TF015/2 TF015/2 Engineering Physics Fizik Kejuruteraan Paper 2 Kertas 2 Semester 1 Semester I Session 201012011 Sesi 2010/2011 21;2 hours 2~jam

PERPUSTAKAAN KOlEJ MATRIKULASI PAHANG

CAWANGAN JENGKA

BAHAGIAN MATRIKULASI

KEMENTERIAN PELAJARAN MALAYSIA MATRiCULATION DIVISION

MINISTRY OF EDUCATION MALAYSIA

PEPERIKSAAN SEMESTER PROGRAM MATRIKULASI MATRiCULATION PROGRAMME EXAMINATION

FIZIK KEJURUTERAAN Kertas 2

2 jam 30 minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO.

Kertas soalan ini mengandungi 21 halaman bercetak. This booklet consists of 21 printed pages.

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ARAHAN KEPADA CALON:

Kertas soalan ini mengandungi 8 soalan.

lawab soalan nombor 1 dan mana-mana lima soalan yang lain. Hanya enam jawapan pertama akan diperiksa.

Semua jawapan hendaklah ditulis pada buku jawapan yang disediakan. Gunakan muka surat bam bagi nombor soalan yang berbeza.

Kalkulator elektronik boleh digunakan.

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INSTRUCTIONS TO CANDIDATE:

This question booklet consists of 8 questions.

Answer question 1 and any other five questions. Only the first six answers will be graded.

All answers must be written in the answer booklet provided. Use a new page for each question.

The use of electronic calculator is permitted.

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Laju cahaya dalam vakum

Ketelapan ruang bebas

Ketelusan ruang bebas

Magnitud cas elektron

Pemalar Planck

lisim rehat elektron

lisim rehat neutron

lisim rehat proton

1isim rehat deuteron

Pemalar gas molar

Pemalar Rydberg

Pemalar Avogadro

Pemalar Boltzmann

Pemalar kegravitian

Pecutan graviti

Penukar unit jisim atom

Penukar elektron volt

Pemalar Hukum Coulomb

Tekanan atmosfera

Ketumpatan air

Senarai Nilai-Nilai Pemalar

c

e

h

R

/1/4

k

G

g

1 u

eV

k::=_l_ 47[6'0

atm

A

::= 3.00 x 108 m S-I

= 8.85 x 10-12 F m- I

= 1.60 x 10- 19 C

= 6.6256 x 10-34 1 s

= 9.11 x 10-31 kg = 5.48 x 10-4 u

= 1.67 x 10-27 kg = 1.008664 u

= 1.67 x 10-27 kg = 1.007276 u

= 3.34 x 10-27 kg = 2.013553 u

= 8.314 1 K- 1 mol-I

= 109678 cm- I

= 1.097 x 107 m-I

::= 6.02 x 1023 mol-I

= 1.38 x 10-23 1 K- I

=9.81ms-2

::= 1.66 x 10-27 kg

= 931.5 M~V

= 1.6 x 10- 19 1

=1.013x10 5 Pa

= 1000 kg m-3

c

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List Of Selected Constant Values

Speed of light in vacuum

Permeability constant

Permittivity constant

Elementary charge

Planck constant

Electron mass

Neutron mass

Proton mass

Deuteron mass

Universal gas constant

Rydberg constant

Avogadro constant

Boltzmann constant

Gravitational constant

Free-fall acceleration

Atomic mass unit

Electron volt

Constant of proportionality

for Coulomb's law

Atmospheric pressure

Density of water

c

J10

&0

e

h

me

R

NA

k

G

g

1 u

eV

k=_l_ 4Jrco

atm

= 3.00 x 108 m S-l

= 8.85 x 10- 12 F m- I

= 1.60 x 10- 19 C

= 6.6256 x 10-34 J s

= 9. 11 x 10-3 J kg = 5.48 x 10-4 u

= 1.67 x 10-27 kg = 1.008664 u

= 1.67 x 10-27 kg = 1.007276 u

= 3.34 x 10-27 kg = 2.013553 u

= 8.314 J K- 1 mol- 1

J= 109678 cm­= 1.097 x 107 m- I

= 6.02 x 1023 mol- I

= 1.38 x 10-23 J K- I

= 6.67 x 10- 11 N m2 kg-2

= 9.81 m S-2

= 1.66 x 10-27 kg

= 931.5 M~V

= 1.6 x 10-19 J

= 1.013x10 5 Pa

= 1000kgm-3

5

c

1

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Jawab soalan nombor 1 dan mana-mana lima saalan yang lain.

RAJAH 1

RAJAH 1 menunjukkan ujikaji satu bandul rod yang berayun pada paksi 0 berjarak h dari pusat jisim, C. Tempoh ayunan, T untuk h yang berbeza disenaraikan dalam JADUAL 1.

Hubungan antara h dan T diberikan oleh rumus,

gT 2

h = H -- ­4Jr 2

dengan g ialah pecutan graviti dan H pemalar.

JADUAL 1

h(cm) T(s) r(s2)

5.0 1.55 10.0 1.48 20.0 1.34 30.0 1.18 40.0 1.01 50.0 0.77 60.0 0.45

(a) Salin dan lengkapkan JADUAL 1. [2 markah]

(b) Plot graf h melawan fl. [6 markah]

(c) Tentukan kecerunan graf. [3 markah]

(d) Dengan menggunakan kecerunan graf~ hitung g. [2 markah]

(e) Tentukan H dari graf. [2 markah]

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Answer question 1 and any other five questions.

FIGURE 1

FIGURE 1 shows an experiment of a rod pendulum which oscillates about its axis 0 at a distance h from its center of mass, C. The period of oscillation, T for different h is tabulated in TABLE 1.

The relationship between hand T is given by equation,

a T'­h = H __0_

4;r2

where g is acceleration due to gravity and H is a constant.

TABLE 1

h(cm) T(s) Y(s-) 5.0 1.55

10.0 1.48 20.0 1.34 30.0 1.18 40.0 1.01 50.0 0.77 60.0 0.45

(a) Copy and complete TABLE 1.

(b) Plot a graph of h against Y. [2 marks]

[6 marks] (c) Determine the gradient of the graph.

[3 marks] (d) Using the gradient from the graph, calculate g.

[2 marks] (e) Determine H from the graph.

[2 marks]

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2 (a) (i) Takrifkan halaju purata.

(ii) Takrifkan halaju seketika.

(iii) Apabila satu objek bergerak dengan halaju malar, adakah halaju purata objek pada sebarang sela masa, berbeza daripada halaju seketikanya?

[3 markah]

(b) Satu bola dilontar menegak ke atas dengan halaju 5 m S-l. Dengan mengandaikan tiada rintangan udara, hitung

(i) ketinggian maksimum dicapai bola dari titik ia dilepaskan.

(ii) masa diambil untuk mencapai ketinggian tersebut.

(iii) masa penerbangan. [7 markah]

(c)

, ,, , , , , , , , , , , , , , , , , , , , , , , , ,

>1 R

RAJAH 2

Satu bola dilontar ke atas dari atas bangunan yang tingginya 35 m seperti pada RAJAH 2. Halaju awal bola ialah 20 m S-l dan arahnya 40° dari paksi mengufuk. Hitung

(i) masa untuk bola sampai ke tanah.

(ii) jarak R. [5 markah]

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2 (a) (i) Define average velocity.

(ii) Define instantaneous velocity.

(iii) When an object moves with constant velocity, does its average velocity during any time interval, differ from its instantaneous velocity?

[3 marks]

(b) A ball is thrown vertically upward with a velocity of 5 m S-I. By assuming there is no air resistance, calculate

(i) the maximum height achieved by the ball above the point of release.

(ii) the time taken to reach this height.

(iii) the time of flight. [7 marks]

(c)

-1 " ,u=20ms ' , ,40° ,, , , , , ,, , , , ,, , , , , , , , , , , , , ,

( )

R

FIGURE 2

A ball is thrown upward from the top of a 35 m building as shown in FIGURE 2. The initial velocity of the ball is 20 m S-1 and its direction is at 40° from the horizontal axis. Calculate

(i) the time to reach the ground.

(ii) the distance R. [5 marks]

Q

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3 (a) Takrifkan

(i) Prinsip keabadian tenaga.

(ii) Teorem kerja-tenaga.

(iii) Daya geseran. [3 markah]

(b) - -,,-'"

li:~~

Q

RAJAH 3

Satu bongkah dilepaskan dari titik P dan menggelongsor tanpa geseran sehingga mencapai titik Q. Bahagian PQ adalah sukuan satu bu!atan berjejari 2.0 m, seperti pada RAJAH 3. Menggunakan prinsip keabadian tenaga, hitung laju bongkah pada titik Q.

[3 markah]

(c)

p - -- - ­ - - ­

"

I, :,,,,, II

,

RAJAH 4

RAJAH 4 menunjukkan satu bongkah berjisim mj = 2.2 kg terletak di atas satah condong pada sudut 30°. Pekali geseran kinetik ialah 0.22. Bongkah dihubung menggunakan satu tali ringan melalui taka! tanpa geseran dengan bongkah lain berjisim Itl2 = 2.7 kg yang digantung secara menegak. Sistem ini dilepaskan dari keadaan pegun.

(i) Lukis rajahjasad bebas yang menunjukkan daya-daya yang bertindak ke atas bongkah-bongkah semasa kedua-duanya sedang bergerak.

(ii) Hitung pecutan kedua-dua bongkah.

(iii) Hitung tegangan tali. [9 markah]

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3 (a) Define

(i) Principle of conservation of energy.

(ii) Work-energy theorem.

(iii) Frictional force. [3 marks]

(b) p -----------...

... ,,'" : I

I

I

I

I I

I , I

t\:;?~

Q

FIGURE 3

A block is released at point P and slides without friction until it reaches point Q. Section PQ is a quadrant of a circle of 2.0 m radius, as shown in FIGURE 3. Using the principle of conservation of energy, calculate the speed of the block at Q.

[3 marks]

(c)

FIGURE 4

FIGURE 4 shows a block of mass mj = 2.2 kg on an inclined plane of an angle 30°. The coefficient of kinetic friction is 0.22. The block is connected by a light string that passes over a frictionless pulley to another block of mass m2 = 2.7 kg which hangs vertically. The system is released from rest.

(i) Draw the free body diagram showing the forces acting on the blocks when they are in motion.

(ii) Calculate the acceleration of the blocks.

(iii) Calculate the tension in the string. [9 marks]

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4 (a) (i) Apakahjenis daya yang diperlukan supaya satu objek berjisim m bergerak dalam satu bulatan berjejari r pada laju sudut seragam OJ?

(ii) Lukis rajah yang menunjukkan arah daya tersebut. [2 markah]

(b)

RAJAH 5

Satu sfera berjisim 100 g diikat pada" seutas tali tak kenyal. Ia bergerak pada laju malar 3.0 m S-I dalam satu bulatan menegak berjejari 50 em seperti pada RAJAH 5.

(i) Lakar satu rajahjasad bebas yang menunjukkan daya-daya yang bertindak ke atas objek semasa berada di atas dan di bawah bulatan.

(ii) Hitung tegangan pada tali apabila objek berada di atas dan di bawah bulatan.

(iii) Hitung laju minimum objek apabila berada di atas bulatan supaya objek itu tidak berubah daripada lintasan membulat.

[9 markah]

(e) Satu bola berjisim 100 g diikat pada hujung seutas tali 60 em panjang dan dipusingkan. Bola itu melakukan 2 pusingan lengkap setiap saat dalam satu bulatan mengufuk. Hitung peeutan memusat bola.

[4 markah]

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4 (a) (i) What type of force is required to make an object of mass m move in a circle of radius r with uniform angular speed OJ?

(ii) Draw a diagram to show the direction of that force. [2 marks]

(b) H. m

~-\

FIGURE 5

A sphere of mass 100 g is tied to an inelastic string. It moves in a vertical circle of radius 50 cm at a constant speed of3.0 m S-1 as shown in FIGURE 5.

(i) Sketch a free body diagram showing forces acting on the object at the top and bottom of the circle.

(ii) Calculate the tension in the string when the object is at the top and bottom of the circle.

(iii) Calculate the minimum speed of the object at the top of the circle so that the object will not depart from the circular path.

[9 marks]

(c) A ball of mass 100 g is attached to one end of a string 60 cm long and whirled. The ball makes 2 complete revolutions per second in a horizontal circle. Calculate the centripetal acceleration of the ball.

[4 marks]

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5 (a) (i) Takrifkan halaju sudut purata.

(ii) Takrifkan peeutan sudut seketika.

(iii)

/ft-o

.A ·B

RAJAH 6

Dua zarah, A dan B pada satu jasad tegar berputar pada satu paksi tetap 0 seperti pada RAJAH 6. Adakah halaju linear dan halaju sudut bagi zarah A dan B sarna?

[4 markah]

(b) Satu roda tenaga berdiameter 80 em memerlukan 5 s untuk meneapai 100 putaran per minit bermula daripada laju 50 putaran per minit.

(i) Hitung peeutan sudut.

(ii) Berapakah bilangan putaran yang dilalui? [5 markah]

(e) Satu kipas kapal berputar pada satu peeutan sudut malar 4.50 rad S-2.

(i) Jika laju sudut kipas ialah 1.50 rad S-1 pada t = 0, berapakah sesaran sudut yang dilalui kipas dalam masa 3.0 s?

(ii) Berapakah putaran yang dibuat oleh kipas dalam masa tersebut?

(iii) Hitung laju sudut kipas pada t = 1.5 s. [6 markah]

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5 (a) (i) Define average angular velocity.

(ii) Define instantaneous angular acceleration.

(iii)

.A ·B

~o

FIGURE 6

Two particles, A and B on a rigid body rotate about a fixed axis 0 as shown in FIGURE 6. Are the linear and angular velocities ofA and B the same?

[4 marks]

(b) A flywheel of 80 cm in diameter requires 5 s to go from initial speed of 50 revolutions per minute to 100 revolutions per minute.

(i) Calculate its angular acceleration.

(ii) How many revolutions does it make? [5 marks]

(c) A ship propeller rotates with a constant angular acceleration of 4.50 rad s-2.

(i) If the angular speed of the propeller is 1.50 rad S-l at t = 0, through what angular displacement does the propeller rotates in 3.0 s?

(ii) How many revolutions has the propeller rotated during this time interval?

(iii) Calculate the angular speed of the propeller at t = 1.5 s. [6 marks]

111

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(a) (i) Terangkan secara ringkas tentang gerakan hannonik ringkas.

(ii) Nyatakan prinsip superposisi gelombang. [2 markah]

(b) x (em)

5.0

4.0 t (5)

-5.0

RAJAH 7

Satu objek melakukan gerakan hannonik ringkas dengan sesaran, x berubah terhadap masa, t seperti pada RAJAH 7.

(i) Tentukan persamaan sesaran, x dalam fungsi masa, t bagi ayunan yang ditunjukkan dalam RAJAH 7.

(ii) Menggunakan skala graf yang sama seperti dalam RAJAH 7, lakar dan labelkan graf halaju-masa dan pecutan-masa bagi ayunan objek.

[8 markah]

(c) Dua gelombang maju diwakili oleh persamaan berikut:

YI (x, t) = 5sin n(t + 2x) Y2 (x, t) = 5sin n(t - 2x)

dengan Y1, Y2 dan x dalam sentimeter serta t dalam saat.

(i) Tulis persamaan bagi gelombang pegun yang dihasilkan apabila dua gelombang bertindih.

(ii) Tentukan tiga nilai x terkecil (x >0) yang sepadan dengan kedudukan antinod bagi gelombang pegun yang diperolehi dalam (c) (i).

[5 markah]

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6 (a) (i) Explain briefly what is simple harmonic motion.

(ii) State the principle of superposition of waves. [2 marh]

(b) x (em)

5.0

4.0 t(s)

-5.0

FIGURE 7

An object executes simple harmonic motion whose displacement, x varies with time. t as shown in FIGURE 7.

(i) Determine the equation of displacement x as a function of time, t for the oscillations as shown in FIGURE 7.

Oi) Using the same scale as in FIGURE 7, sketch and label the velocity-time and acceleration-time graphs of the oscillating object.

[8 marks]

(c) Two progressive waves are represented by the following equations:

Y1(x, t) = 5 sin If(t + 2x) Y2 (x, t) = 5sin If(t - 2x)

where Yl, Y2 and x are in centimeter and t in second.

(i) Write an expression for the stationary wave produced when both waves are superimposed.

(ii) Determine three smallest values of x (x >0) that correspond to antinode positions from stationary wave obtained in (c) (i).

[5 marh]

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7 (a) Takrifkan

(i) tegasan.

(ii) terikan.

(iii) modulus Young. [3 markah]

(b) Lakar dan labelkan lengkung tegasan-terikan bagi pepejal kenyal untuk menunjukkan titik alah, kekuatan tegangan muktamad dan kekuatan peeah.

[4 markah]

(c)

I. waya,

il+-- pemberat

RAJAH 8

RAJAH 8 menunjukkan satu pemberat 5.0 x 102 N digantung pada hujung satu wayar yang mempunyai luas keratan rentas 0.01 em2

. Wayar itu meregang dari panjang asal 200.00 em ke 200.50 em. Tentukan

(i) tegasan wayar.

(ii) terikan wayar.

(iii) modulus Young wayar. [6 markah]

(d) Modulus Young bagi keluli ialah beribu kali ganda lebih besar daripada getah. Dengan mengandaikan semua faktor lain adalah sarna, adakah ini membawa maksud keluli meregang dengan lebih mudah berbanding getah? Jelaskan.

[2 markah]

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7 (a) Define

(i) stress.

(ii) strain.

(iii) Young's modulus. [3 marks]

(b) Sketch and label stress-strain curve for an elastic solid to include yield point, ultimate tensile strength and breaking strength.

[4 marks]

(c)

I. wuc

L~+--weight

FIGURE 8

FIGURE 8 shows a 5.0 x 102N weight is hung from the end ofa wire of 2cross-sectional area 0.01 cm . The wire stretches from its original length of

200.00 cm to 200.50 em. Detennine

(i) the stress on the wire.

(ii) the strain on the wire.

(iii) the Young's modulus of the wire. [6 marh]

(d) Young's modulus for steel is thousands of times greater than that for rubber. By assuming that all other factors being equal, does this mean that steel stretches much more easily than rubber? Explain.

[2 marks]

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8 (a) Lakarkan graf yang sesuai untuk gas unggul yang memenuhi setiap satu keadaan berikut:

(i) Tekanan bagi gas berjisim tetap pada suhu malar berkadar songsang dengan isipadunya.

(ii) Isipadu bagi gas berjisim tetap pada tekanan malar berkadar terns dengan suhu mutlaknya.

(iii) Tekanan bagi gas berjisim tetap pada isipadu malar berkadar terns dengan suhu mutlaknya.

[3 markah]

(b) (i) Terangkan secara ringkas tenaga dalam dan bilangan darjah kebebasan bagi satu gas unggul. Nyatakan hubungan antara kedua-duanya.

(ii) Gas hidrogen (M = 2 g mol-I) dan nitrogen (M = 28 g mol-I) dicampur serentak. Hitung nisbah laju punca min kuasa dua antara gas hidrogen dengan nitrogen.

[5 markah]

(c)

20.0 ------ p

10.0 ,R: 'Q

'----------'----------'------ V (x] 0-3 m3)

20.0 V

RAJAH 9

Satu silinder mengandungi satu mol gas unggul mengembang dari keadaan P ke keadaan Qpada suhu malar. Seternsnya gas dimampatkan pada tekanan malar ke keadaan R sebelum dipanaskan sehingga kembali ke keadaan P seperti pada RAJAH 9. Tentukan

(i) suhu gas pada keadaan R.

(ii) suhu gas pada keadaan P.

(iii) isipadu gas pada keadaan Q. [7 markah]

KERTAS SOALAN TAMAT

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8 (a) Sketch a suitable graph for an ideal gas to fulfill each of the following conditions:

(i) The pressure of a fixed mass of gas at constant temperature is inversely proportional to its volume.

(ii) The volume of a fixed mass of gas at constant pressure is directly proportional to its absolute temperature.

(iii) The pressure of a fixed mass of gas at constant volume is directly proportional to its absolute temperature.

[3 marks]

(b) (i) Explain briefly the internal energy and number of degree of freedom of an ideal gas. State the relationship between them.

(ii) Hydrogen (M = 2 g mor l ) and nitrogen (M = 28 g mor l ) gases are mixed at the same time. Calculate the root mean square speed ratio between hydrogen and nitrogen.

[5 marks]

(c) P (xl0~ Pa)

20.0 ----- ­ p

10.0 :Q , , , , , I I , ,

-----'--------',---- V (x 10-3 m3) 20.0 V

FIGURE 9

A cylinder containing one mol of an ideal gas expands from state P to state Q at constant temperature. The gas is then compressed at constant pressure to state R before it is heated until it returns to state P as shown in FIGURE 9. Detern1ine

(i) the temperature of the gas at state R.

(ii) the temperature of the gas at state P.

(iii) the volume of the gas at state Q. [7 marks]

END OF QUESTION BOOKLET

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