of minimum deviation, then Calculate the incident and refracted and emergent angles in this case. (17.36, 38.68, 30)

27. Thin prism refracts the rays by an angle of (4) degrees and its main angle equals 8. Determine its refractive index (1.5)

28. A thin prism its angle is 8. Determine the angular size between the red and violet colors, given that the refractive index of the prism to the violet color is 1.7 and to the red color is 1. 5. (1.6°)

29. A light ray falls on one face of a triangular prism with an angle equals (30°) with the surface, it is emerged perpendicular on the other face, and if the refractive index of the prism 3 determine its angle (A). (30°)

30. 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 its angle of emergence from the prism [ = 48.6]

31. A ray of light falls in air on one face of a triangular gas prism whose angel is 72

o. It is refracted by an angle 30

o and emerges tangentially to the other face

find: a- The critical angle between glass and air. b- The refractive index of the prism material. c- The sine of the first angle of incidence.

32. Consider light that passes from air, with n = 1, into water, with n = 1.33). If the angle; of incidence in air is 30°, what is the angle of refraction in water

33. Alight ray falls one side of an equilateral triangular prism its refractive index is 1.5 Find the smallest incident angel which allows the light ray to emerge from the other side (without showing total reflection).

34. A ray of' light falls in air on one face of a triangular glass prism whose angle is 72°. It is refracted by an angle 30° and emerges tangentially to the other Find:

a) The critical angle between glass and air. b) The refractive index of the prism material. c) The sine of the first angle of incidence.

35. A thin prism has an angle of 4°. Its refractive index is 1.5 find the angel of deviation of light passing through it.

36. The graph in front of you represents the relationship between the incidence angles () and the deviation angles (α) of l ight ray falling on one face of a triangular prism. Using the values shown in tile figure Calculate:

a) The emergence angle of the ray. b) The refractive angle of the prism. c) The refractive index of the prism

37. If the critical angle between gasoline and air is 41.8°, and between glass and air is 37.3 °, Find:

15

(1) The absolute refractive index of gasoline. (2) The relative refractive index between glass and gasoline (3) The critical angle between glass and gasoline

38-The following table illustrates the relation between sine the angle of incidence

of light ray in air (sin Φ) and sine the angle of refraction in glass (sin θ).

Sin Φ 0 0.15 0.3 A 0.6 0.75 0.9

Sin θ 0 0.1 0.2 0.3 0.4 0.5 B

Draw a graph relation (sin Φ) on the Y-axis (sin θ) on the X-axis then, find:

a- The value of (A) and (B). (0.45, 0.6)

b- The refractive index of the glass. (1.5)

40-In young‟s double slit experiment, the frequency of the used light is 6x1014

Hz,

the distance between the two slits is 0.0002meter and the distance between the

double slit screen and the 3rd

screen is 1 meter. Calculate the distance between two

successive illuminated fringes, knowing that the speed of light in air = 3x108m/s.

Why the central fringe is illuminated?

39.

16

41-The following table gives the values of (sin Φ) and the corresponding (sin θ). Where Φ represents the angle of incidence of light in air and θ represents the angle of refraction of light in medium.

Sin Φ 0 0.35 0.50 0.65 0.77 0.87 0.95 0.99

Sin θ X 0.23 0.33 0.43 0.51 0.58 0.63 Y

Plot a graphical relation between (sin Φ) on the ordinate and the corresponding (sin

θ) on the abscissa. From the graph, find:

a- The value of each (X) and (Y).

b- The absolute refractive index of considered medium.

c- The sin of the critical angle for the considered medium.

(X=0, Y = 0.66 n = 1.5, ΦC = 0.667)

42. The refractive indices of a thin prism for red and blue lights are 1.44 and 1.56

respectively. If the angle of the prism in 6°, Find:

(1) The mean deviation of the prism.

(2) The angular size between red and blue lights.

(3) The dispersive power of the prism. 43. The given figure shows a triangular prism of refractive index 1.6 placed inside a basin made of thin glass filled with water of refractive index 1.3 a light ray is incident as sown in figure. Follow the light ray until it emerges from the basin to air. Then find. n =1.6 (1) The angle of emergence from the prism. (2) The angle of emergence from air.

17

Revision Question

1) Choose:

Each of this fig. represents the change of density of solid to change in temperature.

2) If the iron density 7.9 gm/cm3 so it can be written as:

(a) 7.9 Kg/rn3 (b) 79 Kg/rn3 (c) 790 Kg/rn3 (d) 7900 Kg/rn3

3) To calculate the atmospheric pressure in N/rn2 by measuring the mercury height of

barometer we need to know.

(a) The cross section area of tube of barometer.

(b) The depth of Hg. in the trough where the tube of the barometer inverted.

(C) Kind of material of the tube.

(d) Mercury density

4) U shaped tube contain water, is used as manometer to measure the gas pressure

enclosed in several c1inders each alone

1. When we connect (A) to one side as shown, the height

differences of water is 30 cm and when connects the cylinder (B)

by the same way to the manometer, the height difference (22

cm)

First: When cylinder (A) connect to one side and the cylinder (B) to

the other side at the same time the height difference of water in cm

(a) 52 (b) 8 (c) 38 (d) 30

Second: How the height (h) difference affected when we use a U shaped

tube of wider sides.

(a) Does not change (b) increase (c) decrease

Third: If we increase the amount of water in the two sides so the height difference

(Ah) in the two sides.

(a) Increase (b) decrease (c) still fixed

18

Fourth: If Hg is used (density 13.6 gm/cm

3) instead of water (ρ l gm/cm

3) so the

height difference of the liquid in the two sides in cm.

(a) 13.6 (b) 1 (c) 0.1 (d) 0.588

5) Which of the fig is correct (for two weights) in order that balance occurs in the

same level?

6) Metallic sphere hung by thread in spring „balances as shown out of displaced

beaker has its opening above small beaker placed on balance‟s,

(a) The decrease in spring balance‟s” reading more than the increase in reading of

balance (c).

(b) The decrease in spring balance (s) less than the increase of balance

reading (c).

(c) The decrease in spring balance (s) equal to the increase of

the balance(c).

(d) No change in the reading of the two balances.

When the ball sinks (placed on its bottom). So: -

(a) decrease in (s) reading and increase in (c) reading. (b)

Increase in(s) reading and increase in (c) reading. (c) zero

reading for (s) and no change in (c) reading.

(d) No change in (s) no change in (c).

7) Body (B) of mass 200 Kg tied by thread in the bottom of a lake as shown the

tension is 500 N when the mass of the displaced water in (kg) equal.

(a) 200 (B) 500 (c) 250 (d) 150 Where (g = 10 m/s2)

If the water of the lake is salty water so the tension in that chain

(a) Increase

(b)Decrease

(c) still constant

8) The measurement of sedimentation rate is application of

(a) surface tension (b) Archimedes principle (c) viscosity (d) adhesive faces.

19

(9) Draw graph of the total pressure at a point inside a liquid (P) and the depth (h) if

liquid in deep container, from the graph. Show how to find the density of that liquid.

(10) What meant by:-

(1) The specific weight of substance =15

(2) The mechanical advantage of hydraulic press 5

(3) The up thrust force of a body suspended in a liquid is 50N

(11) Complete

)1 (The tension in thread (1(=.........

)2 (The tension in thread (2)=…….

)3 The unit of pressure ------, its D.F is ------ but viscosity unit is ------, its D.F is ---

--- "D.F means dimensional formula"

)4 (When equal volumes of different metals immersed in the same liquid so ------

equals due to the equality of -------- . .

(5(The body suspends in a liquid when ………………..

(6) When the blood corpuscles are divided, the sedimentation……….. rate than the

natural rate

(12) Give reason for

(1) The apparent weight of suspended a body in liquid equal to zero.

(2) The sedimentation rate can be considered as a test of some diseases.

(13) Compare between the velocities of a liquid at two points the radius of 1st tube 3

times the radius of the other.

(14)Wooden parallelogram of dimension 10, 20, 16 cm.

placed on a table as shown in the fig ρ wood 800 kg/m3.

Find the pressure on the surface of the table. If the piece

placed on the table (g = 10 m/s2). and when this wooden

block is floating on water surface by its largest area.

1. Find the pressure of water by the lower surface of wood.

2. Find the pressure on the lower surface of wooden piece exerts by water.

3. Find the height of immersed part (DJ) of the parallelogram.

4. The mm. mass placed on the wooden piece needed to be completely immersed

in water. (0.64 Kg, 8 Cm,

800N/m2)

(15) What is meant by:-

• The coefficient of viscosity 2 N.S/m2.

• Volume (flow rate) 20 liter/sec.

20

(16) Give reason for: -

1. To decrease the fuel consumption the velocity does not exceed specific value.

2. It is possible for nose bleeding at high altitudes.

3. Pascal principle does not apply on gases or solids.

(17) Calculate the mass ratio of gold and silver in alloy. If its mass 4.335 kg, in air and

the mass in water is 4.0265kg relative density of gold = 19.2, Silver= 10.5.

(18) Put (√) or (x) for each of the following.

1. The up thrust force increase on a body due to the increase of its weight.

2. Using a Barometer tube of large diameter decrease the height of mercury.

3. A piece of ice float on water in beaker when it melt the height of water increase.

4. The force on the bottom of container filled with water may be more or less than the

weight of water inside it.

5. Pressure 600 Torr more than I bar.

6. In the hydraulic press the pressure increases due to increase of its area of cross

section.

(Ans. x. x. x.√. x. x.)

(19) Mention:

Pascal‟s principle. Discuss one of its applications. By drawing

(20) Prove that the pressure at the bottom of a liquid increases by increasing the depth.

(21) A U shaped tube the cross-section area of one branch I cm2 and the other 0.1 cm

2

containing mercury. Calculate the mass of water that must be added to wide branch in

order to raise mercury in the narrow branch by 1cm. (14.96 gm)

(22) State when it is true:

1. The apparent weight of a body = 0 and when it is negative.

2. The length of mercury column in a barometric tube does not represent the

atmospheric pressure.

3. In the Hydraulic press A

F

a

f

(23) In the fig We have two pistons connected together with a lever has

the ratio of its arms 2 : 1 So if 50

1

40

1

1

1

2

2 A

aand

A

a

Calculate F2, and Calculate the mechanical advantage knowing that f1= 20N

(20000N.1000)

21

Problems

1- A mercury manometer is used to measure the pressure of a gas inside a container.

The surface of the mercury inside the free side of the manometer is lower than that

in the other side attached to the container by 20 cm. What is the value of the

pressure in "bar" units of the gas enclosed in the container, given that the

atmospheric pressure when performing such measurements was 105 Pascal, density

of mercury = 13600 kg m-3

and g = 10 m/s2

2- A layer of water of thickness 50 cm rests on a layer of mercury of thickness 20

cm. what is the difference in pressure at two points, one at the interface between

water and mercury and the other at the bottom of the mercury layer. (the density of

water = 1000 kg/m3, the density of mercury = 13600 kg/m

3, the acceleration of

gravity = 10m/s2)

3- (Egypt 95) the following table illustrates the relation between the pressure (P) at a

point inside the water of a lake and the depth (h) of this point below the water

surface.

h (m) 4 8 12 16 20

P (bar) 1.4 1.8 x 2.6 3

Plot a graph relating (P) on the ordinate and (h) on the abscissa. From the graph

find:

a. The pressure (x) at depth 12 m.

b. The value of the atmospheric pressure above the water surface of the lake in

N/m2.

c. The density of water of the lake.

4- (Egypt 95) The diameters of the small and the large piston of a hydraulic press

are 2 cm and 24 cm respectively. if a force of 200 N acts on the small piston

(knowing that the acceleration due to gravity = 10 m/s2). Calculate:

1- The maximum mass that can be lifted by the large piston.

2- The mechanical advantage of the press.

3- The pressure of both large and small pistons.

5- Find the total pressure and the total force acting on the base of a vessel

containing salty water of density 1030 Kg / m3, if the surface area of the vessel is

1000 Cm2, the height of water in it is one meter, the surface of water is exposed to

atm. Air, the acceleration due to gravity is 9.8 m/s2 and the atm. Pressure is 1.013 x

105 N / m

2.

22

6- (Egypt 90) A submarine is located horizontally in seawater. The interior of the

submarine is maintained at sea level atmospheric pressure. Find the force acting on

one of the submarine‟s windows of circular shape of radius 21 cm and whose

center is at depth of 50 m from the sea level.

7- (Egypt 90) a submarine is located horizontally at a depth 50 m. from sea level. the

pressure inside the submarine is kept at atmospheric pressure 1.013x105 N/m

2

calculate:

a. The force acting on the submarine‟s window of circular shape of radius 21 cm

if w = 1030 kg/m3.

b. The force acting on one side of the submarine‟s tail fin which has rectangular

shape of length 3 m, and width 1 m at the same depth.

c. Total force acting on the two sides of the tail fin.

8- A submarine sinks to a depth of 40 m. What is the total force acting on the door

of its cabin whose diameter is 80 Cm, if the pressure inside the submarine is kept at

atm. Pressure ( water = 1030 Kg / m3)

9- U - Shaped tube, the height of the water in one branch is 19 Cm above the

separating surface between water and oil. Find the height of the oil in the second

branch that balance with water column if the density of water 1000Kg / m3 and that

for oil = 800 Kg / m3.

10- The difference in the water pressure at the ground floor is 3.4 atm. Pressure.

What is the max. height water can reach in the building.

11- A water layer of a thickness of 1 m floats over a mercury layer of thickness

0.2 m. What is the difference in pressure between 2 points; one at the surface of

the water and the second at the bottom of the mercury layer ( water = 1000 Kg /

m3

, mercury = 13600 Kg / m3).

12- Barometer records 75 Cm Hg at the base of a mountain and 60 Cm Hg at its top.

Calculate the height of the mountain knowing that the average density of air is

1.25 Kg / m3 and Hg = 13.6 x 10

3 Kg/m

3.

13- A man carries a mercuric barometer whose reading at the ground floor is 76

Cm Hg, and at upper floor is 74.15 Cm Hg. If the height of the building is 200 m,

find the average density of the air between these 2 points. ( Hg = 13.6 x 103

kg/m3, acceleration due to gravity 9.8 m/s

2).

14- A mercury manometer is used to measure the pressure of a gas in a reservoir. The

level of the Hg in the free branch is higher than that in the second branch by 36

Cm. Find the pressure of the enclosed gas in units:

a. Cm Hg

b. atm. Pressure

23

c. N/m

2 knowing that 1 atm. Pressure equals 1.013 x 10

5 N/m

2.

15- The small and large pistons in a hydraulic press have the diameter of 2 Cm, 24

Cm respectively. When a force 200 N is acted on its small piston. Find:

a. The maximum mass that can be lifted by the large piston.

b. The mechanical advantage of the press

c. The pressure of the small and large pistons

16- The areas of the small and large pistons in a hydraulic press are 2 Cm2 and

50 cm2 respectively. Find the mechanical advantage of the press, then calculate the

force required to lift one ton. Find the distance moved by the small piston in order

to move the large one by 2 Cm.

17- The cross sectional area of the small and large pistons in a hydraulic press are

4x10–2

m2 and 1200 cm

2 respectively. If the force acting on the small piston is

200 N and the free fall acceleration is 10 m/s2. Find:

a. The maximum mass that can be lifted by the large piston.

b. The mechanical advantage of the press.

18- A bargain hunter purchases a "gold" crown at a flea market. After she gets home,

she hangs the crown from a scale and finds its weight to be 7.84 N. She then

weighs the crown while it is immersed in water, and the scale reads 6.86 N. Is

the crown made of pure gold? Explain.

19- A piece of metal weigh 50 N in air, 36 N in water, and 41 N in an unknown liquid.

Find the densities of the following:

a. the metal

b. the unknown liquid

20. A metallic cylinder has an area of 60 cm2and height of 90 cm the density of its

material is 7900 kg/m3.Find the pressure when its area is placed on the ground. Then

find the pressing force.

21. Find the average pressure by which the ground reacts on the foot of a ballerina of

mass 50 kg, when she stands on her through a touching area of 10 cm2

22. How high would water rise in the pipes of a building if the water pressure gauge

shows the pressure at the ground floor to be 2 x 105 Pa?( g = 9.8 m/s

2)

23. Calculate the depth of a lake, if the pressure at its bottom is 4 atm. The density of

its water is 1000 kg/m3and the Pa = 1.013 x 10

5 N/m

2)

24. A vessel is filled with 100 cm in height of water and 50 cm in height of oil above

the first layer. If the density of oil is 800 kg/m3

calculate the pressure exerted from the

two liquids on the bottom, then find the total pressure given that the atmosphere

24

pressure equals to 1.0130 x 10

5 Pascal. ( ρ Water =

1000 Kg / m3 )

25 Solid parallelogram of dimensions 10 cm x 20 cm x 40 cm and density of 2700

kg/m3 is placed on flat surface. Calculate its maximum and minimum Pressures.

(Consider the acceleration due to gravity 9.8 m/ s2).

26. Calculate the pressure acting on a body of submarine, at depth 50 in under the

surface of water which has density 1030 Kg/m3.

27. A submarine lies 10 m below the sea surface, given that the density of sea water is

1030 kg/m3 and the atmospheric pressure 1.013 x 10

5 N/m

2 Calculate

a- The pressing force acting on a circular window of radius 30 cm.

b- The pressing force acting on a rectangle side on one side of the tail fin of

dimensions 2m x 3m.

c- The total force on both sides of the tail fin.

28. A layer of water of thickness 50 cm rests on a layer of mercury of thickness 20 cm.

What is the difference in pressure at two points, one at the interface between water and

mercury and the other at the bottom of the mercury layer? (The density of water 1000

kg/m3, the density of mercury 13600 kg/m

3, the acceleration of gravity g = 10 m/ s

2).

29.If the pressure difference needed for a car tyre is 3 x 105 N/m

2 find the absolute

pressure in the tyre if Pa = I x105 N/m

2)

30. Find the work done to pump 15 m3 of water through a pipe when the difference in

pressure is 2.8 x 105N/m

2.

31. The water pressure acting on water tap at second floor is 2.5 x 105 N/m

2- if the

height of each floor is 4m and the tap above the ground of any of these floor is lm , if

ρw=1000Kg/m3,g=10 m/ s

2).

a. Calculate height of water surface above the ground in a tank supplies this

house by water knowing that the tank is closed.

b. Calculate the water pressure on a tap in the fourth floor.

32. A tube of cross sectional area of 100 cm2 is fixed at the top of a closed cubic

reservoir of length 2 in if the water rises in the tube to distance 2.5 m. calculate the

force acting on each side of the reservoir ( g = 10 m/s2 ρW =1000 Kg/m

3.

33. If the height of water above the separating surface in one side of a U- shaped tube

is 5 cm and that of oil in the other side is 5.55 cm. find the density of oil if the density

of water is 1000 kg/m3.

34. U shaped tube of cross-section area 2 cm2

has amount of water. 9 cm3

of kerosene

has been poured in one side, so the height difference of water in the two sides is 3.6

cm find the volume of benzene poured in the other side till the level of water becomes

the same in the two sides. (ρW =1000 Kg/m3.ρ benzene 900 Kg/m

3 )

25

35. U- shaped tube contains some mercury of density 13600 kg/m

3. Water of density

1000 kg/m3 is poured from one of its branches to a height of 49.6 cm then oil of

density 800 kg/m3 is poured above water in the same - branch to a height 40 cm. Find:

a. the height of mercury in the other branch above the separating surface between

water and mercury.

b. the height of water must be poured over mercury to equalize mercury level in the

two branches.

36. A u-shaped tube of height 40 cm, and cross-section area 2 cm2, water is poured till

it reaches-the middle of the tube, then oil is poured till the branch is completely filled.

Find :

a. the height of water above the separating surface if the density of oil is 800 kg /m3

and that of water is 1000 kg/m3

b. mass of oil inside the tube .

37 A U- shaped tube , whose cross sectional area is uniform 4 cm2 contain water , a

suitable amount of oil of weight = 0.32 N is poured in one of its arms Calculate the

height of water column above the level of the separating surface in the other arm if

RD. of oil = 0.8 , ρW =1000 Kg/m3.g=10 m/s

2 .

38. The reading of barometer on the ground floor is 76 Cm .Hg. Find its reading in the

upper floor if ρair =1.25Kg/m3.and height of this building is 60 m.( ρ mercury 13600

Kg/m3.

39. If the atmospheric pressure is 76 cm Hg, find the length of the water barometer

that reads such pressure.(Given that ρ Hg = 13600Kg/m3

& ρ water =1000 Kg/m3& g=

9.8 m/s2 ) - From the result, explain why water cannot be used as barometric liquid?

40. What is the air pressure at the upper floor of a building of 20 m height, if its value

at the ground floor is 76 cm and the average density of air between the two floors is

1.25 kg/m3 ( ρ mercury = 1360 Kg/m

3, g= 9.8 m/s

2)

41. Calculate the height of a building if the reading of the barometer is 76 cm Hg at its

ground and 75.2 cm Hg at its top. Given that the average density of air is1.25 kg /m3

and the density of mercury is 13600 kg/m3

42. The readings of a barometer are 76 cm Hg at the bottom of a mountain and 73.5

cm Hg at its top. Find the height of such a mountain given that the density of air is

1.29 kg /m3 and that of mercury is 13600 kg /m

3.

43. A building of a height 40 m and the reading of the mercury barometer is 76 cm Hg at its ground floor and 75.6 cm Hg at the top floor. Calculate the average density of air if the density of mercury is 13600 kg/m

3.

44. If the height of mercury in the open branch is higher than that attached to a gas reservoir by 21 mm. find the gas pressure, given that Pa = 1.013 x 10

5pascal and the

relative density of mercury is 13.6

26

45. Three gas tanks A, B, & C a mercury manometer is used to determine the pressure in each tank It is found that mercury in the free side of the manometer is raised by 4 cm with respect to A, while it falls by the same value when the manometer is respect to B. but it does not rise or fall when the tank C: is joined to the manometer. Calculate the gas pressure in each tank given that the density of mercury is 13600 kg/m

3 and Pa

= 1.013 x 105 N/m

2,g=9.8m/s

2.

46. In a hydraulic press, the large piston has area 1200 cm2and the small piston has

area 4 x 10-4

m2, If a force of 200 N is applied on the small piston, find:

a. The mechanical advantage of the press.

b. The maximum load that can be raised by the large piston.

47. The small and large piston diameters of a hydraulic pump are 6 cm & 30 cm respectively. Calculate the force that must be applied to the small piston to be balanced with a mass of 1 ton on the large piston what is the distance moved by the large piston when the small one moves 40 cm

48. The diameter of the large piston of a hydraulic press is 37.5 cm and the area of the small piston is 2.5 cm

2. If a force of 60 N is applied to the small piston:

a. What is the resulting force exerted by the large piston?

b. What is the increase in pressure under the small piston?

C. What is the increase in pressure under the large piston?

49. The areas of the small and large pistons in a hydraulic press are 6 cm2and 72 cm

2

respectively. Find:

a. the mechanical advantage of the press.

b. The force required to lift one 600Kg. (g=9.8 m/s2)

c. The distance moved by the small piston in order to move the large piston 4 cm

50. In the figure the mass of the large piston =1200Kg, its cross sectional area is 0.04 m

2 and cross sectional area of small piston =-25 cm

2 and its mass negligible, given

that the relative density of the oil 0.8, calculate:

a. The pressure affecting under the large piston directly.

b. The pressure affecting under the large piston directly.

c. the large force may be acting on the small piston

that give balance state

51 - Calculate the total pressure and the total force acting on the base of an aquarium if

the area of the base is 100 cm2, ρw = 1000 kg /m

3 and g = 10 m/s

2 and depth 20 m.

(1.0536 x 105 N/m

2, 1053.6 N)

52 - A submarine is designed to bear maximum pressure of 12 atmospheric pressure.

Find the maximum depth and the force acting on its window if its dimensions are 40 x

27

70 cm. given ρHg = 13600 kg/m

3, ρw = 1000 kg/m

3 and Pa = 76 cm. Hg.

(124.0306 m, 34.72 N ).

53 -A submarine located horizontally in sea water at a depth 50 m. The interior of the

submarine is maintained at atmospheric pressure. Find the force acting on one of the

submarine's window of circular shape of radius 21 cm. (ρ of sea water = 1030 kg/m3).

(6.995x104N)

54- If air pressure at the base of the mountain is 75 & at its top is 60 Cm.Hg.. Find the

height of the mountain if ρHg = 13600 kg/.m3 & ρair, = 1.25 kg/m

3 (1632 m).

55 - A layer of water of depth 1 m floats on a layer of Hg of depth 0.2 m. Calculate the

difference in pressure between two points one on the surface & on the base of Hg.

(36456 N/m2)

56 - A layer of water of thickness 50 cm. rest on a layer of mercury of thickness 20

cm. what is the difference in pressure at two points, one at the interface between water

and mercury and the other at the bottom of the mercury layer.

(ρw = 1000 kg/m3 ρHg = 13600 kg/m

3 . g = 10 m/s

2 ) ( 0.272 x 10

5 Pascal )

57 - A vertical tube 0.8 m long is one quarter full of mercury of density 13600 kg/m3

and three quarters full of paraffin of density 800 kg/m3. What pressure is exerted by

the liquids at the bottom of the tube? (31360 N/m2)

58 - Find the ratio between average pressure acting on the upper half side of a

rectangular tank full of alcohol and the average pressure acting on the lower half side

of the same tank. (1: 3)

59 - A u-shaped tube of similar cross-sectional area containing mercury of density

13600 kg/m3. A liquid of density 1230 kg /m

3 is poured in one of its branches.

Calculate the height of the liquid if the vertical distance between the two surfaces of

mercury in the two tubes is 3.69 cm (40.8 cm.)

60 - A u-shaped tube of cross sectional areas of its branches is 2 cm2, 4 cm

2

respectively containing mercury. Water is poured in the large branch. Calculate the height of water column if the surface of mercury drops by 2 cm. given PHg = 13600 kg/m

3, ρw = 1000 kg/ m

3 (20.4 cm.)

61 - A manometer is used to measure the pressure of an enclosed gas, the level mercury in the opened limb is higher than that in the closed one by 38 Cm.Hg Calculate the gas pressure in (a) cm. Hg (b) atmospheres (c) N/m2

(114 cm. Hg , 1.5 atmosphere , 1.519 x 105 N/m

2 )

62 - A hydraulic press the ratio between areas of small and large pistons is 4: 200, if a force of I 98 N acted on the, small piston, calculate the load in kg. That can be lifted by the large piston (500 kg)

63 - A hydraulic press has its small piston 2 cm. in diameter; its large piston is 12 cm. in diameter. If the efficiency is 100 % calculate the force exerted by the large piston if

28

the small piston is acted upon by 40 N. It the small piston is moved through 10 cm. How much is the large piston moved. (1440N, 0.28 cm).

64 - The areas of the small and the large pistons in the hydraulic press are 4 cm2, 60

cm2. Calculate:

(a) The mechanical advantage of the press.

(b) The force required to lift a mass 2 tons.

(c) The distance moved by the small piston if the large piston moves 3 cm. (15-1306.7N.45cm)

65 - In a gas station the diameter of the compressed air cylinder in the hydraulic press is 2 cm and the diameter of the large piston is 32 cm. Calculate the force of air pressure required to lift a car of mass 1800 kg. (g= 10 m/s

2) (70.3125 N)

66 - The small & large pistons in a hydraulic press have the diameters 2 cm & 24 cm respectively. When a force 200 N is acted on its small piston Find:

(a) The maximum mass can be lifted by the large piston.

(b) The mechanical advantage of the press.

(c) The pressure acting on the small piston and on the large piston.

(2880 kg & 144 & 636942.6 N/m2)

67 - For the system as shown; the cylinder on the left at (L) has a mass of 600 kg and cross sectional area of 800 cm

2 . The

piston on the right at (S) has cross sectional area 25 cm 2 and

negligible weight. If the apparatuses filled with oil (ρ = 0.78 g/cm

3) what is the force (f) required to hold the system in

equilibrium as shown? (30.87N).

68. A balloon of mass 0.45Kg and volume 0.5cm3 contains hydrogen gas of

density 0.1Kg/cm3, the density of air 1.3Kg/cm

3. Find:

a. The lifting force.

b. The acceleration by which the balloon moves.

69. A solid of density 2600 kg/m3, has a mass 15.5 gm. in water, 16.8 gm. in a

certain liquid calculate the mass of, the solid in air, and the density of the liquid.

(0.02518 kg, 872.9 kg/m3)

70. A cube of ice of density 920 kg/m3

is floating in water. Find the volume of the

floating part to the whole body. If a weight of 10 kg. is placed on it, it sinks. Find

the volume of ice. (8% , 0.125m3 )

71. A piece of wood mass 20 gm. in air, a lead sinker of mass 30 gm. when put in

water. The two pieces are tied together and have mass 22 gm. in water. Find the

density of wood (714 kg/m3)

29

72. A floating deck 20 m. long and 10m. Width is loaded with 10 cars; the mass of

each is 2000 kg. Find the extra depth to which the boat will sink in the sea, pw =

1030 kg/ m3) ( 9.7 cm )

73. A body (X) of mass 200 kg. is anchored to the bottom of a lake by a light

chain. The tension in the chain is 500 N. calculate the volume of the body.

(0.25 m3).

74. A boat of mass 10 kg. 4 % of its volume submerges in Agar the maximum

number of men carried without sinking if the mass of each man is 62.5 kg.(ρw=

1000 kg/m3). (3 men).

75. A balloon is filled with hydrogen, whose density is 0.09'kg/m3, until its

volume becomes 14x104 m

3. What is the lifting force of the balloon if the air

density is 1.29 kg/m3

and the mass of the balloon with its attachments (without

gas) = 105 kg. The acceleration due to gravity. = 10 m/s

2. (6.8 x 10

5 N).

76. Apiece of metal weighs 50 N in air, 36 N in water, and 41 N in an unknown

liquid. Find the densities of the following:

a. the metal

b. the unknown liquid

77. A 2.8 kg rectangular air mattress is 2.00 m long, 0.500 m wide and 0.100 m

thick. What mass can it support in water before sinking?

78. A ferry boat is 4.0 m wide and 6.0 m long. When a truck pulls onto it, the boat

sinks 4.00 cm in the water. What is the weight of the truck?

79. An empty rubber balloon has a mass of 0.0120 kg. The balloon is filled with

helium at 0°C, 1 atm pressure, and a density of 0.179 kg/m3. The filled balloon

has a radius of 0.5m.3

a. What is the magnitude of the buoyant force acting on the balloon? (The

density of air 1.25.)

b. What is the magnitude of the net force acting on the balloon?

80. An object weighs 315 N in air. When tied to a string, incepted to a balance,

and immersed in water, it weight 265 N. When it is immersed in oil, it weighs 269

N. Find the following:

a. the density of the object b. the density of the oil

81. A sample of an unknown material weighs 300 N in air and 200 N when

submerged in an alcohol solution with a density of 0.70 x 103 kg/m

3. What is the

density of the material?

82. Three bodies of 0.1m3 for each, their masses are 100, 120 & 140 kg

respectively. They are placed in a liquid of relative density of 1.2 find the

30

resultant force acting on each one in magnitude and direction. Given that g = 10

m/s2

83. Three bodies of 0.2 m3 for each, their masses are 140, 160 & 180 kg

respectively. They are placed in a liquid of relative density of 0.8 find the

resultant force acting on each one in magnitude and direction. Given that g = 10

m/s2

84. A hydrogen balloon of volume = 600 m3 the mass of it with its accessories is

500 kg find the maximum up thrust force acting on it if the density of hydrogen is

0.1 kg /m3 and that of air is 1.2 kg/m

3.

85. Balloon is filled with hydrogen gas of density 0.09 kg/m3 till its volume

becomes 14 x 104 m

3. Find the lifting force acting on the balloon to raise it. Given

that the density of air is 1.29 kg/m3, mass of the balloon with its accessories

(without the gas) is 105 kg and g = 10 m/s

2

86. A wooden parallelogram of dimensions 3 m x 2.5 m and height of 1.5 m If its

mass is 2700 kg it is put in water find :

a. The depth of the immersed part in water ( ρ water = 1000kg/m3)

b. The excess weight on the piece needed to immerse 1.2 m in water

c. The minimum mass must be put to be wholly immersed

87. A wooden parallelogram of dimensions 2 m x 1.5 m and height of 1.4 m If its

mass is 3000 kg it is put in water find :

a. The depth of the immersed part in water (ρ water = 1000kg/m3)

b. The excess weight on the piece needed to immerse 1.2 m in water

c. The minimum mass must be put to be wholly immersed.

88. A wooden cube of side = 4 cm floats on the surface of water such that its

quarter appears. What is the mass of such a cube?

89. A wooden cube of volume 0.2 m3 and density of 600 kg/ m

3 is placed on a

liquid of density 800 kg /m3 calculate the percentage of the floating part. Then

find the force needed to be acted on the cube to immerse it completely.

90. A wooden cube carries a mass of 400 gm, it is immersed completely under the

surface of water. When the mass is removed the cube rises up 4 cm. Find its side

length.

91. A wooden cylinder 30 cm long is floating vertically so that 6 cm long appears

above the free surface of oil of density 700 kg / m3 if the thickness of oil is 14 cm

lies above the water layer. Find the density of wood

92. A ship of vertical sides is loaded by 10 cars of 2000 kg each. If the breadth is

10 m find the excess depth to which the ship sinks. Given that the excess depth to

which the ship sinks. Given that the density of sea water is 1030 kg/m3.

31

93. Parallelogram of wood of dimension, 6 m, 3 m, 2 m of density 600 kg/m

3

floats on water. Find the depth of the immersed part if a body of mass 11800 kg

put on it. What is the min. mass must be put to be wholly immersed.

94. Apiece of wood of density 800 kg / m3, floats on water, such that, the volume

of the immersed part is 8 cm3, find:

a. Its mass.

b. The volume of the apparent part. Given that the density of water is 1000 kg

/m3 and the acceleration of gravity g =10 m/s

2

95. A wooden cylinder 10 cm long floats vertically such that 2 cm of its length

appears above the surface of an oil layer of height 5 cm lies over an other layer of

water in a deep vessel if the relative density of oil is 0.8 what is the relative

density of wood given that the density of water is 1000 kg /m3

96. A hollow wooden box of base area 1 m2 floats on water and 0.5m of its height

is immersed. Calculate the height of immersed part when it carries a metal cube of

side 0.4 m inside it. ρ water =1000 Kg/m3, ρ metal =7812.5Kg /m

3.

97. A metallic piece weights 350 N in air & 252 N when being immersed in water

calculate

a. The volume of such a piece.

b. Its relative density.

98. A metallic piece weights 1.96 N in water and 2.156 N in oil, Calculate the

density of its material and the density of oil. Given that the mass of the piece in air

is 300 gm & g= 9.8 m/s2

99. Calculate the tension force needed for a body in the bottom of a lake to be

suspended in water given that the weight of the body is 300 N & its volume is

0.04 m3.

100. A metallic body of density 2700 kg /m3 contains a cavity. Its mass in air is

1080 gm and 640 gm in water. Find the cavity volume.

101. A piece of wood of density 600 kg/m3 and its mass in air 300 gm fixed by a

string in the bottom of a container filled with water, if that piece wholly immersed

in water, Calculate the tension in the string. (g=9.8m/s2)

102. A rectangular metal block has a mass of 0.6 kg and dimensions 0.05 m, 0.04

in, 0.03 m. calculate the density of the metal. The same block is now suspended

from a balance so that the block is completely immersed in glycerin of density

1250 Kg/m3. What will be the reading of the balance?(g=9.8m/s

2)

103. A hollow ball its outer volume is 0.004 m3 and inner volume is 0.003 m

3 filled

with liquid of relative density 0.8 if its apparent weight in water is 10 N. Calculate

the density of its material. Where g = 10 m/s2

32

104. Piece of copper hung in a balance its mass in air is 765 gm and 675 gm in

water and 652.5 gm glycerin. If ρwater =1000 Kg/m3. Find ρcopper and ρ glycerin.

105. A piece of metal weights 0.5 N in air and 0.35 N when immersed in water.

Calculate:

a. Its relative density.

b. Its apparent weight in a liquid of density 800 kg /m 3

106. A body has a volume 7.5x 10-3

m3

and density 800 kg/m3. It is fixed by a

string in the bottom of a container filled with water such that it is wholly

immersed .the density of water is 1000 kg/m3 and g = 10 m/s

2 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 immersed fraction

of the volume.

107. A plastic cylinder of mass 1.5 Kg and relative density 0.8 and of cross-

sectional area 3 x 103 cm

3 floats vertically in water Find the length of the

submerged part in water. If oil of density 600 kg/m3 is poured above the water

surface until it covers the cylinder completely. .What will be the change in the

length of the submerged cylinder in water?

108. A solid weighs 405 gm in air and 105 gm when totally immersed in a liquid of

relative density 0.9. Calculate: The relative density of the solid.

109. A cube of ice its length 10 cm above surface of water in vessel, what happens

for the surface of water when the cube of ice melting , given that density of ice

920 Kg/m3, Density of water 1000 Kg/m

3 ?

110. A metallic cube of 10 cm side length weights 68 N when it is immersed in

water. Calculate its apparent weight when being immersed in glycerin. Given the

relative density of glycerin is 1.26.

111. A plastic ball its mass 270 gm and its density 900 Kg/m3 , floats at the

separating surface between water and kerosene , what is the volume V1 which is

immersed below the separating surface if ρW=1000 Kg/m3 g = 9.8 m/s

2 and RD. of

kerosene = 0.8.

112. A body of volume 0.01 m3 and density 600 Kg/m

3 is fixed with a thread to the

base of a vessel filled with water such that it becomes completely immersed if

( ρ W= 1000 Kg/m3

, g= 10 m/s2

) Calculate.

a. Up thrust force.

b. Tension in thread.

c. Up thrust force when the thread is cut and volume of the part which appears

above the water surface.

33

113. A piece of metal is immersed in water, benzene, and glycerin the decrease in

its - weight is 2N, 1.8N, 2.254N respectively. Calculate the density of benzene and

that of benzene if p W= 1000 Kg/m3, g =10 m/s

2.

114. A steel cube of 0.1 m side length. It floats in a basin contains mercury the

water is poured till it covers the upper surface. Find the height of water over the

separation surface. Given that the density of steel is 7935 kg/m3

& P Hg = 13600 kg

/ m3.

115. A hollow wooden cube of length 40 cm and its mass 20 kg floats vertically on

the water of density 1000 kg/m3. Calculate the length of immersed part of the

cube, and then calculate the mass which must be put on the cube to immerse

vertically the half of its volume only.

116. Solid right circular cylinder of length 10 cm and radius 2 cm has its axis

vertical and its top end is 15 cm below the surface of a fluid of relative density

1.3; calculate the thrust on:

a. The upper,

b. The lower end of the cylinder due to the fluid.

c. From your results, deduce the loss of weight of the cylinder on immersion in

the fluid. (2.45 N, b. 4.08 N, c. 1.63 N). 117. Water flows through a tube of diameter 2cm with velocity 10m/sec, Calculate

the quantity of water that flows in a minute. Then calculate the total time to fill

a tank of volume 20m3 with water.

118. A water pipe of diameter 4 cm and the speed of water in it is 2 m/s. If the pipe

becomes of radius 1 cm at its end, find:

a. The speed of water at the narrow end.

b. The volume of water that flows across its sectional area per minute.

c. The mass of the water flowing per. minute.

119. Water pipe inters a house at the ground floor, if its radius 3 cm, velocity of

water is 2 m/s, at upper floor its radius becomes 1.5 cm. Calculate the velocity

of water there.

120. A pipe of cross-section area of 4 cm2 the velocity of water flow is 10 m/s. if it

ended by 100 holes each of cross-section 1mm2 Find the velocity of water that

flow from each hole.

121. The average speed of the blood through the aorta of radius 0.7 cm, is 0.33

m/s. Find the number of the major arteries to which the blood is distributed,

given that the radius of each artery is 0.35 cm. and the velocity of the blood in

the artery is 0.044 m/s.

34

122. Water pipe of radius 1.5 cm inters house, the water velocity is 0.2 m/s. If the

radius becomes 0.5 cm at its end. Calculate

(a) The velocity of water at that end.

(b) The volume of water flow in one minute at any cross section.

123. A tube has a diameter of 10 cm. where the speed of water at that section is 1

m/s. At the end of the tube the diameter becomes 2.5 cm. Calculate the speed

of water at the narrow section, then find the mass of water that flows per

minute across any of its cross-sectional area. (ρ water = 1000 Kg/m3 , π = 3.14).

124. Major artery divided into 40 capillaries each of radius 0.2 cm if the radius of

the major artery is 0.6 cm, and its blood velocity is 0.1 m/s. Calculate the

blood velocity in each capillary.

125. The velocity of the blood through a main blood vein of diameter 0.6 cm is

0.03 m/s. The blood is distributed through 30 arteries the radius of each is 0.4

mm. Find the speed of the blood in each artery.

126. Two square shaped flat surface (plate) of side 40 cm. oil film of thickness 2

cm between them if a force of 50 N act on the upper plate it moves by velocity

1 m/s. Calculate the coefficient of viscosity.

127. In the figure shown the radius of the tube at a =

20 cm at d=10cm at b= 4 cm and at c = 6 cm

calculate the rate of volume flow at a if water

inters the tube at a by a velocity = 1 m/s then

calculate the velocity of the water flow at d and c

if the velocity of the flow at b = 2 m/s

128. The shown figure:

given that the radius of the tube at (a) is 30 cm and

the velocity of water entering at the same point is 2

m/s, the velocity of the water flow at (c) is 4 m/s

and at (e) is 3 m/s where the radius the tube at (b)

is 20 cm at (c) is 15 cm, at (d) is 10 cm and at (e)

is 5 cm.

Calculate:

1- The rate volume of water entering at (a)

2- The velocity of the water flow at b and d.

(0.5652 m3/s ,405 m/s ,8.25 m/s)