forces and motion - yuhuaphysics.com 063 fizik tg4 b2 2015(fsy4p) n.pdf · • menyatakan maksud...

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MODUL • Fizik TINGKATAN 4

•Menyatakanmaksudjarakdansesaran/Define distance and displacement

•Menyatakanmaksudlajudanhalajudanmenyatakanv= st/Define speed and velocity and state that v = s

t•Menyatakanmaksudpecutandannyahpecutandanmenyatakana = v – u

tDefine acceleration and deceleration and state that a = v – u

t•MenghitunglajudanhalajuCalculate speed and velocity

•MenghitungpecutandannyahpecutanCalculate acceleration and deceleration

•MenyelesaikanmasalahgerakanlineardenganpecutanseragamdenganSolve problems on linear motion with uniform acceleration using

(i) v = u + at

(ii) s = ut + 12

at2

(iii) v2 = u2 + 2as

•Melakardanmentafsirkangrafsesaran-masadanhalaju-masaPlot and interpret displacement-time and velocity-time graphs

•Membuatkesimpulandaripadabentukgrafsesaran-masaapabila jasaddalamkeadaan:Deduce from the shape of a displacement-time graph when a body is:

(i) rehat/at rest(ii) bergerakdenganhalajuseragam/moving with uniform velocity(iii) bergerakdenganhalajutidakseragam/moving with non-uniform velocity

•Menentukanjarak,sesarandanhalajudaripadagrafsesaran-masaDetermine distance, displacement and velocity from a displacement-time graph

•Membuatkesimpulandaripadabentukgrafhalaju-masaapabila jasaddalamkeadaan:Deduce from the shape of a velocity-time graph when a body is:

(i) rehat/at rest

(ii) bergerakdenganhalajuseragam/moving with uniform velocity

(iii) bergerakdenganpecutanseragam/moving with uniform acceleration

•Menentukanjarak,sesaran,halajudanpecutandaripadagrafhalaju-masaDetermine distance, displacement, velocity and acceleration from a velocity-time graph

•MenyelesaikanmasalahgerakanlineardenganpecutanseragamSolve problems on linear motion with uniform acceleration

•MenerangkanapaituinersiaExplain what inertia is

•MenghubungkaitkanjisimdenganinersiaRelate mass to inertia

•MembericontohsituasiyangmelibatkaninersiaGive examples of situations involving inertia

•Mencadangkancarauntukmengurangkankesannegatif inersiaSuggest ways to reduce the negative effects of inertia

DAYA DAN GERAKANFORCES AND MOTION2

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2.1 MENGANALISIS GERAKAN LINEAR/ANALYSING LINEAR MOTION

2.2 MENGANALISIS GRAF GERAKAN/ANALYSING MOTION GRAPHS

2.3 MEMAHAMI INERSIA/UNDERSTANDING INERTIA

Fizik Tg4 B2 2015(FSY4p).indd 44 10/20/15 2:23 PM

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•Menyatakanmaksudmomentumsuatuobjek/Define the momentum of an object•Menyatakanmaksudmomentumsebagaihasildarabjisim(m)danhalaju(v), iaitumomentum= mv

Define momentum as the product of mass (m) and velocity (v), i.e. momentum = mv

•MenyatakanPrinsipKeabadianMomentumState the Principle of Conservation of Momentum

•MenghuraikanaplikasiPrinsipKeabadianMomentumDescribe applications of Conservation of Momentum

•MenyelesaikanmasalahyangmelibatkanmomentumSolve problems involving momentum

•MenghuraikankesandayaseimbangyangbertindakkeatasobjekDescribe the effects of balanced forces acting on the object

•MenghuraikankesandayayangtidakseimbangyangbertindakkeatasobjekDescribe the effects of unbalanced forces acting on an object

•MenyelesaikanmasalahdenganmenggunakanF = maSolve problems using F = ma

•MenerangkanapaituimpulsExplain what an impulsive force is

•MembericontohsituasiyangmelibatkandayaimpulsGive examples of situations involving impulsive forces

•Menyatakanmaksudimpulssebagaiperubahanmomentum,iaituFt = mv – muDefine impulse as a change of momentum, i.e. Ft = mv – mu

•Menyatakanmaksuddayaimpulssebagaikadarperubahanmomentumdalamperlanggaranatauletupan,iaitu/Define impulsive force as the rate of change of momentum in a collision or explosion, i.e.

F = mv – mut

•Menerangkansituasidimanamenambahkanataumengurangkanmasaperlanggaranterhadapnilaidayaimpuls Explain the effect of increasing or decreasing the time of impact on the magnitude of the impulsive force•Menghuraikansituasidimanadayaimpulsperludikurangkandancarauntukmengurangkannya

Describe situations where an impulsive force needs to be reduced and suggest ways to reduce it

•MenghuraikansituasidimanadayaimpulsmendatangkanmanfaatDescribe situations where an impulsive force is beneficial

•MenyelesaikanmasalahyangmelibatkandayaimpulsSolve problems involving impulsive forces

•Menghuraikankepentinganciri-cirikeselamatandalamkenderaanDescribe the importance of safety features in vehicles

•Menerangkanpecutanyangdisebabkanolehgraviti/Explain acceleration due to gravity•Menyatakanapaitumedangraviti/State what a gravitational field is•Menyatakanmaksudkekuatanmedangraviti/Define gravitational field strength•Menentukannilaipecutanyangdisebabkanolehgraviti/Determine the value of acceleration due to gravity•MenyatakanmaksudBerat(W)sebagaihasildarabjisim(m)danpecutanyangdisebabkanoleh graviti (g), iaitu W = mg

Define weight (W) as the product of mass (m) and acceleration due to gravity (g), i.e W = mg

•MenyelesaikanmasalahyangmelibatkanpecutangravitiSolve problems involving acceleration due to gravity

2.4 MENGANALISIS MOMENTUM/ANALYSING MOMENTUM

2.5 MEMAHAMI KESAN DAYA/UNDERSTANDING THE EFFECT OF FORCE

2.8 MEMAHAMI GRAVITI/UNDERSTANDING GRAVITY

2.7 CIRI-CIRI KESELAMATAN YANG DIPERLUKAN DALAM KENDERAANBEING AWARE OF THE NEED FOR SAFETY FEATURES IN VEHICLES

2.6 MENGANALISIS IMPULS DAN DAYA IMPULS/ANALYSING IMPULSE AND IMPULSIVE FORCE


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•MenghuraikansituasikeseimbangandayaDescribe situations where forces are in equilibrium

•MenyatakanapaitudayapaduanState what a resultant force is

•TambahkanduadayauntukmenentukandayapaduanAdd two forces to determine the resultant force

•MeleraikandayakepadaduakomponendayaResolve a force into two effective component forces

•MenyelesaikanmasalahyangmelibatkankeseimbangandayaSolve problems involving forces in equilibrium

•Menyatakanmaksudkerja(W)sebagaihasildarabdaya(F)yangdikenakandansesaran(s)objekdalamarahdayatersebut, iaituW = Fs Define work (W) as the product of an applied force (F) and displacement (s) of an object in the direction of the applied force, i.e W = Fs

•Menyatakanapabilakerjadilakukan,tenagadipindahkandaripadasatuobjekkeobjeklainState that when work is done, energy is transferred from one object to another

•Menyatakanmaksudtenagakinetik,Ek,danmenyatakanbahawaEk=12

mv2

Define kinetic energy, Ek, and state that Ek = 12

mv2

•Menyatakanmaksudtenagakeupayaangraviti,Ep, danmenyatakanbahawaEp = mghDefine gravitational potential energy, Ep, and state that Ep = mgh

•MenyatakanPrinsipKeabadianTenaga/State the Principle of Conservation of Energy

•Menyatakanmaksudkuasa,P,danmenyatakanbahawaP= TenagaMasa

Define power, P, and state that P = EnergyTime

•MenerangkanapaitukecekapanperalatanExplain what efficiency of a device is

•Menyelesaikanmasalahyangmelibatkankerja,tenaga,kuasadankecekapanSolve problems involving work, energy, power and efficiency

•MenyatakanmaksudkekenyalanDefine elasticity

•MenyatakanHukumHookeState Hooke’s Law

•Menyatakanmaksudtenagakeupayaankenyal,Ep,danmenyatakanbahawaEp=12

kx2

Define elastic potential energy, Ep, and state that Ep = 12

kx2

•Menentukanfaktor-faktoryangmempengaruhikekenyalanDetermine the factors that affect elasticity

•MenghuraikanaplikasikekenyalanDescribe applications of elasticity

•MenyelesaikanmasalahyangmelibatkankekenyalanSolve problems involving elasticity

2.9 MENGANALISIS KESEIMBANGAN DAYA ANALYSING FORCES IN EQUILIBRIUM

2.10 MEMAHAMI KERJA, TENAGA, KUASA DAN KECEKAPAN UNDERSTANDING WORK, ENGERY, POWER AND EFFICIENCY

2.11 MEMAHAMI KEKENYALAN UNDERSTANDING ELASTICITY


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Rajah di sebelah kanan menunjukkan beza antara jarak dan sesaran. Apabila Ah Chong berjalan kaki di sepanjang Jalan Baik dari rumah A ke sekolah B,The diagram on the right shows the difference between distance and displacement. When Ah Chong walked from House A to School B, along Good Road,

Jarak/Distance = Panjang laluan di sepanjang Jalan Baik Length of the road along Good RoadSesaran/Displacement = Panjang garis lurus AB / Length of the straight line AB Rumah

House

SekolahSchool

Jalan BaikGood Road

A

B

Rahim berjalan dari rumahnya ke simpang sejauh 1.5 km dari rumahnya. Kemudian dia berpatah balik dan berhenti di warung Pak Din yang sejauh 0.5 km dari rumahnya. Rahim walked from his house to the junction which is 1.5 km from his house. Then he turned back and stopped at Pak Din’s stall which is 0.5 km from his house.

(a) Berapakah sesaran Rahim dari rumahnya/What is Rahim’s displacement from his house (i) apabila dia sampai di simpang?/when he reached the junction?

1.5 km ke timur

1.5 km to the east

(ii) apabila dia berada di warung Pak Din?/when he was at Pak Din’s stall?

0.5 km ke barat

0.5 km to the west

(b) Selepas bersarapan pagi, Rahim berjalan pulang ke rumahnya. Apabila dia sampai di rumahnya,After breakfast, Rahim walked back to his house. When he reached home,

(i) berapakah jumlah jarak yang dilalui oleh Rahim?/what was the total distance travelled by Rahim?

1.5 km + 1.5 km + 0.5 km + 0.5 km = 4 km

(ii) berapakah jumlah sesaran Rahim dari rumahnya?/what was Rahim’s total displacement from his house?

0 km

Rumah RahimRahim’s house

0.5 km 1.5 km

Warung Pak DinPak Din’s stall

B O

Utara/North

JarakDistance

1 Jarak ialah jumlah laluan yang dilalui dari satu lokasi ke satu lokasi yang lain

Distance is the total path length travelled from one location to another

Kuantiti/Quantity: Skalar/Scalar Unit SI/SI unit: meter (m)

SesaranDisplacement

1 Sesaran ialah/Displacement is

(a) jarak dalam arah tertentu./the distance in a specific direction .

(b) jarak antara dua lokasi yang diukur sepanjang laluan yang paling pendek yang menghubungkannya dalam arah tertentu.

the distance between two locations measured along the shortest path connecting them in a specific direction.

(c) jarak kedudukan akhir dari kedudukan awal dalam arah tertentu.the distance of its final position from its initial position in a specified direction.

Kuantiti/Quantity: Vektor/Vector Unit SI/SI unit: meter (m)

MENGANALISIS GERAKAN LINEARANALYSING LINEAR MOTION2.1

Contoh/Examples

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Definisi Laju dan HalajuDefine Speed and Velocity

LajuSpeed

1 Laju ialah kadar perubahan jarak

Speed is the rate of change of distance

Laju, v = Jarak dilalui

Masa yang diambilSpeed, v =

Distance travelledTime taken

Kuantiti/Quantity: Skalar/Scalar Unit SI/SI unit: m s

2 Laju purata/Average speed

v = Jumlah jarak dilalui, s

Jumlah masa yang diambil, t v = Total distance travelled, s

Total time taken, t

Laju sekata Laju yang magnitudnya kekal sama tanpa mempertimbangkan arahnya.

Uniform speed Speed that remains the same in magnitude regardless of its direction.

HalajuVelocity

1 Halaju ialah kadar perubahan sesaran

Velocity is the rate of change of displacement

Halaju, v = Sesaran

Masa yang diambilVelocity, v =

DisplacementTime taken

Kuantiti/Quantity: Vektor/Vector Unit SI/SI unit: m s

2 Halaju purata/Average velocity

v = Sesaran, s

Jumlah masa yang diambil, t v = Displacement, s

Total time taken, t

Halaju sekata Halaju yang magnitud dan arahnya kekal sama.

Uniform velocity Velocity that remains the same in magnitude and direction .

3 Suatu objek mempunyai halaju tak sekata jika: An object has a non-uniform velocity if:

(a) arah gerakan berubah atau gerakan tidak linear.

the direction of motion changes or the motion is not linear.

(b) magnitud halaju berubah.

the magnitude of its velocity changes.

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Sebuah kapal terbang menuju ke utara selama 1 jam dengan halaju300 km j–1. Kemudian, kapal terbang bergerak ke timur selama 1 jam dengan halaju 400 km j–1. An aeroplane flies towards the north for 1 hour with a velocity of 300 km h–1. Then, the plane moves to the east for 1 hour with a velocity of 400 km h–1. (a) Berapakah laju purata kapal terbang itu? What is the average speed of the plane?

Laju purata = Jumlah jarakJumlah masa Average speed =

Total distanceTotal time

Jarak OA = LajuOA × MasaOA Distance OA = SpeedOA × TimeOA

= 300 km j–1 × 1 jam = 300 km h–1 × 1 hour = 300 km = 300 km Jarak AB = LajuAB × MasaAB Distance AB = SpeedAB × TimeAB

= 400 km j–1 × 1 jam = 400 km h–1 × 1 hour = 400 km = 400 km

∴ Laju purata = (300 km + 400 km)

2 jam ∴ Average speed =

(300 km + 400 km)2 hours

= 700 km2 jam = 350 km j–1 =

700 km2 hours = 350 km h–1

(b) Berapakah halaju purata kapal terbang itu? What is the average velocity of the plane?

Dari (a); From (a);

JarakOA = 300 km DistanceOA = 300 kmJarakAB = 400 km DistanceAB = 400 km

∴ SesaranOB = (300 km)2 + (400 km)2 ∴ DisplacementOB = (300 km)2 + (400 km)2 = 500 km = 500 km

∴ Halaju purata = SesaranMasa

∴ Average velocity = Displacement

Time

= 500 km

2 j = 500 km

2 h

= 250 km j–1 = 250 km h–1

400 km j–1

300 km j–1

A

O

B

Contoh/Examples 1

Bacaan meter had laju bagi sebuah kereta yang bergerak ke arah utara menunjukkan 80 km j–1. Sebuah kereta yang lain bergerak pada 80 km j–1 menuju ke selatan. Adakah kelajuan kedua-dua kereta itu sama? Adakah halaju kedua-dua kereta itu sama? Terangkan jawapan anda.The speedometer reading for a car travelling north shows 80 km h–1. Another car is travelling at 80 km h–1 towards the south. Is the speed of both cars the same? Is the velocity of both cars the same? Explain your answer.

Kelajuan kedua-dua kereta itu adalah sama iaitu 80 km j–1 tetapi halaju adalah tidak sama kerana arah

kedua-dua kereta itu berbeza.

The speed of both cars is the same, that is, 80 km h–1 but the velocity is not the same because the cars are in different

directions.

Contoh/Examples 2

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Pecutan sifar bermaksud suatu objek berada dalam keadaan pegun atau bergerak pada halaju malar, a = 0

Zero acceleration means an object is at rest or is moving at a constant velocity, a = 0

‘a positif ’ (pecutan): Halaju suatu objek bertambah dari halaju awal, u, kepada halaju akhir, v yang lebih tinggi.

‘positive a’ (acceleration): The velocity of an object increases from an initial velocity, u, to a higher final velocity, v.

‘a negatif ’ (nyahpecutan): Halaju suatu objek berkurang dari halaju awal, u, kepada halaju akhir, v yang lebih rendah.

‘negative a’ (deceleration): The velocity of an object decreases from an initial velocity, u, to a lower final velocity, v.

Seorang penunggang basikal bermula dari keadaan rehat dan menambahkan halajunya pada kadar seragam sehingga dia mencapai halaju 4.0 m s–1 dalam 5.0 s. Berapakah purata pecutannya?A cyclist starts from rest and increases his velocity at a constant rate until he reaches a velocity of 4.0 m s–1 in 5.0 s.What is his average acceleration?

Halaju awal/Initial velocity = 0

Halaju akhir/Final velocity = 4.0 m s–1

Masa yang diambil/Time taken = 5.0 s

pecutan, a = v – u

t acceleration, a = v – u

t

a = (4.0 – 0) m s–1

5.0 s

= 0.8 m s–2

1 Pecutan, a, didefinisikan sebagai kadar perubahan halaju .

Acceleration, a, is defined as the rate of change of velocity .

2 Formula dan unit SI: Formula and SI unit:

Pecutan, a = Perubahan halaju

Masa yang diambil Acceleration, a = Change in velocity

Time taken

= Halaju akhir, v – Halaju awal, u

Masa yang diambil, t = Final velocity, v – Initial velocity, u

Time taken, t

= v – u

t = v – u

t

Unit SI/SI unit: m s–2

Definisi pecutan dan nyahpecutanDefinition of acceleration and deceleration

Contoh/Examples


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1 Perhatikan gerakan sebuah kereta dalam Rajah (a) dan Rajah (b) yang merupakan gambar stroboskop. Observe the motion of the car in Diagram (a) and Diagram (b) which are stroboscopic pictures.

Rajah (a)/Diagram (a)

Rajah (b)/Diagram (b)

(i) Huraikan perubahan halaju sebuah kereta dalam Rajah (a). Adakah kereta memecut atau menyahpecut? Describe the changes in velocity of the car in Diagram (a). Is the car accelerating or decelerating?

Jarak antara dua gambar berturut-turut bertambah. Halaju kereta itu bertambah. Kereta itu memecut.

The distance between two consecutive images increases. Velocity of the car is increasing. The car accelerates.

(ii) Huraikan perubahan halaju sebuah kereta dalam Rajah (b). Adakah kereta memecut atau menyahpecut? Describe the changes in velocity of the car in Diagram (b). Is the car accelerating or decelerating?

Jarak antara dua gambar berturut-turut berkurang. Halaju kereta itu berkurang. Kereta itu mengalami

nyahpecutan.

The distance between two consecutive images decreases. Velocity of the car is decreasing. The car decelerates.

2 Isikan tempat kosong: Fill in the blanks:

(a) Laju malar 10 m s–1 Jarak sejauh 10 m dilalui setiap saat

A constant speed of 10 m s–1 A distance of 10 m is travelled every second

(b) Halaju malar –10 m s–1 Sesaran sejauh 10 m yang dilalui setiap saat dalam arah bertentangan

A constant velocity of –10 m s–1 A displacement of 10 m is travelled every second in the opposite direction.

(c) Pecutan malar 4 m s–2 Halaju meningkat dengan 4 m s–1 setiap saat

A constant acceleration of 4 m s–2 Velocity increases by 4 m s–1 every second

(d) Nyahpecutan malar 4 m s–2 Halaju berkurang dengan 4 m s–1 setiap saat

A constant deceleration of 4 m s–2 Velocity decreases by 4 m s–1 every second

(a) (b)

(a) (b)

Contoh/Examples


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Hubung kait Sesaran, Halaju, Pecutan dan MasaRelating Displacement, Velocity, Acceleration and Time

Jangka masa detik:Ticker timer:

• Iadisambungkebekalankuasa arus ulang-alik 50 Hz. Apabila dihidupkan, bilah pengetuk akan bergetar 50 kali sesaat.

It is connected to an alternating current supply of 50 Hz. When it is switched on, the iron strip will vibrate 50 times per second.

• Masadiambiluntukmembuat50titikpadapitadetikialah1saat.Jadi,selangmasaantaraduatitikyang

berturutan ialah 150

s = 0.02 s.

The time taken to make 50 dots on the ticker tape is 1 second. Hence, the time interval between 2 consecutive dots

is 150

s = 0.02 s.

• 1detikdidefinisikansebagai selang masa antara 2 titik .

1 tick is defined as the time interval between 2 dots .

6 – 12 V a.c.

Jangka masa detikTicker timerTroli dinamik

Dynamic trolley

Aktiviti 1 Kaedah pengiraanActivity 1 Method of calculation

Menyiasat gerakan dalam makmal iaitu menentukan jarak / sesaran, kelajuan / halaju, masa dan pecutan /nyahpecutanTo investigate motion in laboratory to determine distance / displacement, speed / velocity, time and acceleration /deceleration

10 ticks/detik

8.0 cm BA


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LANGKAH 1: Menentukan masa diambil untuk 1 detik.STEP 1: Determination of time taken for 1 tick.

(a) Masa yang diambil untuk 50 detik = 1 saat

(b) Masa yang diambil untuk 1 detik = 0.02 s

(c) Masa yang diambil dari A ke B = 10 detik

= 0.2 s

(a) Time taken for 50 ticks = 1 second

(b) Time taken for 1 tick = 0.02 s

(c) Time taken from A to B = 10 ticks

= 0.2 s

LANGKAH 2: Menentukan sesaranSTEP 2: Determination of displacement

Sesaran suatu objek ditentukan dengan mengukur panjang pita detik yang ditarik melalui jangka masa detikThe displacement of the object is determined by measuring the length of the ticker tape that is pulled through the ticker time

Sesaran A ke B = 8.0 cm

Displacement from A to B = 8.0 cm

LANGKAH 3: Menentukan halajuSTEP 3: Determination of velocity

Halaju, v = SesaranMasa

= 8.0 cm0.2 s

= 40.0 cm s–1

Velocity, v = Displacement

Time

= 8.0 cm0.2 s

= 40.0 cm s–1

LANGKAH 4: Menentukan pecutanSTEP 4: Determination of acceleration

1.5 cm 3.5 cm 5.5 cm 7.5 cm

A υ νB C D E

Dari jalur pertama: Halaju pertama, u, pada ABFrom the first strip: Initial velocity, u, at AB

uAB = 1.5 cm0.2 s

= 7.5 cm s–1

Dari jalur terakhir: Halaju terakhir, v, pada DEFrom the final strip: Final velocity, v, at DE

vAB = 7.5 cm0.2 s

= 37.5 cm s–1

Selang masa, bagi perubahan halaju, tThe time interval, t, for the change in the velocity

t = (4 – 1) × 0.2 s = 0.6 s

Pecutan/Acceleration,

a = (37.5 – 7.5) cm s–1

0.6 s = 50.0 cm s–2

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1

Arah pergerakanDirection of motion

0.2 cm 1.4 cm

Berdasarkan rajah di atas, hitungkan pecutan objek itu.Based on the diagram above, calculate the acceleration of the object.

Penyelesaian/Solution

u = 0.2 cm0.02 s

= 10 cm s–1

v = 1.4 cm0.02 s

= 70 cm s–1

t = (5 – 1) × 0.02 s = 0.08 s

a = (70 – 10) cm s–1

0.08 s = 750 cm s–2 = 7.5 m s–2

2

BA C D E2.0 cm 4.0 cm 6.0 cm 8.0 cm

Arah pergerakanDirection of motion

Rajah di atas menunjukkan suatu pita detik yang mengandungi 5 detik untuk setiap selang AB-BC-CD dan DE. Hitungkan pecutan objek itu.The diagram above shows a ticker tape contains 5 ticks for every interval AB-BC-CD and DE. Calculate the acceleration of the object.


u = 8.0 cm0.1 s

= 80.0 cm s–1

v = 2.0 cm0.1 s

= 20.0 cm s–1

t = (4 – 1) × 0.1 s = 0.3 s

a = (20.0 – 80.0)

0.3 s = –200 cm s–2 = –2.0 m s–2

3 Rajah di sebelah menunjukkan carta pita detik bagi sebuah troli yang bergerak. Frekuensi bagi jangka masa detik ialah 50 Hz. Setiap jalur pita merupakan panjang 10 detik. The diagram on the right shows a ticker tape chart for a moving trolley. The frequency of the ticker-timer used is 50 Hz. Each strip of the tape is a 10-ticks length.

(a) Berapakah selang masa antara dua titik?What is the time interval between two dots?

0.02 s

(b) Berapakah selang masa untuk satu jalur?What is the time interval for one strip?

0.02 × 10 = 0.2 s

(c) Berapakah halaju awal?What is the initial velocity?

u = 2.0 cm0.2 s

= 10.0 cm s–1

(d) Berapakah halaju akhir?/What is the final velocity?

v = 12.0 cm

0.2 s = 60.0 cm s–1

(e) Berapakah selang masa yang diambil untuk berubah dari halaju awal kepada halaju akhirnya?What is the time interval to change from its initial velocity to its final velocity?

t = (11 – 1) × 0.2 s = 2.0 s

(f) Berapakah pecutan objek itu?/What is the acceleration of the object?

a = (60.0 – 10.0) cm s–1

2.0 s = 25.0 cm s–2

12.0

Panjang 10 detik/cm10-tick length/cm

0

2.0

4.0

6.0

8.0

10.0

Detik/Ticks

Jalur pitaStrip of the tape

t = 5 detik × 0.02 = 0.1 s

KBAT

Latihan/Exercises


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Selesaikan masalah pada gerakan linear dengan pecutan seragamSolve problems on linear motion with uniform acceleration

(1) v = u + at (2) s = u + v2 t (3) s = ut + ½ at2 (4) v2 = u2 + 2as

di mana/where:s: sesaran/displacementu: halaju awal/initial velocity

v: halaju akhir/final velocitya: pecutan/acceleration

t: masa/time

Aktiviti 2 Untuk mengenal pasti jenis gerakanActivity 2 To identify the types of motion

PITA DETIK DAN CARTATICKER TAPE AND CHARTS

Panjang/Length (cm)

Arah gerakanDirectionof motion

Detik/Ticks

Jenis gerakan: Type of motion:

Laju malar

Constant speed

Jarak dilalui antara dua titik berturutan:Distance between two consecutive dots:

Sama

equal

1 2 3 4 5 6

4.0

0.5

1.2

1.9

2.6

3.3

Panjang/Length (cm)


Detik/Ticks

• Jarakantaraduatitikberturutan bertambah secara seragam.

The distance between two consecutive dots increases

uniformly.

• Halajuobjekitu bertambah secara seragam.

The velocity of the object increases uniformly.

• Objekitubergerakpada pecutan seragam.

The object moves at a uniform acceleration .

Panjang/Length (cm)


Detik/Ticks

• Jarakantaraduatitikberturutan berkurang secara seragam.

The distance between two consecutive dots decreases

uniformly.

• Halajuobjekitu berkurang secara seragam.

The velocity of the object decreases uniformly.

• Objekitubergerakpada nyahpecutan seragam.

The object moves at a uniform deceleration .

(i)

(ii)

(iii)


2

UNIT



1 Sebuah kereta memecut dari keadaan rehat ke 25 m s–1 dalam 4 s. Cari pecutan kereta itu.A car accelerates from rest to 25 m s–1 in 4 s. Find the acceleration of the car.


u = 0, v = 25 m s–1, t = 4 s, a = ?

v = u + at a = v – ut

= 25 m s–1 – 04 s

= 6.25 m s–2

2 Sebuah kereta memecut dari keadaan rehat pada 3 m s–2

sepanjang suatu jalan lurus. Berapakah sesaran yang dilalui oleh kereta itu selepas 4 s?A car accelerates from rest at 3 m s–2 along a straight road. How far has the car travelled after 4 s?

Penyelesaian/Solutionu = 0, a = 3 m s–2, t = 4 s, sesaran/displacement = ?

s = ut + 12

at2

= 0 + 12

(3 m s–2)(4 s)2 = 24 m

3 Sebuah kereta bergerak dengan halaju 20 m s–1 sepanjang jalan lurus. Pemandu itu menekan brek selama 5 s. Ia

menyebabkan nyahpecutan 3 m s–2, berapakah halaju akhir kereta itu?A car is travelling at 20 m s–1 along a straight road. The driver brakes for 5 s. This causes a deceleration of 3 m s–2. What is the final velocity of the car?

Penyelesaian/Solutionu = 20 m s–1, t = 5 s, a = –3 m s–2, v = ?v = u + at = 20 m s–1 + (–3 m s–2)(5 s) = 5 m s–1

4 Sebuah kereta bergerak dengan halaju malar 40 m s–1. Pemandu ternampak suatu penghalang di hadapannya dan dia segera menekan brek. Dia dapat memberhentikan keretanya dalam masa 8 s. Jarak

antara penghalang itu dari kereta apabila pemandu ternampak penghalang itu ialah 180 m. Berapakah jarak penghalang itu dari kereta selepas ia berhenti?A car was moving at a constant velocity of 40 m s–1. The driver saw an obstacle in front and he immediately stepped on the brake pedal. He managed to stop the car in 8 s. The distance of the obstacle from the car when the driver spotted it was 180 m. How far was the obstacle from the car after it stopped?


u = 40 m s–1, v = 0, t = 8 s, s = ?

s = u + v2 t = (40 m s–1 + 0)(8 s)

2 = 160 m

Jarak penghalang dari kereta itu selepas berhenti / The distance of the obstacle from the car after it stopped = 180 m – 160 m= 20 m

t = 4 s

0 m s–1

Sesaran / Displacement

a = 3 m s–2

t = 5 s

20 m s–1 v

a = –3 m s–2

KBAT

Latihan/Exercises


2

UNIT



Daripada graf gerakan, anda akan memahami:From motion graphs, you will understand:(i) berapa jauh yang telah dilalui oleh sesuatu objek – (jarak, sesaran) how far an object has travelled – (distance, displacement)(ii) berapa cepat ia bergerak – (laju, halaju) how fast it is moving – (speed, velocity)(iii) perubahan halaju terhadap masa – (pecutan / nyahpecutan) change of velocity with time – (acceleration / deceleration)

Lakar dan tafsir graf sesaran-masaPlot and interpret displacement-time graph

Rajah di sebelah kanan menunjukkan gerakan sebuah kereta pada masa yang berlainan.The diagram on the right shows the motion of a car with respect to time.(a) Lakarkan graf sesaran-masa kereta itu. Plot a displacement-time graph for the car.(b) Hitungkan kecerunan graf. Calculate the gradient of the graph.

Kecerunan/Gradient = (50 – 0) m

5 s = 10 m s–1

(c) Apakah unit bagi kecerunan? What is the unit of this gradient?

m s–1

(d) Apakah kuantiti fizik yang ditunjukkan oleh unit ini?What is the physical quantity shown by this unit?

Halaju

Velocity

0 mKedudukan:Position

10 m 20 m 30 m 40 m 50 m

t = 0 s 1 s 2 s 3 s 4 s 5 s

00

10

20

30

40

50

1 2 3

Masa/Time (s)

Kedu

duka

n/Po

sitio

n (m

)

4 5

Kecerunan graf = HalajuThe gradient = Velocityof the graph

Membuat kesimpulan daripada bentuk graf sesaran-masaDeduction from the shape of a displacement-time graph

Objek pada keadaan rehat

Object at rest

Sesaran/Displacement,s/m

t/s0

Objekberadadalamkeadaan rehat kerana ia berada

pada kedudukan yang sama pada bila-bila masa.

The object is at rest because it is at the same position at any time.

Halaju = kecerunan grafVelocity = gradient of the graph

= 0 m s–1

Graf sesaran-masaDisplacement-time graph

MENGANALISIS GRAF GERAKANANALYSING MOTION GRAPH2.2


2

UNIT



Objek bergerak dengan halaju

malarObject moving at constant velocity

t/s0

20

5


• Objekbergerakpadahalaju malar kerana sesaran bertambah secara seragam dalam setiap saat.

Object travels at constant velocity because displacement increases constantly in every second.

• Garislurusgrafmempunyaikecerunanyang tetap .

The straight line of the graph has a constant gradient. • Halaju =kecerunan

Velocity = gradient

= 4 m s–1

Objek bergerak dengan pecutan

Object moving with acceleration

t/s0


• Objekbergerakdenganpecutankeranakadarperubahan

sesaran bertambah . Object moves with acceleratiom because the rate of change of

displacement is increasing .

• Kecerunanlengkungan bertambah , dan ini

menunjukkan halaju bertambah.

The gradient of the curve is increasing showing that the

velocity is increasing.

• Objekmengalami pecutan .

The object experiences acceleration .

Menentukan jarak, sesaran dan halaju dari graf sesaran-masaDetermine distance, displacement and velocity from the displacement-time graphRajah di bawah menunjukkan graf sesaran-masa bagi suatu objek.The diagram below shows a displacement-time graph of an object.

Berdasarkan graf,Based on the graph,

(a) Hitungkan halaju objek antara calculate the velocity of the object between (i) A dan/and B (ii) B dan/and C (iii) C dan/and D

v = 20 m10 s

v = 0 v = – 20 m5 s

= 2 m s–1 = –4 m s–1

(b) Gambarkan gerakan objek itu antaraDescribe the motion of the object between

(i) A dan B: halaju malar (ii) B dan C: dalam keadaan rehat

A and B: constant velocity B and C:

at rest

(iii) C dan D: halaju malar tetapi objek bergerak pada arah yang bertentangan

C and D: constant velocity but the object moves in opposite direction

(c) Cari/Find (i) jumlah jarak/total distance (ii) jumlah sesaran/total displacement

= (20 + 0 + 20)m = 40 m = (20 + 0 – 20)m = 0

Sesaran/mDisplacement / m

B C

DA0

20

10 30 35Masa/sTime / s


2

UNIT



Lakar dan tafsir graf halaju-masaPlot and interpret velocity-time graph

Rajah menunjukkan kereta bergerak dari rehat dalam suatu garis lurus.The diagram shows the car move from rest in a straight line.(a) Lakarkan graf halaju-masa bagi

kereta ini. Plot the velocity-time graph for the car.

(b) Hitungkan kecerunan graf. Calculate the gradient of the graph.

KecerunanGradient

= (10 – 0) m s–1

(5 – 0) s = 2 m s–2

(c) Apakah unit bagi kecerunan ini? What is the unit of this gradient?

m s–2

(d) Apakah kuantiti fizik yang ditunjukkan oleh unit ini?What is the physical quantity shown by this unit?

pecutan

acceleration

t = 0 s 1 s 2 s 3 s 4 s 5 s

0 m s–1 2 m s–1 4 m s–1 6 m s–1 8 m s–1 10 m s–1Halaju:Velocity

Graf halaju-masaVelocity-time graph• Kecerunangraf=pecutanataunyahpecutan The gradient of graph = acceleration or deceleration• Luasdibawahgraf=sesaran The area under the graph = displacement

00

2

4

6

8

10

1 2 3 4 5

Masa/Time(s)

Halaju/Velocity(m s–1)

Graf halaju-masaVelocity-time graph

(d) Hitungkan/Calculate (i) laju purata (ii) halaju purata gerakan zarah itu. the average speed the average velocity of the moving particle.

= jumlah jarak

masa

= 40 m35 s

= 1.14 m s–1

= total distance

time

= 40 m35 s

= 1.14 m s–1

= sesaranmasa

= 0

= displacement

time

= 0


2

UNIT



Membuat kesimpulan daripada bentuk graf halaju-masaDeduce from the shape of velocity-time graph

ObjekberadadalamkeadaanrehatObject at rest

Objekbergerakdenganhalaju malar

Object moves with constant velocity

ObjekbergerakdenganpecutanmalarObject moving with constant

acceleration

Objekbergerakdengannyahpecutan malar

Object moves with constant deceleration

Nota/Notes:• Dalamanalisisgerakanlinear,jikahalajusuatuzarahadalahsifar,inibermaknazarahituberhentibergerak. In linear motion analysis, if the velocity of a particle is zero, it means that the particle has stopped moving. • Jikahalajuzarahitumenjadinegatif,makazarahitubergerakdalamarahbertentangandenganarahgerakanawalnya. If the velocity of the particle becomes negative, then the particle is moving opposite to its earlier direction of motion.

• Kecerunan=pecutan= 0

Gradient = acceleration = 0

• Luasdibawahgraf=sesaran= 0

Area under the graph = displacement = 0

• Objekberadadalamkeadaan rehat .

Object is at rest .

• Kecerunan/Gradient = pecutan/acceleration = 0

• Luasdibawahgraf=sesaran= 10 m s–1 × 2 s = 20 m

Area under the graph = displacement = 10 m s–1 × 2 s = 20 m

• Sesarandilalui= 20 m

Displacement travelled = 20 m

• Objekbergerakdenganhalaju malar

Object moves with constant velocity

• Kecerunan/Gradient = malar/constant = 18 m s–1

3 s = 6 m s–2

• Pecutan/Acceleration = 6 m s–2

• Luasdibawahgraf/Area under the graph

= 12 (18 m s–1)(3 s) = 27 m

• Sesarandilalui/Displacement travelled = 27 m

• Objekbergerakdenganpecutan malar

Object moves with constant acceleration

• Kecerunangrafadalah malar dan negatif

The gradient of the graph is constant and negative

• Objekitubergerakdengan nyahpecutan seragam

The object is moving with uniform deceleration

v/m s-1

t/s0

v/m s-¹

t/s0 2

10

v/m s-1

t/s0

18

3

0

v/m s-¹

t/s


2

UNIT



Menentukan jarak, sesaran, halaju dan pecutan daripada graf halaju-masaDetermine distance, displacement, velocity and acceleration from a velocity-time graph

Berikut menunjukkan graf halaju-masa bagi sebuah kereta. Berdasarkan graf, The following shows the velocity-time graph of a car. Based on the graph,

Halaju/Velocity / m s-1

K

L M

N

OJ0

20

–10

10

10 20 30 4035 45 50Masa/sTime / s

(a) hitungkan pecutan kereta itu bagi / calculate the acceleration of the car for (i) JK

a = 20 m s–1

10 s = 2 m s–2

(ii) KL

a = – (20 – 10) m s–1

(20 – 10) s = –1 m s–2

(iii) LM a = 0

(iv) MN

a = – 20 m s–1

10 s = –2 m s–2

(b) Nyatakan jenis gerakan kereta itu bagi State the types of motion of the car for

(i) JK : pecutan malar (ii) KL : nyahpecutan malar (tetap)

constant acceleration constant deceleration

(iii) LM : halaju tetap / malar (iv) MN : nyahpecutan malar (tetap)

constant velocity constant deceleration

(c) Hitungkan jumlah sesaran yang dilalui oleh kereta itu semasa Calculate the total displacement travelled by the car during (i) gerakan bagi 10 s yang pertama (ii) kereta bergerak dengan halaju seragam the first 10 s of motion the car moves with uniform velocity

Sesaran Displacement

= 12

(20 m s–1)(10 s) Sesaran (LM) Displacement

= 10 m s–1 × 10 s = 100 m

= 100 m

(iii) gerakan bagi 10 s yang terakhir the last 10 s of motion

Sesaran / Displacement = 0

(d) Hitungkan / Calculate (i) jumlah jarak bagi keseluruhan perjalanan / the total distance for the whole journey Jarak / Distance

= 12

(10)(20) + 12

(10 + 20)10 + (10)(10) + 12

(5)(10) + 12

(10)(10)

= (100 + 150 + 100 + 25 + 50) m = 425 m

(ii) jumlah sesaran bagi keseluruhan perjalanan. the total displacement for the whole journey. Sesaran / Displacement

= [ 12

(10)(20) + 12

(10 + 20)10 + (10)(10) + 12

(5)(10)] – 12

(10)(10)

= (100 + 150 + 100 + 25) – 50= 325 m

KBAT


2

UNIT



Menyelesaikan masalah gerakan linear dengan pecutan seragamSolve problems on linear motion with uniform acceleration

1 Hitungkan/Calculate (i) halaju bagi OP, QR dan RS

velocity of OP, QR and RS (ii) sesaran/displacement Penyelesaian/Solution:

(i) OP: halaju/velocity = 20 m2 s

= 10 m s–1

QR: halaju/velocity = – 20 m2 s

= –10 m s–1

RS: halaju/velocity = – 10 m1 s

= –10 m s–1

(ii) s = (20 + 0 – 20 – 10)m = –10 m

2 Hitungkan/Calculate (i) pecutan bagi OA dan BC acceleration of OA and BC (ii) jumlah sesaran/total displacement

Penyelesaian/Solution:

(i) OA: pecutan acceleration

= 10 m s–1

10 s = 1 m s–2

BC: pecutan acceleration

= – 10 m s–1

5 s = –2 m s–2

(ii) Jumlah sesaran Total displacement

= 12

(25 + 10)s (10 m s–1)

= 175 m

Halaju / m s-1Velocity / m s-1

A B

CO0

10

5

5 10 15 20 25t/s

Kesimpulan/Conclusion 1 Kecerunan graf s melawan t memberi halaju suatu objek.

Gradient of the graph s against t gives the velocity of an object. 2 Kecerunan graf v melawan t memberi pecutan suatu objek.

Gradient of the graph v against t gives the acceleration of an object. 3 Luas di bawah graf v melawan t memberi sesaran yang dilalui oleh objek.

Area under the graph v against t gives the displacement travelled by the object.

(e) Hitungkan / Calculate (i) laju purata / the average speed (ii) halaju purata / the average velocity

Laju purata / Average speed Halaju purata / Average velocity

= 425 m45 s

= 9.44 m s–1 = 325 m45 s

= 7.22 m s–1

P Q

R

S

O0

20

10

–10

8 t/s21 43 65 7



2

UNIT



Ringkasan bagi bentuk graf gerakanSummary of shapes of motion graphs

GrafGraph

s melawan ts against t

v melawan tv against t

a melawan ta against t

Halaju sifarZero velocity

s

t0

v

t0

Halaju negatifNegative velocity

s

t0

v

t0

Halaju seragamUniform velocity

s

t0

v

t0

a

t0

Pecutan seragamUniform acceleration

s

t0

v

t0

a

t0

Nyahpecutan seragamUniform deceleration

s

t0

v

t0

a

0 t


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