physics 2008 jc prelims

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2008 ACJC H1 P1 and P2 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 D A D D A B D A D D C A D B D Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30 C B A A B B A D C A C B C C D 1(a)

the tesla measures magnetic flux density which is defined as B =LIF

therefore the tesla in SI units is kg s-2 A-1

(b) (i) % uncertainty in E = E

E (100) = (FF +

AA +

ee +

LL ) (100)

= (100

5 + 6--6

10 x 1.04 x100.09 +

5.00.5 +

2.000.01 ) (100)

= 24.15 % = 24.2 %

(ignore the ; add in for students if missed out and annotate with "BOD" benefit of

doubt) (ii)

EE (100) = 24.15 %

E = 0.2415 (3.846 x 1010) Pa

= 0.9289 x 1010 Pa = 0.9 x 1010 Pa ( to 1 sig. fig )

he should expressed value of E as E = (3.8 0.9) 1010 Pa

2

2(a) (i) The e.m.f. of 2.0 V for a source means that 2 J of work done in

transforming non-electrical energy into electrical energy per coulomb charge passes through it.

Or It can also be defined as the 2 J of energy transferred by a source in driving one coulomb charge round a complete circuit

(ii) P.d. of 1.5 V across a resistor means that 1.5 J of electrical energy changed to some other forms of energy when one coulomb charge passes from through the resistor.

or defined as the rate of transformation of electrical energy to other forms of

energy is 1.5 W for every ampere of current passing through the resistor

(b) (i) emf = I (R1 + R2) = (200 x 10-6) x(15 + 10) x 103 = 5.0 V

(ii)

emf = I [Rv R1/(Rv+ R1) + R2] correct expression of R for 15 k // with voltmeter Rv

sub 5.0 V = (250 x 10-6) [15 Rv /(Rv+ 15) + 10]x 103 solving Rv = 30 k

3(a) The 2 waves have a constant phase difference between each other (b) When the 2 waves arrive at the detector in phase, they will interfere

constructively, hence maximum intensity

When the 2 waves arrive at the detector out of phase by , they will interfere destructively, hence minimum intensity

(c) Distance L1 to D = 30.41 m Distance L2 to D = 33.54 m Path Difference = 3.13 m (d) The longest wavelength is when Path Difference = 1 x wavelength Lowest Frequency = 330/3.13 = 105.4 Hz

V

15 k 10 k

A

Rv

3

4(a) A wave can behave with properties of a particle and a particle, the properties

of a wave.

But we can never observe them simultaneously. (b)(i) E = mv2 Hence p2 = 2mE Hence de Broglie's wavelength, = h/p Therefore

mEh

2=

(ii) 1.17 x 10-15 m (iii) Change in energy = 7.5 eV 3.2 eV = 4.3 eV E = hc/ p = h/ Hence E = pc p = 6.88 x 10-19 /3.0 x 108 = 2.29 x 10-27 kg m-1 5a With friction: COE, gain in KE + WD by friction = loss in GPE,

X at lowest pt max PE loss; X is nearest to point of release compared to Y & Z lowest WD by friction max KE gain Max KE (initial KE = 0)

b(i) From point of release to Z, gain in KE = loss in GPE WD by friction Bead just missed reaching loss in GPE WD by friction < 0 Energy lost to friction > loss in GPE = (50.0 103)(9.81)(0.82) = 0.40221 J energy lost to friction = 0.403 J (to 3 sf)

(ii) Energy lost to friction = WD by frictional force F = F (total distance travelled on the track) (1.26 102 ) (total distance travelled) > 0.40221 total distance travelled > 31.92 m

total distance travelled on the curved track just before reaching Z = 32.0 m c(i) Track and Toy B lubricated, hence average frictional force along track is 2.1 103 N hence

difference in energy loss between lubricated and normal condition = [(1.26 102 ) (2.1 103 )] (total distance travelled)

= [0.0105] (31.92) = 0.33516 J Since frictional force is less when system is lubricated, this energy difference is

becomes the KE of Toy B. ) Hence m vB2 = 0.33516 speed of Toy B at Z is vB = 3.66 m s-1

(ii) Since Toy Z and Toy B are identical, a head-on elastic collision will transfer all of Toy Bs kinetic energy to Toy Z at point Z.

Since surface is horizontal, initial speed (horizontal) of Toy Z = 3.66 m s1 Consider y-dirn, 0.40 = 0 + (9.81) t2 hence t = 0.2856 s horizontal distance, d = (3.66)(0.2856) = 1.045 m ]

4

6. (a) Resultant force in all directions is zero. Resultant torque about all/any axes is zero. (b) i. When a single girder is lifted at constant velocity

Tension in AB = Weight of girder = 500 (9.81) = 4910 N (3 sig fig)

ii. Considering forces acting on point B

Using the sine rule:

sin 55 sin 70AB

o oTT =

(3 sig fig) 4280 NT = iii. Considering the system of the Cab, Jib and Cable AC and taking moments

about H

Since crane would still be in equilibrium, Clockwise Moments = Anti-Clockwise Moments

TAB (9.0) + 2500(9.81)(4.5) = 20000(9.81)(2.0) TAB = 31.3 kN (3 sig fig) iv.

Maximum no of girders ( )( )331.3 10 6.4 6

9.81 500= = = (must round down)

v. 1) Weight of Jib at E 2) Tension at A acting along AB 3) Tension at A acting along AC 4) Reaction at D (with components acting up and to the right) Subtract 1 mark for each missing / incorrectly drawn force

vi Angle DAB 1

9.0tan 34.7013

o = =

Angle CAB 1

9.0 3.5tan 54.259.0

o + = =

Hence angle that AC makes with the jib is 19.55o (shown) vii When the crane supports 5 girders, it is in equilibrium and

TAB = weight of 5 girders

Considering the free body of the Jib and taking moments about D, Clockwise Moments = Anti-Clockwise Moments

5(500)(9.81)(9.0) + 2500(9.81)(4.5) = TAC (sin 19.55o)( 2 29 13+ )

TAC = 62.6 kN viii When the speed in raising the load is increasing, there must be a resultant

upward force on the girder. As such, the magnitude of tension in AB would need to be greater than the weight of the girder(s) lifted.

As such, there would be a greater turning moment about point H, making the crane less stable

T TAB 70o

T

OR by resolving forces vertically, 2T sin 35o = 500 x 9.81

5

7a Wavelength distance betw 2 points in phase

Frequency no. of complete waves passing through a fixed point per unit time. b Distance traveled by a wave in time T is one wavelength By definition speed = distance traveled over time Hence v = /T = f c Marks awarded for each correct diagram TW - The vibration of particles in the wave is perpendicular to the direction of travel

of the wave

LW - The vibration of particles in the wave is parallel to the direction of travel of the wave

d No net transfer of energy Amplitude of vibration varies with position Every particle within one wavelength varies in phase from each other e(i) Graph correct (ii) All 5 positions of nodes labeled correctly (iii) When current flows from fixed point to pulley, magnetic force acts upwards.

When current flows from pulley to fixed points, magnetic force acts downwards As the current changes direction and magnitude periodically, the direction of

magnetic force changes direction periodically,

Hence wire vibrates (iv) As the wire vibrates, a wave is formed. The initial wave and the reflected wave from

the pulley (or fixed point) will meet.

Wavelength of the traveling waves depends on the speed which is fixed and the frequency of the source.

SW occurs when the wavelength of the wave formed =

nl

. (n is the number of loops.)

6

8 (a) (i) A photon is a quantum/discrete packet of electromagnetic radiation energy.

(ii) For light of different intensity but same frequency, the energy of the photon remains

the same. Photoelectric emission is the result of direct interaction between each photon and

an electron and the entire energy hf of the photon is absorbed by the electron instantaneously and the photon ceases to exist. Hence, instantaneous emission of electrons occurs.

(iii) 2max

12mv hf =

Accept maxE hf = only if is correctly defined to be the maximum kinetic energy of emitted photoelectron.

maxE

Also accept in place of hf0 , provided f0 is correctly defined to be the threshold frequency, and the entire term is referred to as the work function. hf0

By Einsteins photoelectric equation, the maximum kinetic energy of emitted photoelectrons depends on the frequency of the incident light. Hence increasing the frequency of incident light will increase the maximum kinetic energy of the emitted photoelectrons.

(b) (i) The work function is the minimum energy required to remove an electron from the surface of the metal,

hence it is 3.616 x 10-19 J (no explanation, no credit) (ii) 2

max12

hcmv = 8

20 197

(3.0 10 )3.62 10 3.616 10(5.0 10 )h

=

346.63 10 J sh = (c) (i) 2

max12

hcmv = 34 8

2 1max 7

1 (6.63 10 )(3.0 10 ) 3.616 102 (4.4 10 )mv

9

=

209.045 10 J=

209.045 10= seV 0.565 VsV =

(ii) 2max

1 ( sin 35 )2 sm v eV =

2 2max

1 sin 352 smv eV =

20 2 19(9.045 10 )sin 35 (1.6 10 ) = sV 0.186 VsV =

7

(d) (i)

(ii)

(iii) Increasing the light intensity simply increases the number of photons falling on the metal.

However, the incident photons still impart the same amount of energy hf to every electron because the frequency f of light is kept constant. This means that the maximum kinetic energy of the emitted photoelectrons will remain unchanged, and hence the stopping voltage also remains unchanged with increasing light intensity.

(e) This is to prevent the incident photons from being absorbed by surrounding air molecules, and hence decreasing the intensity of the incident light.

OR This is to prevent the emitted photoelectrons from colliding with the surrounding air molecules, thus losing some of their kinetic energy, and introducing errors into the measurement of their kinetic energy.

OR The target metal used is usually very reactive, e.g. caesium, sodium or potassium, hence the experiment is conducted in a vacuum to prevent oxidation of the target metal.

Candidates answer.

Anglo-Chinese Junior College Physics Preliminary Examination Higher 1

CANDIDATE NAME CLASS

CENTRE NUMBER

INDEX NUMBER

PHYSICS Paper 2 Structured questions Candidates answer on the Question Paper No additional Materials are required

8866/0221 Aug 2008

2 hours

READ THESE INSTRUCTIONS FIRST Write your Name and Index number in the spaces provided at the boxes above and on all the work you hand in. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Section A Answer all questions. Section B

For examiners use only

Section A

1 / 6

2 / 8

3 / 8

4 / 6

5 / 12

Section B 6 / 20

7 / 20

8 / 20

Total / 80

Answer any two question. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.

This paper consists of 16 printed pages

2

DATA AND FORMULAE

Data speed of light in free space, c = 3.00 108 m s1 elementary charge, e = 1.60 1019 C the Planck constant, h = 6.63 1034 J s unified atomic mass constant, u = 1.66 1027 kg rest mass of electron, me = 9.11 1031 kg rest mass of proton, mp = 1.67 1027 kg acceleration of free fall, g = 9.81 m s2 Formulae uniformly accelerated motion, s = ut + 2

1 at 2

v 2 = u 2 + 2as work done on/by a gas, W = p V hydrostatic pressure, p = g h resistors in series, R = R1 + R2 + resistors in parallel, 1/R = 1/R1 + 1/R2 +

AC/8866/02/08

3 For

Examiners Use

Answer all the questions in the spaces provided. 1 (a) Express the tesla in terms of the SI base units.

[2]

(b) The Young's Modulus E of a material of a wire is given by

E =AeFL

where F = tension exerted on the wire, L = original length of the wire, A = cross-sectional area of the wire and e = extension of the wire.

In determining the Young's Modulus E of a material, a student performs an experiment and makes measurements and records the readings as follows: F = (100 5) N L = (2.00 0.01) m A = (1.04 0.09) x 10-6 m2 e = (5.0 0.5) mm (i) Using the given formula, calculate the percentage uncertainty in E.

Percentage uncertainty in E = ________ [2]

(ii) The student expressed E as 3.846 x 1010 Pa. Although his arithmetic and the

units of E are correct, this statement is unsatisfactory. Expressed his results with its associated uncertainty.

E = __________________ Pa [2]

AC/8866/02/08 [Turn over

4 For

Examiners Use

2 Explain what is meant by (i) a battery has an electro-motive force (e.m.f.) of 2.0 V?

[1]

(ii) the potential difference (p.d.) across a resistor is 1.5 V.

[1] (b) A cell of negligible internal resistance is connected in series with a microammeter of

negligible resistance and two resistors whose resistances are 10 k and 15 k. The current is 200 A. (i) calculate the e.m.f. of the cell

e.m.f. = _________V [2]

(ii) When a voltmeter is connected in parallel with the 15- k resistor, the current in the microammeter increases to 250 A.

1. Sketch a diagram of the modified circuit and 2. Calculate the resistance of the voltmeter.

voltmeter resistance = ________ [4]AC/8866/02/08

5 For Examiners

Use 3 (a) What is meant by two sound sources are coherent? [1]

(b) Two loudspeakers L1 and L2 are driven from a common oscillator so that the wave

emitted from L1 and L2 are in phase. The loudspeakers are arranged as shown below. A detector D is used to detect the sound reaching different points along line AB, which is 30.0 m away from the loudspeakers.

(i) When the detector D is moved from A to B, it is observed that the detected signal passes through a series of maximum and minimum sound intensity. Explain why this happens?

A

30.0 m

L1

5.0 m

Detector,D

15.0 m

L2

B

[2]

(ii) Calculate the path difference of the 2 waves arriving at the detector in the position

shown. [3] (iii) Hence, calculate the lowest frequency of the sound that can cause the detector in the

position shown to detect a maximum intensity. (Take speed of sound to be 330 m s1)

[2]


6 For

Examiners Use 4 (a) Explain what is meant by the term wave-particle duality.

[1]

(b) (i) Show that the de Broglie wavelength of a particle of mass m and kinetic

energy E is given by the expression

mEh

2=

[2] (ii) Calculate the de Broglie wavelength of an electron of kinetic energy

1.0 x 10-18 J.

(c) An electron in an atom initially has an energy 7.5 eV above the ground state energy. It makes a transition to a state with an energy of 3.2 eV above the ground state energy and emits a photon in the process. Determine the momentum of the photon emitted.

De Broglie wavelength = m [1]

Momentum = kg m s-1 [2]

AC/8866/02/08

7 For Examiners

Use 5 At an amusement park, a child gently releases a toy roller coaster, Toy B, at the top of a curved track as shown in Fig. 5 below.

During the journey on the track, the toy roller coaster, Toy B, is subjected to the frictional force due to the toys motion on the track. The magnitude of this frictional force depends on several factors such as the type of material that the track is made from, the material and manner in which the toy as well as the track are made, as well as the speed of the toy on the track. The frictional force between the toy and the curved track may be assumed to have an average value of 1.26 102 N throughout the entire track under normal condition

and 2.1 103 N when lubricated. Mass of Toy B = 50.0 g Distance, H of point Z below point of release of Toy B = 0.82 m.

(a) Explain at which of the labelled point (X, Y or Z) of the track would Toy B has the

maximum kinetic energy.

[2] (b) (i) Point Z is below the point of release of Toy B. If Toy B moves along the track

under normal condition, and just missed reaching point Z, find the energy lost to friction.

(ii) Hence find the total distance travelled by Toy B on the curved track from the point

of release to just before point Z.

Distance = __________ [6]

Fig. 5 Toy roller coaster, Toy Z

distance, d

0.40 m

Point of release Toy roller

coaster, Toy B

Y X

H

Z


8 For Examiners

Use (iii) If the track is lubricated, show that the speed of Toy B at point Z is 3.66 m s1.

(c) If the track is lubricated, Toy B will make a head-on elastic collision with the identical stationary toy roller coaster, Toy Z, at point Z. Determine the horizontal distance d, that Toy Z will hit the horizontal surface, which is at 0.40 m below point Z.

(Note that the diagram shows the position of Toy Z after collision and just before leaving the track.)

[4]

AC/8866/02/08

9 For Examiners

Use Section B Answer TWO questions from this section

6 (a) State the conditions for a rigid body to be in equilibrium.

[2]

(b) The figure below shows a crane being used to lift a load of girders, each of which

has a mass of 500 kg. The jib of the crane has a mass of 2500 kg and the cab has a mass of 20 000 kg. The centre of mass of the jib and the cab are at their midpoints, E and F respectively. The hook B, and the cable may be assumed to have negligible mass. Cables AC and AB are two separate cables. G and H are the left and right edges of the base of the cab respectively. D is the point at which the jib is attached to the cab. Point A is at a height of 9.0m from C and 13.0m from D. Point C is at a distance of 0.5m from the left edge of the cab.

(i) Determine the tension in the cable AB when a single girder is lifted at constant velocity.

Tension = ____________ N [1] (ii) Hence or otherwise determine the tension in cable PBR. Tension = ____________ N [2]


10

(iii) Determine the tension in cable AB which will just topple the crane. Tension = ___________ N [4] (iv) Hence determine the maximum number of girders which can be lifted without

the crane toppling over. Number = _________ [1] (v) Sketch a labelled free body diagram of the jib showing on it all the external

forces that are acting on the jib. [3] (vi) Show that the angle that cable AC makes with the jib is 19.55. [2] (vii) Determine the force exerted by the cable AC on the cab at C when the crane

supports 5 girders noting that the jib is in equilibrium Force = _______ N [3] (viii) Explain why the crane will be less stable when the speed at which the load is

being raised is increasing. [2]

For Examiners

Use

AC/8866/02/08

11

For Examiners Use 7 (a) State the meaning of wavelength and frequency as applied to wave motion.

[2]

(b) Deduce, from the definition of speed, the equation for the speed of a wave in terms of its wavelength and frequency.

[3]

(c) Illustrate with the help of diagrams to explain the meaning of the terms longitudinal and transverse when applied to a wave.

[4]


12 For Examiners

Use (d) Distinguish between a progressive wave and a stationary wave by completing the table below

Progressive waves Stationary waves

Energy of transfer energy is transported at a speed given by the product of its frequency and wavelength.

Amplitude of vibration the amplitude of vibration is the same at all points

Phase

All particles between consecutive nodes have the same phase

[3]

AC/8866/02/08

13 For Examiners

Use (e) A horizontal steel wire is fixed at one end and is kept under tension by means of weights suspended over a pulley, as shown in Fig 7 .The tension affects the speed with which waves may travel along the wire.

Fig 7

A low voltage alternating supply is connected to the wire between the fixed end and the pulley. The frequency of the alternating supply can be varied. Magnets are placed near to the center of the horizontal section of the wire in order to produce a magnetic field at right angles to the wire.

The tension of the wire is kept fixed as the frequency of the alternating supply is

varied. As the frequency of the supply is varied and at certain frequencies, stationary waves are produced on the wire.

(i) By drawing on Fig 7 above, show how the amplitudes of the points of the

stationary wave on the wire will vary along the wire from the fixed point to the pulley when the frequency is such that the distance between the fixed end and the pulley corresponds to two wavelengths of the wave on the string.

[1] (ii) On your diagram, label the position of the nodes on the wire. [1] (iii) Explain why the wire vibrates.

[3]

(iv) Explain how the standing wave is being formed in this application and why it

only occurs at particular frequencies.

[3]


14 For Examiners

Use 8 (a) In 1887, Heinrich Hertz observed that when a metallic surface is exposed to monochromatic light, electrons may be emitted. He published these observations in the journal Annalen der Physik and it eventually came to be known as the photoelectric effect.

(i) Explain briefly what is meant by a photon.

[1] (ii) Explain why, for a particular metal and for incident light of suitable frequency,

emission of photoelectrons begins almost instantaneously even if the light has low intensity.

[2] (iii) By stating Einsteins photoelectric equation or otherwise, explain why increasing the

frequency of incident light increases the maximum kinetic energy of the emitted photoelectrons.

[2] (b) A clean surface of potassium in a vacuum is irradiated with light of photon energy

3.616 x 1019 J, electrons are found just to emerge, but when light of wavelength 5.000 x 10-7 m is incident, electrons emerge each with a maximum kinetic energy 3.620 x 10-20 J.

(i) State and explain the value of potassiums work function. Express your answer

in joules and to 4 significant figures.

[2]

AC/8866/02/08

15 For Examiners

Use (ii) Hence estimate the value for Plancks constant.

[2] (c) Assume that the same surface of potassium is used but the wavelength of the

incident light is changed to . Note that the cathode and anode used here are plane plates.

74.4 10 m

Determine the voltage that should be applied between the cathode(emitter) and

anode(collector), assumed to be parallel plates, in order to prevent photoelectrons of maximum kinetic energy from reaching the anode, if electrons are emitted

(i) normal to the cathode.

[2] (ii) at an angle of to the surface of the cathode. 35

[3]


16

AC/8866/02/08

For Examiners

Use (d) (i) Sketch a graph to show the photocurrent-potential (I-V) characteristic

obtained from a photoelectric effect experiment. Indicate the stopping voltage on your graph.

[2] (ii) Sketch, on the same graph, the effect of increasing the intensity of the

incident light. [1]

(iii) Explain why the stopping voltage is independent of the intensity of the

incident radiation.

[2] (e) Give one reason for why a photoelectric experiment is usually conducted in an

evacuated vacuum tube.

[1]

8866/01/AJC2008 [Turn over

PHYSICS 8866/01

Higher 1

Paper 1 Multiple Choice 1 hour

Tuesday 16 September 2008 Additional Materials: Multiple Choice Answer Sheet Soft clean eraser Soft pencil (type B or HB recommended) READ THESE INSTRUCTIONS FIRST Write in soft pencil Do not use staples, paper clips, highlighters, glue or correction fluid. Write your name, PDG on the Answer Sheet in the spaces provided. Shade the last 5 digits of your NRIC/FIN without the letter. There are thirty questions on this paper. Answer all questions. For each question there are four possible answers A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in the question paper.

Candidate Name PDG

ANDERSON JUNIOR COLLEGE

This question paper consists of 10 printed pages and 0 blank page.


2 Data speed of light in free space c = 3.00 x 108 m s-1 elementary charge e = 1.60 x 10-19 C the Planck constant h = 6.63 x 10-34Js unified atomic mass constant u = 1.66 x 10-27 kg

rest mass of electron me = 9.11 x 10-31 kg rest mass of proton mp = 1.67 x 10-27 kg acceleration of free fall g = 9.81 m s-2

Formulae

uniformly accelerated motion 221 attus +=

v2 = u2 + 2as work done on/by a gas W = pV hydrostatic pressure p = gh

electric potential r4

Q = V0

resistors in series R = R1 + R2 + resistors in parallel 1/R = 1/R1 + 1/R2 +


3 1 A student takes 6 readings of the diameter of a rod: 5.9 mm, 6.0 mm, 6.1 mm, 5.8 mm,

6.0 mm, 6.2 mm. The actual diameter of the rod is actually 5 mm. Which of the following best describe the errors in the readings?

random error systematic error A low high B low low C high high D high low

2 The capacitance C of a parallel plate capacitor is defined as the charge stored per unit

potential difference between its plates.

= QCV

What is the unit of capacitance, expressed in SI base units?

A CV-1 B C2kg-1m-2s-2 C A2kg-1m-2 D A2kg-1m-2s4

3 A student carries out an experiment to determine the gravitational acceleration, using a pendulum, and obtains a value 9.81 ms-2. The uncertainties in the measurements are shown. Uncertainty in length L of pendulum = 0.7 % Uncertainty in period T of pendulum = 0.1 %

The equation for the period T of pendulum is = 2 LTg

How should the answer for gravitational acceleration be stated?

A -2(9.8 0.1) m s B -2(9.81 0.09) m s C -2(10 8) m s D -2(10 9) m s

4 Which of the following statements is correct?

A When an object is in motion, its velocity and acceleration are always in the same

direction. B When an object is thrown upwards, its acceleration at the highest point is zero. C When velocity of an object is zero, its acceleration can be non-zero. D When acceleration of an object is zero, its velocity is zero.


45 The figure below shows the displacement-time graph of a moving object from a point P.

Which of the following statements correctly describes the motion for the object?

A It is speeding up towards P. B It is slowing down towards P. C It is speeding up away from P. D It is slowing down away from P. 6 A projectile is fired with an initial speed of 51.2 m s-1 at angle 44.5 above the horizontal on

a long flat firing range. Point A is the maximum height attained by the projectile. What is the vertical component of the speed and location of the projectile 1.50 s after firing?

Speed/m s-1 Location A 21.2 Before point A B 21.2 After point A C 35.6 Before point A D 35.6 After point A 7 The 100 kg mass, which rests on a frictionless table, is attached to a 1 g mass through an

inextensible string that goes round a smooth pulley. What is the acceleration of the 100 kg mass?

A 9.81 10-5 m s-2 B 9.81 10-2 m s-2 C 9.81 m s-2 D 0 m s-2 8 A trolley moving without friction on an air track collides with an identical stationary trolley

and they move off sticking together. Which of the following about the conservation of energy and momentum is correct?

momentum kinetic energy A conserved conserved B conserved not conserved C not conserved conserved D not conserved not conserved

Time /s

Displacement /m

100 kg

1 g


59 Which of the following pairs of forces is an action-reaction pair?

A The force a ladder leaning on a smooth wall exerts on the wall and the normal reaction

force from the wall. B The force a ladder leaning on a smooth wall exerts on the rough floor and the normal

reaction from the floor. C Weight of a parachutist and the pull of the parachute on him when he is moving with

terminal velocity. D Weight of a floating object and the upthrust acting on it. 10 Two identical bar magnets are stored in a light plastic frictionless cylinder of negligible mass.

When the magnets are arranged as shown in the figure below, the balance reads W. If the mass of each magnet is M, which of the following is correct?

A W = Mg B W = 2Mg C Mg < W < 2Mg D W > 2Mg 11 The diagram shows a uniform inclined beam with one end hinged to a wall A and the other

end is supported by a wire at B. The weight of the beam is W and the tension in the wire is T. The angle EAC is 90. What is the direction of the force exerted by the wall on the beam?

A AB B AC C AD D AE

12 A spring obeying Hookes Law has an unstretched length of 50 mm and a spring constant of

200 N m-1. What is the tension in the spring when its length is 65 mm? A 3000 N B 300 N C 30 N D 3 N

NPlastic cylinder

Top-pan balance

S

N

S

B

A

W

T

C

E

D


6

frictionless incline

frictionless level surface

13 A lightweight object and a very heavy object are moving with equal speeds along a level frictionless surface. Both objects subsequently slide up the same frictionless incline. Which object rises to a greater height?

A The heavy object, because it has greater kinetic energy. B The lightweight object, because it weighs less. C They both slide to the same height. D Cannot be determined from the information given. 14 A block of mass m is pushed against a spring of spring constant k. The spring is

compressed by a distance d, the block is then released. It is launched by the spring along a horizontal frictionless surface with a final speed v. A second block, this one having mass 4m is pushed against the same spring and released, gaining a final speed 2v. By what distance was the spring compressed in the second case?

A d B 4d C 16d D 25d

15 To accelerate a car at a constant acceleration, the cars engine must

A develop ever-increasing power. B develop ever-decreasing power. C maintain a constant power output. D maintain a constant turning speed. 16 A warning siren on top of a tall pole is taken to be a point source and radiates sound waves

uniformly in all directions. At a distance 4d, the amplitude of the wave is A.

What is the distance from the siren at the point where the amplitude of the wave is 2A?

A 8d B 4d C 2d D d 17 A beam of initially unpolarised light passes through three polariods P1, P2 and P3. The

polarising axis of each polaroid is shown by an arrow. Polariods P1 and P2 are fixed, with their polarising axes at 45 to one another. What can be the angle of the polarising axis of polaroid P3 so that the intensity of the emergent light is minimum? A 0 B 45 C 90 D 135


718 A tall vertical cylinder is filled with water and a tuning fork vibrating at 400 Hz is held over its

open top. The water is slowly run out and the first resonance of the air column is heard when the water level is 0.21 m below the top of the cylinder. Neglecting end corrections, how far from the top will the water level be when the next resonance is heard?

A 0.32 m B 0.42 m C 0.63 m D 0.84 m 19 If two waves of the same frequency are superposed in phase, the total intensity is

proportional to

A the sum of the intensities of the waves. B the square of the mean value of the two amplitudes. C the square of the difference of the two amplitudes. D the square of the sum of the two amplitudes. 20 A and B shown in the figure below are two coherent sound sources which are in phase.

Point X shows permanent zero displacement. From the options given below, choose the sound wave with the minimum wavelength that can satisfy this condition.

A 180 mm B 90 mm C 60 mm D 45 mm 21 The graphs show the variation with potential difference V of current I for three circuit

elements.

The three circuit elements are a tungsten filament lamp, a metal wire at constant temperature and a semiconductor diode. Which of the following correctly identifies these graphs?

Tungsten filament lamp metal wire semiconductor diode A X Y Z B Y Z X C X Z Y D Z Y X

A B X

90 mm 270 mm


8

L

N

M

K

22 A particular wire in a circuit has a resistance of 5.0 . What is the resistance of another wire made of the same material, has the same cross-sectional area and which is three times as long as the first wire? A 5 B 15 C 45 D 125

23 In the circuit below, resistors X and Y, of resistances R and 2R respectively, are connected

to a 6 V battery of negligible internal resistance. When a voltmeter is connected across Y, it gives a reading of 3 V.

What is the reading of the voltmeter when it is connected across X?

A zero B Between zero and 2 V C 2 V D Between 2 V and 6 V 24 What is the equivalent resistance between the points L and M in the circuit below if each of

the resistors has a resistance of 2 ? A 4 B 3 C 2 D 1


925 The diagram below shows a wire conductor, RS, positioned perpendicular to an uniform

magnetic field directed into the paper.

What is the direction in which the wire could be moved at a constant speed to produce the maximum potential difference across its ends, R and S?

A perpendicular to both the length of the wire and the magnetic field B perpendicular to only the length of the wire C perpendicular to only the magnetic field D in the direction 45 to the length of the wire 26 A plotting compass is placed next to a vertical wire PQ. When there is no current in the wire,

the compass on the horizontal plane ABCD points North as shown in the diagram. Which diagram shows a possible direction for the compass to point when a current passes from Q to P?

A 4 B 3 C 2 D 1 27 The figure below shows a cross-section through a solenoid.

What happens to the current carrying conductor when it is placed along the center axis of the solenoid?

A The conductor moves upward. B The conductor moves downward. C The conductor moves in the direction out of the plane of paper. D The conductor remains stationary.

R

S

P

Q

A

B C

D

current out of plane of paper

current into plane of paper

I current carrying conductor


1028 Let 0 be the de Broglie wavelength of an electron accelerated from rest through a potential

difference of 10 V and let 1 be that of an electron accelerated from rest through a potential difference of 1000 V. The value of the ratio 0/ 1 is A 1/10 B 1 C 10 D 100

29 The graph below shows the relationship between the energy E of a photon of

electromagnetic radiation and its wavelength . Points P and Q marked on the graph represent two types of electromagnetic radiation. Which of the following pairs of electromagnetic radiation correctly identifies P and Q?

P Q A ultraviolet Radio wave B Infra-red X-ray C microwave Gamma ray D microwave ultraviolet 30 Which of the following statements is true when photoelectric effect occurs?

A The maximum speed with which electrons are emitted is proportional to the intensity of

the incident light. B The number of electrons emitted per second is proportional to the intensity of the

incident light. C The maximum energy of the emitted electrons increases with the wavelength of the

incident light. D The wavelength of the incident light must be greater than a certain threshold value.

E

P

Q

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8866/02/AJC2008

PHYSICS 8866/02 Higher 1 Paper 2 2 hours

Tuesday 16 September 2008 Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name and PDG on the spaces provided above. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Section A Answer all questions. Section B Answer any two questions. Write down the numbers of the two questions attempted in the boxes. You are advised to spend about one hour on each section. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.

Candidate Name PDG

ANDERSON JUNIOR COLLEGE

For Examiners Use

Section A (40 marks)

1

2

3

4

5

Section B (40 marks)

Deduction

Total (80 marks)

This question paper consists of 20 printed pages and 0 blank page.

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Data speed of light in free space c = 3.00 x 108 m s-1 elementary charge e = 1.60 x 10-19 C the Planck constant h = 6.63 x 10-34Js unified atomic mass constant u = 1.66 x 10-27 kg rest mass of electron me = 9.11 x 10-31 kg rest mass of proton mp = 1.67 x 10-27 kg acceleration of free fall g = 9.81 m s-2

Formulae

uniformly accelerated motion 221 attus +=

v2 = u2 + 2as work done on/by a gas W = pV hydrostatic pressure p = gh

electric potential r4

Q = V0

resistors in series R = R1 + R2 + resistors in parallel 1/R = 1/R1 + 1/R2 +

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Section A Answer all the questions in the spaces provided.

1 (a) Explain what is meant by the moment of a force.

.. .....[2]

(b) A cubical box ABCD shown in Fig. 1.1 is filled with sand and weighs 890 N. In order to roll the box, a horizontal force F can be applied on one of the upper edges.

Fig. 1.1

(i) Calculate the force F required to just roll the box without slipping.

F = .. N [2]

(ii) State the minimum friction between the box and the floor in (i).

.....[1]

(iii) There exists a more efficient way to roll the box. Determine the magnitude of the smallest possible force that would have to be applied directly to the box to roll it.

minimum force = .. N [2]

2 (a) What is meant by the term superposition when applied to waves?

.............................. .....[1]

F

A

B C

D

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(b) Two loudspeakers L1 and L2 driven from a common oscillator are arranged as shown in Fig. 2.1. A detector is placed at D. It is found that, as the frequency of the oscillator is gradually changed from 200 Hz to 1000 Hz, the detected signal passes through a series of maxima and minima.

Fig. 2.1

(i) Explain how the maxima and minima can be observed at the same point D.

......... ......... ......... ......... ..[2]

(ii) Calculate the frequency at which the first minimum is observed. Assume the speed of sound is 340 m s-1.

frequency = .. [2]

(iii) If the frequency of the oscillator is fixed at 510 Hz, how far from D must the detector be placed in order to observe the first order maximum? (Please note that the zero order maximum is observed at the central point O.)

distance from D = .. m [3]

D L1

L2

40 m

9 m O

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x y

MAGNET rider pivots I

z I

P

3 (a) Define magnetic flux density and the tesla.

.. .. .. .. .. .....[2]

(b) A current I passes through a pivoted rectangular wire frame, P, which is initially balanced. A magnet is then placed near one of the edges of the wire frame, with its magnetic field acting perpendicular to the edge of the wire frame and this causes the wire frame to tilt. A rider of mass m is then placed at a point along a section of the wire frame until the frame regains its balance as shown in Fig. 3.1 below.

Fig. 3.1

(i) Indicate, on Fig 3.1, the direction of the force due to the magnet, on the edge of the frame nearest to the magnet. Label this force F. [1]

(ii) Deduce an expression for the magnetic field strength of the magnet, in terms of x, y, z, m, I and g, where g is the acceleration of free fall. [2]

(iii) State and explain what happens when the polarity of the magnet is reversed.

.. .. .. ..[2]

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4 Fig. 4.1 shows some of the energy levels for an atom of hydrogen.

Fig. 4.1

(a) If the outer electron of the atom is in the ground state, how much energy must be required to remove this electron from the atom?

energy = .. J [1]

(b) (i) Suppose an electron of energy 11.0 eV collides with the atom. Explain the possible result of the interaction if the electron of the atom is in the ground state.

.................... ..[1]

(ii) If the electron of energy 11.0 eV is replaced by a photon of energy 11.0 eV, what will be the result of the interaction?

.................... ..[1]

(c) If an electron returns from the -0.849 eV level to the ground state, what is the wavelength of the photon emitted?

wavelength = .. m [1]

n = n = 5 n = 4

n = 3

n = 2

0- 0.545 eV - 0.849 eV

- 1.51 eV

- 3.41 eV

- 13.60 eV n = 1

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(d) State the region of the electromagnetic spectrum in which this radiation lies.

.....[1]

(e) On Fig.4.1, draw arrows to show

(i) another transition which results in the emission of radiation of wavelength shorter than the radiation in (c) (label this transition P) [1]

(ii) a transition which results from absorption of radiation of wavelength longer than the radiation in (c) (label this transition Q) [1]

5 A mass M is moving at 5.00 m s-1 along a horizontal frictionless guide which bends into a vertical circle of radius r, as illustrated in Fig. 7.1.

Fig. 7.1 Fig. 7.2 and Fig 7.3 show the velocity-time graphs for the vertical and horizontal components respectively of the velocity along the section ABC of the curve.

Fig. 7.2

M A

B

C

r

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Fig. 7.3

(a) With the aid of Fig. 7.2, find an appropriate value for the height of the vertical circle. Hence,

find the value for the radius of the vertical circle, r.

height of vertical circle = .. m [2]

radius of vertical circle, r = .. m [1]

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(b) (i) From Fig. 7.2 and Fig. 7.3, find the vertical and horizontal components of the acceleration of the mass M at B, 200 ms after it passes the point A.

vertical component of the acceleration = .. ms-2 [1]

horizontal component of the acceleration = .. ms-2 [2]

(ii) Hence, find the magnitude and the direction of the resultant acceleration of the mass M at B.

magnitude of acceleration = .. m s-2 [1]

direction of acceleration = [2]

(c) Without detailed mathematical calculation, deduce the total area between the curve and the time axis of Fig. 7.3. Explain your answer. ..... ..... ..... ......... ..... ..... .[2]

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Section B Answer two questions from this section.

6 (a) The floor of an elevator, mass 1800 kg, is at a distance 3.70 m above a spring as shown in

Fig. 6.1. It is at rest on the first floor when its cable snaps. A safety device clamps the elevator against guide rails so that a constant frictional force of 4.40 kN opposes the elevators motion.

Fig 6.1

(i) Show that the acceleration of the elevator is 7.37 m s-2.

acceleration = .. m s-2 [1]

(ii) Calculate the speed of the elevator when it hits the spring.

speed = .. m s-1 [2]

(iii) Calculate the average power developed during this process before it hits the spring.

average power = .. kW [2]

spring

cable

elevatorguide rails

3.7 m

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(iv) The spring is compressed by 0.9 m when the elevator comes to a rest. Using the principle of conservation of energy, determine the force constant of the spring. Assume mass of spring is negligible.

force constant = .. N m-1 [2]

(v) The force constant found in (iv) is known to be accurate to 8%. How should the result be presented?

force constant = .. N m-1 [1]

(b) Consider a woman of mass 60 kg, standing on a scale that reads in kilogram, in the elevator when it is on the first floor as shown in Fig. 6.2. State the reading on the scale after the cable snaps if the safety device fails to work. Explain your answer.

Fig. 6.2

..... ..... ..... ........[3]

cable

elevator

scale

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(c) (i) State the principle of conservation of momentum.

...... .........[1]

(ii) A 0.25 kg skeet is fired at an angle of 30 to the horizontal with a speed of 25 m s-1 as shown in Fig. 6.3. When it reaches the maximum height of 7.96 m, it is hit from below by a 15 g pellet traveling vertically upward at a speed of 200 m s-1. The pellet is embedded in the skeet and they move together along path A.

Fig. 6.3

1. Determine the velocity of the skeet at the maximum height of 7.96 m.

velocity = ... m [1]

direction of velocity = ... [1]

2. Upon collision, skeet and pellet move off together with a velocity v at an angle to the horizontal. By applying (c)(i) to the skeet-pellet system in the vertical direction, show that v sin = 11.321. [2]

3. Determine the time of flight for the skeet-pellet system to complete path A.

time of flight = .. s [2]

30 25 m s-1 200 m s

-1 Path A 7.96 m

skeet

pellet

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4. Suggest with a reason, whether the momentum of the skeet-pellet system is conserved in the presence of air resistance.

......... ......... .........[2]

7 (a) Define wavelength and frequency. Deduce a relation between these quantities and the speed of propagation of a wave.

..... .. ..... ..... ..... ..... ..... ........[3]

(b) Ocean waves, which travel in the open sea at 5 m s-1, arrive at a beach once every 4 s. What is the distance between wave crests in open sea?

distance = .. m [1]

(c) In order to investigate stationary waves on a stretched string, a student set up the apparatus illustrated in the diagram Fig. 7.1.

Fig. 7.1

vibrator weights

pulley string

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(i) Sketch two stationary patterns which could be formed on the string. [2]

(ii) Mark the nodes in each sketch. [1]

(iii) What is meant by a node?

...... ...... .....[1]

(iv) Briefly explain why a stationary wave is observed on the string only at particular frequencies of the vibrator.

...... ...... ...... ...... .....[2]

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(v) If in one of your sketches the distance between nodes is 0.55 m when the frequency of the vibrator is 40 Hz, what is the speed of the waves on the string?

speed = .. m s-1 [1]

(vi) It was found that for a given length of the string under the same tension, the frequency of the vibrator at which a stationary wave is formed is directly proportional to the number of antinodes formed on the string. Using the apparatus shown in the figure, how would you show that the above statement is true?

...... ...... ...... ...... .....[2]

(d) (i) State what is meant by the photoelectric effect.

...... ...... .....[1]

(ii) Give an expression for E, the energy of a photon, in terms of f, its frequency, and h, the Planck constant.

.....[1]

(iii) The work function of a freshly cleaned zinc surface is 3.6 eV. If it is illuminated with ultraviolet radiation of wavelength 253 nm,

1. what will be the maximum kinetic energy of the emitted electrons?

maximum kinetic energy = .. eV [1]

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2. what potential difference would be needed to stop the electrons being emitted?

potential difference = .. V [1]

3. what would be the threshold frequency for the metal surface?

threshold frequency = .. Hz [1]

(e) Light of wavelength 546 nm falls on a potassium surface of area 7.5 cm2 in an evacuated enclosure. The intensity at the surface is 60 mW m-2 and it may be assumed that 1 % of the photons emit electrons from the surface.

(i) Calculate the number of photons arriving at the surface per unit time.

number of photons per second = .. [1]

(ii) Hence calculate the photoelectric current produced.

photoelectric current = .. A [1]

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8 (a) An I-V characteristic for a thermistor is shown in Fig. 8.1

Fig. 8.1

(i) Draw a diagram of a circuit which you could use to take measurements to obtain

this characteristic. [2]

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(ii) The thermistor, the characteristic of which is given in Fig. 8.1, is used in the circuit shown in Fig. 8.2.

Fig. 8.2

It is found that there is a current of 95 mA from the supply. Calculate

1. the current through the 150 resistor,

current = .. A [1]

2. the resistance of the thermistor,

resistance = .. [2] (iii) When the temperature of the thermistor in the circuit in Fig. 8.2 is kept at 0 0C by

immersing it in a mixture of ice and water, it is found that the current from the supply becomes 75 mA. The resulting values of V and I for the thermistor no longer lie on the graph of Fig. 8.1. Suggest why the point corresponding to these values is not on the characteristic.

... ...[2]

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(b) (i) Write down an expression for F, the force on a long, straight conductor of length l carrying a current I at an angle to a uniform magnetic field of flux density B. [1]

(ii) Draw a clear diagram to illustrate the direction of the force, relative to the direction of the current and magnetic field, on the conductor in b(i). Label the force F. [2]

(iii) State two methods of increasing the force on a current carrying conductor, that is within a magnetic field.

... ... ...[2]

(c) Two long straight parallel wires are separated by a distance d. Each carries a current I in the same direction.

(i) Explain, with the aid of sketches, the forces which exist between the two wires. Indicate the directions of the forces. [3]

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(ii) B, the magnetic flux density due to a long straight wire, is given by the expression

B = 0I / 2d Derive an expression for the force per unit length between the two wires. [2]

(d) One particular overhead powerline consists of two parallel cables with a separation of 6.0 m. The current in the cable is 200 A.

(i) Calculate the force per unit length on each cable.

force per unit length = .. N m-1 [1]

(ii) Hence explain why it is not possible, by looking at the cables, to detect the instant at which the current is switched on.

... ... ...[2]

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1

SolutiontoH1PhysicsPrelimPaper1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

A D B C A A A B A B C D C B A

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

C D C D C D B B C A D D C A B

1 A

Ave reading = 6.0mm (far from actual value of 5.0mm) high systematic error. Range of scatter = 0.2mm (small scatter) low random error.

2 D

4212

22

22

2

][

smkgA

skgmsAC

WQVQC

=

=

=

=

3 B

2

2

2

09.081.9%9.0

%9.01.027.0

2

4

2

==

=+=

+==

=

msg

PPPT

Lg

gLT

TLg

4 C

2

5 A

6 A

: vy = uy + at = -51.2 sin 44.5 + 9.81(1.5)

= -21.2 ms-1

vy is acting upwards, hence location of projectile must be before point A.

7 A

Taking the two masses as one system, there is only one force acting on the system to cause motion, namely the weight of the 1 gram mass.

251081.9001.10081.9001.0

==msaa

8 B

Without external net force, momentum is conserved. Any motion resulting from collision in which the colliding bodies stick together is inelastic.

9 A

10 B

For top magnet: F = Mg

For bottom magnet: R = Mg + F = 2Mg

The balance reads R = W = 2Mg

11 C

For 3 forces, all forces must pass through a common point for the system to stay in equilibrium.

12 D

F = kx

= 200 [(65-50)x10-3]

= 3 N

F

M

Mg + F

R

R

3

13 C

mv2 = mgh the value of h is the same since v remains unchanged and h is indept of m

14 B

15 A

P = Fv

F const a const v increases linearly P increases linearly

16 C

Find the relationship between the amplitude of the wave and the distance from the source.

2AI

2

1r

I

Therefore r

A 1 . The amplitude is inversely proportional to the distance. Hence, when the amplitude is twice (A to 2A), the distance is halved (4d to 2d).

17 D

The light wave emerging from P2 has oscillation along the 45 polarising axis. This light wave is blocked only when it passes through a polariod of polarising axis perpendicular to its oscillation. Hence the polarising axis of P3 is 45 + 90 = 135

18 C

first resonance : 0.21 = (1/4) wavelength

Next resonance : (3/4) wavelength = (3/4)( 4 x 0.21) = 0.63 m

ddvm

mvdd

mvkx

424

21

21

2

2

2

2

22

==

=

'))(('

4

19 D

intensity is proportional to square of amplitude

20 C

path difference = AX BX = 90 mm = (n + )

n = 1, = 60 mm, n = 2 , = 36 mm (not in the option)

Hence, C is the ans.

(note : n=0, = 180 mm , not minimum)

21 D

22 B

Using R = l / A R l Hence R = 3 x 5 = 15

23 B

p.d across X = (R / 3R) x 6 = 2 V

Voltmeter reading is between 0 V and 2 V since it records p.d lower than the actual value as it records 3 V rather than (2R / 3R) x 6 = 4 V .

24 C

2 resistor between K and N does not contribute to overall resistance. Hence overall resistance = [1/(2 + 2) + 1/(2 + 2)]-1

= 2 25 A

E = Blv when the wire is moving perpendicular to both the length of the wire and the magnetic field

5

26 D

The direction of the magnetic field caused by the current is anti-clockwise. Using vector addition, the arrow would most likely be horizontal.

27 D

The direction of the current is parallel to the direction of the B field.

28 C

= h/p KE = p2/m = qV => p = (2qmV) => = h/(2qmV)

0/ 1 = (2qmV1) /(2qmV0) = (1000/10)= 10

29 A

P has higher energy , lower than that of Q

In the options, only A satisfies the conditions.

30 B

intensity = nhf/t per unit area n/t intensity

n is the no. of photons. n/t affects ne/t

Bresultant

BEarthBcurrent

P

Q

N

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8866/02/AJC2008

2008 H1 Prelim Paper 2 Suggestion Solutions Section A 1(a) It is the product of a force and the perpendicular distance from the line of action of the

force to a pivot (bi) Let x be the side of a box.

Take moment about an axis through A: Fx = W(x) F = 890/2 = 445 N (ii) 445 N (iii) To overcome the same anti-clockwise moment by the weight, the minimum possible

force must act perpendicular to the distance furthest away from pivot A. Fmin y = W(x) Fmin 2 x = W(x) Fmin = 445/ 2 = 315 N 2

a) b)

It means that when two or more waves of the same type superpose or meet at a point in space, the resultant amplitude at the point is the vector sum of all the individual wave amplitudes at that point. (i) Sound waves from the two sources will meet or superpose at the point D. If they meet

with constructive interference, a loud sound (maxima) will be detected. This will occur when the path difference of the two sound waves at D is an integral multiple of the wavelength. If they meet with destructive interference, a soft or no sound (minima) will be detected. This will occur when the path difference is (n + ) times of the wavelength where n is any integer. For the arrangement above, the path difference is fixed at the point D. When the frequency of the sound is changed, the wavelength will change accordingly. At certain values of frequency, ( hence its wavelength), when it fulfills the conditions for maxima or minima as stated earlier, maxima and minima will be observed at the point D.

(ii) L2D = (92 +402) = 41 m Path difference = L2D L1D = 41 40 = 1 m For first minimum, path difference = = 1 From v = f = v/f = 340/f Hence, (340/f) = 1 f = (340) = 170 Hz

(iii) f = 510 Hz, = 340/510 = 0.667 m using two-source interference equation, = ax/D, maxima separation x = 0.667 x 40/9 = 2.963 m zero order maxima is 9/2 =4.5 m below D. first order maxima is 4.5 2.963 = 1.537 = 1.54 m below point D

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x y

MAGNET rider pivots I

z I

P

3 a) Magnetic flux density at a point is the force per unit length of conductor per unit current carried, placed at that point at right angles to the field. The tesla is newton per metre per ampere. (N m-1 A-1) bi) ii) Clockwise moments = Anti-clockwise moments Fy = mgx BIzy = mgx B = mgx / Izy iii) The wire frame tilts in the opposite direction OR the wire frame is no longer balanced. The force on the edge of the frame nearest to the magnet is in the opposite direction. 4

(a) Energy required = 0 (-13.60) = 13.60 eV = 13.60x1.60x10-19 = 2.18x10-18J (b)(i) The electron of the atom will absorb 10.19 eV of energy and be excited to the n=2 level. The incident electron will have 0.81 eV of energy left.

(ii) no change because the energy of the photon does not match the energy of any transition (from the ground state) (c) Energy released = [-0.849-(-13.60)] = 12.75 eV = 12.75x1.60x10-19=2.04x10-18 = hc/ = 6.63x 10-34 x 3.00x108/2.04x10-18= 9.75 x 10-8 m (d) Ultraviolet region

(e)

n = n = 5

n = 4

n = 3

n = 2

0 - 0.545 eV - 0.849 eV

- 1.51 eV

- 3.41 eV

- 13.60 eV n = 1

Q P

F(1m)

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5 (a) From Fig. 7.2, area under the graph = vertical displacement traveled by mass from A to C = height of circle = 32 (0.5 5010-3) = 0.800 m (3sf) height of circle = diameter of circle

r = 0.800 0.400 m (3sf)2

= Check: Using COE: Total Energy at C = Total Energy at A

( )

2 2

2 2

2 2 2 2

1 12 21 12 2

5 3 0.81549 m2 2 9.81

0.408 m (3sf)2

c A

c A

A c

mv mgh mv

v gh v

v vhg

hr

+ =

+ = = = =

= =

(b)

Fig. 7.2

Fig. 7.3

ay = ( ) -23

3.5 0.4 23.8 ms (3sf)170 300 10

= ax = ( )

( ) -230 4

19.5 ms (3sf)100 305 10

=

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(ii)

Resultant acceleration ( ) ( )2 223.8 19.5= + -230.8 ms (3sf)=

= 1 19.5tan 39.3 (3sf)23.8

= The direction of the acceleration is 39.3 south of west.

(c) The total area between the curve and the time axis is zero. This is because the net horizontal displacement traveled by the mass M from A to C is zero.

Section B 6(ai) Fnet = mg - f (1800)a = (1800)(9.81) 4400 a = 7.366 ms-2 = 7.37 m s-2 (ii) : v2 = u2 + 2as = 0 + 2(7.37)(3.7) v = 7.3850 = 7.38 m s-1 (iii) = Fnet = (1800)(7.37)()(7.3850) / 1000 = 48.985 = 49.0 kW (iv) Total initial energy of elevator = Total final energy of spring mgx + mv2 = kx2 + fx (1800)(9.81)(0.9) + 0.5(1800)(7.3850)2 = 0.5(0.9)2k + 4400(0.9) k = 1.507 x 105 = 1.51 x 105 N m-1 (v) k = 0.08k = 0.08(1.507 x 105) = 0.1 x 105 k = (1.5 0.1) x 105 N m-1 (b) 0 kg.

When cable breaks, woman & scale fall with the same acceleration, g = 9.81 m s-2. The reaction force between them is zero. Hence scale reads zero.

ay

ax

aresultant

5

8866/02/AJC2008

(ci) The total momentum of a system is constant provided no external resultant force acts on it.

(ii) 1. v = 25 cos30 = 21.7 m s-1 direction = horizontal to the right 2. before collision after collision

By COM in vertical direction: total initial p = total final p : (mu)pellet + (mu)skeet = (mv)pellet + (mv)skeet 0.015(200) + 0 = (0.25 + 0.015) v sin v sin = 11.321 3. : s = ut + at2 7.96 = (-v sin )t + (9.81) t2 t = 2.87s 4. No, because the drag force due to air resistance acts as an external force acting on the

system. This changes the momentum of the system. 7 a)

b) c)

Wavelength is the distance between two consecutive points in a wave that are at the same stage of oscillation. Frequency f is the number of complete oscillations per unit time made by a point in a wave. Time taken by a wave to travel a distance of one wavelength is the period T = 1/f Speed = distance / time => v = /T = /(1/f) = f v = f 5 = (1/4) = 5x4 = 20 m (i)

(any two)

25 cos 30200

v

v cos v sin

N N

NN N

N N N N

6

8866/02/AJC2008

d) e)

(ii) Mark the nodes in each sketch. (iii) The node N means a point where it has permanent zero displacement, no

oscillation.

(iv) Only certain stationary waveforms are possible to be formed on the string with the two ends as nodes. That is, the string will oscillate with certain values of the frequency. In order to observe the stationary waveforms, the frequency of the vibrator must be equal to the certain values of the frequency of the string. This is called resonance effect. Hence stationary wave is observed at particular frequencies of the vibrator.

(v) v = f = 40x 0.55x2 = 44 ms-1

(vi) Adjust the frequency of the vibrator until a stationary waveform is observed. Note

the frequency f and count the number of antinodes N formed points where maximum amplitude is observed.

Vary the frequency of the vibrator until another waveform is observed and note the value of f and N Repeat the experiment 6 times and plot a graph of f against N. the graph obtained should be a straight line passing through origin if the statement is true.

(i) It refers to the phenomenon that when some metal surfaces are illuminated by light or electromagnetic radiation of certain frequencies, electrons are emitted from the surfaces.

(ii) E = hf (iii) 1. using hf = + KE hf = hc/ = 6.63x 10-34 x 3.00x108/(256x10-9x1.60x10-19) = 4.914 eV 4.914 = 3.6 + KE => KE = 4.914 3.6 = 1.314 = 1.31 eV

2. KE = qV stopping potential V = 1.31 V

3. = hf0 f0 = /h = 3.6x1.60x10-19/6.63x10-34 = 8.69x1014 Hz (i) nhf/t = intensity x area where f = c/

n/t = 60x10-3 x7.5 x 10-4/ [(6.63x10-34x 3.00x108)/546 x 10-9] = 1.235 x 1014 = 1.24 x 1014

(ii) current = (n/t)x1%xe = 1.235 x 1014 x 10-2x 1.60 x 10-19 = 1.976 x 10-7 A = 2.0 x 10-7 A

7

8866/02/AJC2008

B I l

F = BIl sin 1m correct indication of force 1m correct indication of , I and l

8.(ai) (ii) 1. p.d across the 150 resistor = 9V. Hence current through, I = V/R = 9 / 150 = 60 m A

2. Current through the thermistor = 95 60 = 35 mA From the graph, p.d across the thermistor = 5.6 V Rthermistor = V / I = 5.6 / 35 x 10-3 = 160 (iii) Fig 4.1 shows characteristic values of the thermistor where the resistance decreases as

the temperature increases and this can be seen from the graph, as the p.d across thermistor increases, the temperature increases and resistance decreases.

When placed in ice, its temperature is kept constant and its resistance ios maintained at a certain value. Therefore values recorded will not fall on the characteristic.

bi) F = BIl sin ii)

iii) - Increase magnetic flux density - Increase current in conductor - Increase length of conductor.

mA

V

8

8866/02/AJC2008

ci)

Consider 2 conductors X and Y each carrying a current I directed out of the plane of the paper. Current in X causes a magnetic field at Y. Direction of magnetic field at Y is vertically upwards. According to FLHR, Y experiences a force directed towards X. Similarly, Current in Y causes a magnetic field at X. Direction of magnetic field at Y is vertically downwards. According to FLHR, X experiences a force directed towards Y.

Hence there is a force of attraction between them.

ii) The field of one wire is perpendicular to the other, hence, = 900. F = BIL ; Force per unit length = F / L = B x I = B = 0I / 2d x I = 0I2 / 2d di) F = 0I2 / 2d = (4 x 10-7 x 2002) / 2 (6) = 1.33 x 10-3 Nm-1 ii) This force is very small, compared to the weight of the cables. Hence the movement is

not visible by just looking at cables.

d

X Y

B

F

Name: .. HT group: ...

CATHOLIC JUNIOR COLLEGE

JC2 PRELIMINARY EXAMINATION 2008

PHYSICS 8866/ 1 Higher 1 PAPER 1 Multiple Choice

Friday 12 September 2008

1 hour Additional materials: MCQ answer sheet Soft clean eraser Soft pencil (type B or HB is recommended)

READ THESE INSTRUCTIONS FIRST Write in soft pencil Do not use staples, paper clips, highlighters, glue or correction fluid Write your name and tutorial group on the Answer Sheet in the spaces provided unless this has been done for you. There are thirty questions in this paper. Answer all questions. For each question there are four possible answers A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the separate sheet. Read the instructions on the Answer Sheet very carefully. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet.

This question paper consists of 13 printed pages.

PHYSICS DATA: speed of light in free space, c = 3.00 x 108 m s-1

elementary charge, e = 1.60 x 10-19 C

the Planck constant, h = 6.63 x 10-34 J s

unified atomic mass constant, u = 1.66 x 10-27 kg

rest mass of electron, me = 9.11 x 10-31 kg

rest mass of proton, mP = 1.67 x 10-27 kg

acceleration of free fall, g = 9.81 m s-2

PHYSICS FORMULAE: uniformly accelerated motion, s = u t + a t2 v2 = u2 + 2 a s

work done on / by a gas, W = p V Hydrostatic pressure P = gh electric potential, V =

rEQ

o4

resistors in series, R = R1 + R2 + ...

resistors in parallel, 1/R = 1/R1 + 1/R2 + ...

2

1 The power generated by an ideal wind turbine is given by 3

21 b)(vkP = where k is a constant of the turbine,

is density of the fluid passing through the turbine, v is the velocity of the fluid. The possible units of k and b are:

Units of k Units of b

A no units m s-1

B

m2 m s-1

C

no units m3

D

m2 m3

2 Systematic and random errors may be compared by contrasting the following pairs of

properties: P1: error can possibly be eliminated P2: error cannot possibly be eliminated Q1: error is of constant sign and magnitude Q2: error is of varying sign and magnitude R1: error will be reduced by averaging repeated measurements R2: error will not be reduced by averaging repeated measurements Which properties apply to systematic errors?

A P1, Q1, R2 B P1, Q2, R2 C P2, Q2, R1 D P2, Q1, R1

3 The true value of a quantity x is x0. In an experiment, the quantity is measured many times and

the number N of readings, giving a value x, is plotted against x. Which of the following graphs best shows measurements that are precise but not accurate?

A B C D

N

x x0

N

x x0

N

x x0 x

N

x0

3

4 A fighter-bomber is traveling in level flight at a speed of 55 m s-1. It is on a bombing run to its target, a tank moving at 30 m s-1 head on. Given its altitude is 400 m from the ground level, when should the pilot release the bomb if he wants to score a direct hit? Assume negligible air resistance.

A When the plane is 230 m away from the tank.

B When the plane is 450 m away from the tank.

C When the plane is 770 m away from the tank.

D When the plane is 1100 m away from the tank.

5 An object, thrown vertically upwards, rises to a certain height and then falls back to its starting

point. Assuming that air resistance cannot be neglected, which of the following statements is correct?

A When the object is rising, the magnitude of its deceleration is greater than the acceleration due to gravity.

B The time of flight for the upward motion is greater than the time of flight for the downward motion.

C The speed of the object when it is thrown up is equal its speed when it returns to the starting point.

D The acceleration of the object at the highest point is zero.

4

6 A disc is sliding across a horizontal, frictionless icy surface when it collides inelastically with a

wall at right angles to its path, and then rebounds along its original path. Which of the following graphs shows the variation with time t of the momentum p of the disc?

A B C D

p

t t 0 0 0 t

p

t 0

p p

7 A helicopter which has blades of diameter 5.0 m is hovering above the ground at a particular

instance. Its blades are rotating in such a way that they are pushing air downwards at a speed of 18 m s-1. The density of the surrounding air can be taken as 1.02 kg m-3. The upward force acting on the blades is

A 360 N B 1400 N C 6500 N D 26000 N

F / N

20

t / s 6 3

8 An object of mass 20 kg, initially at rest moves along a straight line on a smooth horizontal surface. A force F acts on the object in its direction of motion. In the figure below, a graph of F against time t is shown What is the velocity of the object at t = 6 s?

A 1.5 m s-1 B 3.0 m s-1 C 4.5 m s-1 D 7.0 m s-1

5

9 Figure 9.1 shows the directions and lines of action of two forces applied to a circular disc.

Which one of the arrows in Figure 9.2 best represents the line of action of the third force that will keep the disc in equilibrium?

3N

4N 4N A

B

D

C

Figure 9.1 Figure 9.2

10 A rod with negligible weight is suspended from three identical springs. With a weight W

hanging from the middle of the rod, the extension of each spring is x. The middle spring is then removed and the weight increased to 3W. What is the new extension of each spring?

A 2

5x B 2

7x C 2

9x D 2

11x

W

6

11 The weight indicated on a balance is X when a beaker of water is placed on it. A solid object

has weight Y in air and displaces weight Z of water when completely immersed. The given diagram shows the object suspended from a spring balance and completely immersed in the beaker of water. What are the readings on the spring balance and the weighing machine in the given arrangement?

Spring balance Weight balance A Y Z

X

B Y + Z

X + Y - Z

C Y + Z

X + Y

D Y - Z X + Z

Spring balance

Weighing machine

12 A ball, thrown vertically upwards, rises to a height h and then falls to its starting point. Air

resistance may be taken as negligible. Which graph best shows the variation of kinetic energy Ek of the ball with the distance s travelled?

A B C D

Ek

s

Ek

s 0 0 h h

Ek

0 h s s

Ek

0 h

7

13 The diagram shows an arrangement which consists of a wheel of circumference 0.40 m driven

by the electric motor of overall efficiency 80 %. A rope is passed over the wheel. One end of the rope is attached to a spring balance and the other end supports a load of 100 N. When the wheel is turning at a rate of 50 rev s-1, the balance reading is 25 N.

What is the electrical power supplied to the electric motor?

A 1.50 kW B 1.88 kW C 2.34 kW D 2.93 kW

50 rev s-1

load = 100 N Spring balance reading = 25 N

14 Two coherent waves each of intensity I meet in phase at a point K. What is the resultant

intensity at K?

A I B 2I C 3I D 4I

15 The principle of superposition applies only if

A the waves travel with the same speed

B the sources of the waves are coherent

C the waves have the same frequency

D the waves are of the same kind

16 S1 and S2 are two identical, small loud-speakers 0.50 m apart and connected to the same audio frequency generator. They vibrate in phase producing sound waves of wavelength 0.40 m.

A microphone detects a minimum in the pattern of superposition at the point P. If P is 12.00 m from S2 and PS1 > PS2 then the least possible distance of P from S1 is

A 12.15 m B 12.20 m C 12.40 m D 12.60 m

S1 S2 P

8

17 Air filled pipes of equal length are represented in figure below.

In what ratio are the frequencies of the fundamental vibrations of the pipes?

A 1: 2: 1 B 1: 2: 3 C 2: 1: 2 D 3: 2: 1

fa fb fc

18 The graph below shows the variation of the current I through a lamp with potential difference V

across it.

Which of the following graphs shows best represents the variation of power P dissipated in the same lamp, with I2?

A B C D

19 A 10 resistor is connected across three identical cells each having an e.m.f. of 1.5 V and internal resistance of 3 . What is the current flowing through the resistor?

A 0.079 A B 0.12 A C 0.14 A D 1.7 A

10

9

20 Four identical lamps, each carrying a label 1.5 V, 0.5 A, are connected to a cell of 12 V and

zero internal resistance as shown in the circuit below. The resistor R is added to the circuit so that the lamps are working at normal brightness.

What is the value of R?

A 2.3 B 3.3 C 5.3 D 6.3

21 In the circuit shown, a potential difference of 8 V is applied across XY. X is at a higher potential relative to Y.

What is the potential at A if B is earthed?

A - 1 V B + 1 V C - 5 V D + 5 V

A

B

22 An electron is moving along the axis of a solenoid carrying a current. Which of the following is

a correct statement about the electromagnetic force acting on the electron?

A The force acts radially inwards.

B The force acts radially outwards.

C The force acts in the direction of motion.

D No force acts.

10

23 A small plastic sphere carrying a negative charge is maintained at a constant height by the action of a downward vertical electric field. A uniform magnetic field is applied in the same direction as the electric field. What does the sphere do?

A Move downwards in a spiral path

B Move in a horizontal circle

C Move upwards in a spiral path

D Remain stationary

24 An electron enters the space between two parallel charged plates with an initial velocity u.

While in the electric field its direction changes by 30 and it emerges with a velocity v.

What is the relation between v and u?

A

ocos30uv = B

ocos30u v = C osin30

uv = D osin30u v =

25 The figure below shows four long, straight current-carrying wires P, Q, R and S. which are perpendicular to the plane of the paper. They pass through the corners of a square. Point O is the point of intersection of the diagonals of the square. The currents in all four wires have the same magnitude. The currents in wires P, Q and R flow into the plane of the paper while that in S flows out of the plane of the paper. Which arrow shows the direction of the resultant magnetic field at O?

P

S

O

D

C

B A

R

Q

11

26 A straight, horizontal, current-carrying wire lies at right angles to a horizontal magnetic field. The field exerts a vertical force of 8.0 mN on the wire. The wire is rotated, in its horizontal plane, through 30 as shown. The flux density of the magnetic field is halved.

What is the vertical force on the wire?

A 2.0 mN B 3.5 mN C 4.6 mN D 8.0 mN

27 The work function of a metal may be defined as

A the minimum frequency of the incident electromagnetic radiation required to cause photoelectric emission

B the minimum wavelength of the incident electromagnetic radiation required to cause photoelectric emission.

C the minimum energy of photons incident on a surface required to cause photoelectric emission

D the minimum energy required to take an electron from the interior to the surface to cause photoelectric emission.

28 A simple model of the energy levels in an atom has only three levels, X, Y, and Z. A transition from level X to level Z produces radiation of wavelength 400 nm; a transition from level Y to level Z produces a radiation of wavelength 700 nm. Which of the following deductions made by the student about the energy level scheme is correct?

A The wavelength of radiation emitted in a transition from level X to Y is 300 nm

B The wavelength of radiation absorbed in a transition from levels X to Y is 300 nm

C Level Y has a greater energy than levels X and Z

D Levels X has a greater energy than levels Y or Z 29 White light from a tungsten filament lamp is passed through sodium vapour and viewed through

a spectrometer. Which of the following best describes the spectrum which would be seen?

12

A coloured lines on a black background

B coloured lines on a white background

C dark lines on a coloured background

D dark lines on a white background

30

The graph shows the variation with frequency f of the maximum kinetic energy Ek of photoelectrons emitted from a metal surface S.

E

00 f

k

Which one of the following graphs shows the corresponding variation for a metal surface with a higher work function? The dotted line on each graph below shows the variation for the metal with the higher work function and the solid line shows the variation of metal S.

A E

00 f

k

B E

00 f

k

C E

00 f

k

D E

00 f

k

THE END

13

Name: .. HT group: ...

CATHOLIC JUNIOR COLLEGE

JC2 PRELIMINARY EXAMINATION 2008

PHYSICS 8866/ 2 Higher 1 PAPER 2 Structured Questions

Wednesday 27 August 2008

2 hours Candidates answer on the Question Paper No additional materials are required.

READ THESE INSTRUCTIONS FIRST Write your name and tutorial group on all the work you hand in. Write in dark blue or black pen in the spaces provided on the Question Paper. You may use a soft pencil for any diagrams, graphs or rough working Do not use staples, paper clips, highlighters, glue or correction fluid Section A Answer all questions Section B Answer any two questions The number of marks is given in brackets [ ] at the end of each question or part question.

For examiners Use

Section A

1 2

3 4

5

Section B

6 7

8

Total

This question paper consists of 20 printed pages.

2

PHYSICS DATA: speed of light in free space, c = 3.00 x 108 m s-1

elementary charge, e = 1.60 x 10-19 C

the Planck constant, h = 6.63 x 10-34 J s

unified atomic mass constant, u = 1.66 x 10-27 kg

rest mass of electron, me = 9.11 x 10-31 kg

rest mass of proton, mP = 1.67 x 10-27 kg

acceleration of free fall, g = 9.81 m s-2

PHYSICS FORMULAE: uniformly accelerated motion, s = u t + a t2 v2 = u2 + 2 a s

work done on / by a gas, W = p V Hydrostatic pressure P = gh electric potential, V =

rEQ

o4

resistors in series, R = R1 + R2 + ...

resistors in parallel, 1/R = 1/R1 + 1/R2 + ...

physics 2008 jc prelims

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