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TAMPINES JUNIOR COLLEGE PRELIMINARY EXAMINATIONS

CANDIDATE

NAME

TUTOR

NAME 1 4

PHYSICS

Paper 1 Multiple Choice

Additional Material: Multiple Choice Answer Sheet

22 September 2015

1 hour 15 minutes

READ THESE INSTRUCTIONS FIRST

Write in soft pencil.

Do not use staples, paper clips, highlighters, glue or correction fluid.

Write your name and class on the Answer Sheet in the spaces provided.

There are forty questions on this paper. Answer all questions. For each question there are

four options A, B, C and D.

Choose the one you consider correct and record your choice in soft pencil on the separate

Answer 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.

CIVICS

GROUP

This document consists of 15 printed pages.

3

1. The SI unit of energy, the joule, expressed in base units is

A kg m2 s–1

B kg m s–2

C kg m2 s–2

D kg m-1 s–2

2. A Formula One car travels a distance of (100 1) m from rest. If the acceleration of the car is (23.1 0.5) m s-2, what would be its final velocity at the end of the distance covered?

A (68 1) m s-1

B (68 2) m s-1

C (68.0 2.2) m s-1

D (67.97 0.03) m s-1

3. Which one of the following groups contains three vector quantities?

A displacement, velocity, momentum

B displacement, velocity, kinetic energy

C force, work done, moment

D work done, acceleration, power

4. A hinged trapdoor is held closed in the horizontal position by a cable. Three forces act on

the trapdoor: the weight W of the door, the tension T in the cable and the force H at the

hinge.

Which list gives the three forces in increasing order of magnitude?

A H, T, W B T, H, W C W, H, T D W, T, H

4

5. An object is accelerated from rest by a constant force. Which of the following graphs correctly shows the variation of the displacement with time squared, and the variation of the momentum with displacement of the object?

displacement vs (time)2

momentum vs displacement

A Graph 1 Graph 2

B Graph 2 Graph 3

C Graph 3 Graph 1

D Graph 3 Graph 3

6. A truck of mass 1800 kg is travelling on a level road at a constant speed of 25 m s -1. A

driving force of 1200 N is needed for the truck to maintain this constant speed.

The truck encounters a slope with an inclination of 20 o and attempts to move up the slope at

the same speed of 25 m s-1. What is the power required by the truck to do so?

A 30 kW

B 45 kW

C 75 kW

D 181 kW

5

7. A 2.0 kg mass is attached to an unstretched spring fixed to a support, and placed on a

smooth slope inclined at 40o to the horizontal. The spring constant is 400 N m-1. When the

mass is released, it slides down before stopping momentarily. What is the extension of the

spring at this instant?

A 0.032 m B 0.049 m C 0.063 m D 0.98 m

8. Which of the following pairs of forces is not a valid example of action and reaction to which

Newton’s Third Law of motion applies?

A The weight of a satellite in orbit around the Earth and the attractive force on the Earth’s

centre of mass due to the satellite

B The forces of repulsion experienced by two parallel wires carrying currents in opposite

directions

C The forces of attraction felt by two gas molecules passing near to each other.

D The weight of an object resting on the table and the force acting on the object due to the

table supporting it.

9. A body, initially at rest, explodes into two fragments of masses M and 3M having total

kinetic energy E. The kinetic energy of the fragment of mass M after the explosion is

A E/4 B E/3 C 2E/3 D 3E/4

10. A projectile of mass m is fired with initial speed u at an angle θ to horizontal ground, as

shown in the diagram below. Neglecting air resistance, which of the following about the

change in momentum of the mass between its launch point and its landing point is correct?

6 A projectile of mass m is fired with initial speed u at an angle θ to horizontal ground, as

shown in the diagram below. Neglecting air resistance, which of the following about the change in momentum of the mass between its launch point and its landing point is correct?

Magnitude Direction A Zero Undefined

B 2mu sin θ Upwards

C 2mu cos θ To the right

D 2mu sin θ Downwards

u

θ

Magnitude Direction

A 2mu cos θ Upwards

B 2mu sin θ Upwards

C 2mu cos θ To the right

D 2mu sin θ Downwards

40o

6

11. An object of mass 2.0 kg is moving at a velocity of 5.0 m s-1 at time t = 0. The net force F on

the object varies with time t as shown in the diagram.

12 An object of mass 2.0 kg is moving at a velocity of 5.0 m s-1 at time t = 0. The net force F on the object varies with time t as shown in the diagram.

Which one of the following graphs best represents how the momentum p of the object varies with time t?

t / s

F / N

2 4 6

8 10 12

-10

-5

0

5

10

2 4 6 8 10 12 t / s

p / N s

10

20

30

40

50

t / s

p / N s

2 4 6 8 10 12

10

20

30

40

50

t / s 2 4 6 8 10 12

p / N s

10

20

30

40

50

t / s

p / N s

2 4 6 8 10 12

10

20

30

40

50 A

B

C

D

Which one of the following graphs best represents how the momentum p of the object varies

with time t?

12 An object of mass 2.0 kg is moving at a velocity of 5.0 m s-1 at time t = 0. The net force F on the object varies with time t as shown in the diagram.

Which one of the following graphs best represents how the momentum p of the object varies with time t?

t / s

F / N

2 4 6

8 10 12

-10

-5

0

5

10

2 4 6 8 10 12 t / s

p / N s

10

20

30

40

50

t / s

p / N s

2 4 6 8 10 12

10

20

30

40

50

t / s 2 4 6 8 10 12

p / N s

10

20

30

40

50

t / s

p / N s

2 4 6 8 10 12

10

20

30

40

50 A

B

C

D

12. An inelastic string, hanging a pendulum bob, is tied to the free end of a horizontal bar of

length l. The bar is set to rotate about a vertical axis at the other end with a period T. The

string is found to make an angle with the vertical and the pendulum bob is at a distance r

from the axis.

l

horizontal bar inelastic string

axis of rotation

Which of the following is a correct expression for tan ?

A gT

r2

24 B

gT

l2

24 C

gT

lrr2

22 )(4 D

Tg

l2

r pendulum bob

7

13. A stone of weight W tied to a piece of string is swung in a vertical circle. At the top most of

its path, the tension in the string is T and the centripetal force is F.

Which of the following statements is true when the stone is at the top most of the path?

A F = W - T

B F = W + T

C Net force acting downward on the stone is F + W + T.

D Net force acting downward on the stone is F + W – T.

14. The table below gives the gravitational potential values at various points in the field of a planet.

Distance from surface / km Potential / kJ kg-1

0 - 544.6

220 - 369.2

230 - 345.8

240 - 322.5

Infinity 0

What is the gravitational acceleration at a height of 230 km above the surface of this planet?

A 1.50 m s-2 B 2.34 m s-2 C 3.46 m s-2 D 9.81 m s-2

15. The period of oscillation T of a simple pendulum of length L is given by

g

LT 2

where g is the acceleration of free fall. For a pendulum of length 0.80 m oscillating with an

amplitude of 1.5 cm, what is the maximum velocity of the pendulum in cm s-1?

A 1.8 B 2.7 C 3.5 D 5.3

16. A particle performing simple harmonic motion has an acceleration a given by a = - kx where

x is the displacement of the particle from equilibrium. What is the frequency of oscillation of

this particle?

A 2

k B

2

k C k2 D k2

8

17. A charged, polished metal sphere has a radius of 0.20 m. The insulation of air breaks down

when the electric field near the surface of the sphere reaches 3.0 x 106 V m-1. Assuming

that the charge on the sphere acts as if it were all situated at the centre, what is the

maximum charge that can be stored on this sphere?

A 13 μC B 37 μC C 53 μC D 67 μC

18. The graph shows the I-V characteristics of three electrical components, a diode, a filament

lamp and a resistor, plotted on the same axes.

Which statement is correct?

A The resistance of the diode equals that of the filament lamp at about 1.2V.

B The resistance of the diode is constant above 0.8V.

C The resistance of the filament lamp is twice that of the resistor at 1.0 V.

D The resistance of the resistor equals that of the filament lamp when V = 0.8 V.

19 A filament lamp is rated as “120V, 40W”.

The lamp is connected into a circuit so that it lights up normally.

Which statement is correct?

A The charge passing through the filament in one second is 3.0 C.

B The lamp transfer 40 J for each coulomb passing through the filament.

C The lamp transfers 120 J in 3.0 s.

D The supply provides 40 J to the lamp when the current is 3 A.

20. Ice water at 0oC is poured into a cup carved from ice at 0oC. Assume there is no energy

exchange with the surroundings. Which statement is correct?

A Some of the ice will become water.

B Some of the water will become ice.

C No ice will melt and no water will freeze.

D What will happen depends on the mass of ice and water.

9

21. When a lump of ice at 0 oC of 3.0 g was added to a beaker of warm water, the resulting water temperature was 7 0C less than the initial temperature of the warm water at the instant when all the ice had melted.

If another identical lump of ice at the same initial temperature is added to the same beaker, at the instant when all the ice had melted, the temperature will

A decrease by another 7 0C B will not change at all C decrease by more than 7 0C D decrease by less than 7 0C

22. 5000J of work is being done on an ideal gas as it gets compressed at a constant

temperature. What is the thermal energy absorbed by the gas in this process?

A Zero.

B Equal to 5000 J.

C Equal to –5000 J.

D Cannot be determined with given information

23. Three long wires W1 , W2, W3, carrying the same current I are arranged in the configuration

as shown below.

What is the direction of the resultant force acting on W1?

A Downwards

B Upwards

C To the right.

D To the left

temperature change = 7 0C

ice

temperature change = ?

water

ice

10

24. A small coil is positioned so that its axis lies along the axis of a large bar magnet as

shown in Fig 24.1.

The average magnetic flux density B through the coil varies with the distance x between

the face of the magnet and the plane of the coil as shown in Fig 24.2

Fig 24.2

If the coil is moved along the axis away from the magnet from x = a to x = b with constant

speed, which graph shows correctly how the emf induced in the coil E will vary with time t?

11

25. When a resistor is connected across a sinusoidal A.C. source of peak voltage 170 V, the

average power dissipated is 40 W. Two such identical resistors are now connected in

series to the electrical mains of 220 V r.m.s.

What would be the total power dissipated?

A 33.5 W B 67.0 W C 80.0 W D 134 W

26. A mains transformer has a 240 V r.m.s. ac input and a 12 V r.m.s. output. It is used to light three 12 V, 24 W lamps in parallel.

Assuming that there are no power losses in the transformer, the r.m.s. current, in ampere, drawn from the mains is

A 0.10 B 0.30 C 2.00 D 6.00

27. A wave pulse is moving, as illustrated, with uniform speed v along a rope.

Which of the graphs below correctly shows the relation between the displacement s of

point P and time t ?

A

B

C

D

12

28. If one of the slits of a standard Young’s double slit demonstration of interference in light is

painted over so that it transmits only half the light intensity of the other, which of the

following is correct?

A The fringe pattern will vanish completely.

B Only the bright lines will become dimmer.

C Only the bright lines will become brighter.

D The dark lines will become brighter and the bright lines will become dimmer.

29. The graph shows stopping potential of emitted electrons against incoming photon frequency

for a certain metal surface.

What changes, if any, would occur in the graph for a metal of lower work function?

Gradient x-intercept

A Higher Higher

B Same Lower

C Same Higher

D Lower Lower

30. Some of the energy levels of the hydrogen atom are shown below.

Electrons of energy 2.06 x 10-18 J collide with hydrogen atoms. How many spectral lines will

be observed from the hydrogen atoms?

A 0 B 3 C 6 D 10

13

31. To observe diffraction rings by a carbon film, a beam of electrons is accelerated from rest

across a potential difference of V so that the de Broglie wavelength of the electrons is 1.0

x 10-10 m. What is the value for V?

A 90 V B 150 V C 270 V D 330 V

32. To obtain X-rays, a cathode was heated by current I to produce electrons which are then

accelerated across a potential difference V to hit a metal target. The bold curve in Fig 32

shows intensity against wavelength of the X-ray spectrum produced. The dotted graph

was obtained when the process was repeated with changes. Which of the following in the

table shows the changes made in the repeated process?

Fig 32

Cathode current I Potential difference V Metal target

A Higher Lower Unchanged

B Higher Higher Unchanged

C Lower Lower Different

D Lower Higher Different

33. The accelerating potential difference in an X-ray tube is 20 kV.

What is the shortest wavelength of the X-ray photon emitted from the X-ray tube?

A 116.22 10 m

B 106.22 10 m

C 111.61 10 m

D 101.61 10 m

14

34. Which of the following statement about the production of laser is false?

A Population inversion enhances the chance of stimulated emission taking place.

B Meta stable state ensures that there is no spontaneous emission.

C Meta stable state is needed for population inversion to take place.

D Stimulated emission of photon can occur in a direction that is not in line with the direction

of the laser beam.

35. The diagram below shows the energy levels for the atoms of a 4-level laser system.

Which set of life-times for electrons residing in that energy state is possible if E2 is the

metastable state for this laser system?

E1 E2 E3

A 10-7 s 10-3 s 10-9 s

B 10-3 s 10-8 s 10-7 s

C 10-7 s 10-9 s 10-3 s

D 10-8 s 10-3 s 10-2 s

36. Which statement about conduction of electricity in solids is correct?

A Free electrons are found both in the conduction band and in the valence band.

B In an intrinsic semiconductor, electrons travel in the opposite direction to holes.

C In a metal, there is large energy gap between the conduction and valence bands.

D The presence of impurities in an intrinsic semiconductor is used to increase its resistance.

Energy

Eground

E1

E2

E3

15

37. A nuclide Y has the notation Ya

b. If M is the mass of nucleus, m1 is the mass of a proton

and m2 is the mass of a neutron, what is the binding energy per nucleon of this nucleus?

A [bm2 + am1 – M]c2

B [bm1 + am2 – M]c2/(a+b)

C [bm2 + (b – a)m1 – M]c2/b

D [bm1 + (a – b)m2 – M]c2/a

38. Radioactive source consists of 64 x 1012 atoms of nuclei P which has a half-life of 2 days.

Another source consists of 8 x 1012 atoms of nuclide Q which has a half-life of 3 days. After

how long will the number of radioactive nuclei of P and Q be equal?

A 6 days

B 9 days

C 12 days

D 18 days

39. In the Rutherford alpha particle scattering experiment, alpha particles passing through a

thin gold foil were scattered by the nuclei. Which of the following paths show correctly how

an alpha particle may be scattered by a gold nucleus?

40. An electron is incident on a rectangular potential barrier with a kinetic energy of 2.0 eV.

The barrier height is 6.0 eV and its width is d = 10100.1 m. The probability of the

electron tunnelling through the barrier is T. What would be the probability in terms of T if

the barrier width is reduced to 0.8 x 10-10 m?

A T0.2 B T0.8 C 1.3T D 2.2T

-End of paper-

16

Answers

1 2 3 4 5 6 7 8 9 10

C A A C A D C D D D

11 12 13 14 15 16 17 18 19 20

C A B B D B A A C C

21 22 23 24 25 26 27 28 29 30

D C D A B B D D B C

31 32 33 34 35 36 37 38 39 40

B B A B A B D D A B


CANDIDATE

NAME

TUTOR

NAME 1 4

PHYSICS

Paper 2 Structured Questions

2 September 2015

1 hour 45 minutes


Candidates answer on the Question Paper.

Write in dark blue or black pen.

You may use a soft pencil for any diagrams, graphs or

rough working.

Do not use paper clips, highlighters, glue or correction

fluid.

Answer all questions.

The number of marks is given in brackets [ ] at the end of

each question or part question.

For Examiner’s Use

1 9

2 10

3 6

4 6

5 8

6 6

7 15

8 12

Total / 72

CIVICS

GROUP


3

1 A girl of mass 50 kg falls vertically onto a trampoline, as shown in Fig 1.1.

Fig 1.1

The trampoline consists of a central section supported by springy material. At time t = 0, the girl

starts to fall. The girl hits the trampoline and rebounds vertically. The variation with time t of

velocity v of the girl is illustrated by Fig 1.2.

Fig 1.2

Use Fig 1.2 to answer the following questions.

(a) Determine the height fallen by the girl before she hits the trampoline.

Height = ……………………. m [2]

4

(b) Compare, without calculation, the acceleration of the girl before and after the rebound. Explain your answer.

…………………………………………………………………………………………………………...

…………………………………………………………………………………………………………...

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

(c) Compare, without calculation, the potential energy of the girl at t = 0 and t = 1.85 s. Explain your answer.

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

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

(d) The time interval during which the girl is in contact with the trampoline is shown on

the graph as rebound time. Determine the average resultant force on the girl during

this time.

Average force = …………………….. N [3]

2 (a) State the First Law of Thermodynamics.

………………………………………………………………………………………………………......

……………………………………………………………………………………….………………......

………………………………………………………………………………………………….……......

…………………………………………………………………………………………………………...

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

5

(b) A fixed mass of ideal gas is made to undergo the following processes as shown in Fig

2.1 below.

Fig 2.1

(i) Use data from Fig 2.1 to determine if process BC is isothermal. Explain your working.

[2]

(ii) The temperature of the gas at C is 385 K. Calculate the temperature of the gas at A.

Temperature at A = ___________ K [2]

Pressure / 105 Pa

Volume /104 m

3

5.0 6.0 7.0 8.0 9.0

2.0

1.0

3.0

C

B

4.0 10.0

0

A

6

(iii) Use the First Law of Thermodynamics to explain whether there is net heat supplied

or extracted when the gas is taken through the processes ABCA.

…………………………………………………………………….…………………………………......

………………………………………………….……………………………………………………......

………………………………………………….……………………………………………………......

………………………………………………….……………………………………………………......

………………………………………………….……………………………………………………......

…………………………………………………………………………………………………………...

………………………………………………………………………………………………………. [4]

3 (a) Fig 3.1 shows a long horizontal wire PQ carrying a steady current of 50 A in the direction

QP. A copper wire RS of diameter 0.40 mm hangs horizontally at a distance of 0.15 m

below wire PQ using some threads.

If the density of copper is 8930 kg m-3, determine the direction and the magnitude of the

minimum current in the wire RS so that there is no tension in the threads.

Assume that the magnetic force per unit length is given by d

II

l

F o

2

21 where I1 and I2

are the currents flowing in the respective wires and d is the distance between them.

Direction is …………………………. [1]

Minimum current = ……………………. A [2]

7

(b) A stiff straight copper wire XY is held fixed in a uniform magnetic field of flux density 2.6

x 10-3 T as shown in Fig 3.2. A sinusoidal alternating current of r.m.s. value 1.7 A passes

through the wire.

Fig 3.2

Calculate the maximum force exerted on the wire.

Maximum force = …………………….. N [3]

4 A charged particle passes through a region of uniform magnetic field of flux density 0.74

T with a radius of 23 cm as shown in Fig. 4.1.

Fig 4.1

8

(a) The particle is positively charged. State the direction of the magnetic field.

Direction is ……………………………………………………… [1]

(b) The speed v of the particle is 8.2 × 106 m s-1. Calculate the specific charge (charge

per unit mass) of the particle.

Specific charge = ……………………………. C kg-1 [2]

(c) The particle has a charge 1.6 × 10-19 C. Using your answer to (b), determine the mass

of the particle in terms of the unified mass constant u.

Mass = ………………………………… u [2]

(d) The particle is the nucleus of an atom. Suggest the composition of this nucleus.

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

9

5. Two sources S1 and S2 operate in phase to produce circular waves as shown in Fig. 5.1.

(Note that the circles represent crests.)

Along the line XY, there is a series of alternate maxima and minima.

(a) Explain what lines L1 to L6 represent and whether point A, as indicated in Fig. 5.1, is a

point of constructive or destructive interference.

………………………………………………….……………………………………………………......

…………………………………………………………………………………………………………...

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

(b) State the relationship between the magnitude of the path difference S1P – S2P and

wavelength, for any point P on the lines L1 to L6.

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

(c) Draw, on Fig. 5.1, a line to show one direction along which the waves have minimum

amplitude. Label this line as Z. [1]

Fig. 5.1

10

(d) If the separation of the sources is increased, state what would happen to the spacing

of the maxima.

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

(e) In a separate experiment using a ripple tank, two source interference of water waves,

using double-slit arrangement, were not be observed when the slits are wide.

However, narrowing the slits with the same previous separation produced obvious

interference patterns. Suggest why.

………………………………………………….……………………………………………………......

…………………………………………………………………………………………………………...

…………………………………………………………………………………………………………..

………………………………………………….……………………………………………………......

…………………………………………………………………………………………………………...

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

6. A junction is formed between slices of p-type and n-type semiconductor material, as shown

in Fig. 6.1.

(a) On Fig. 6.1, draw an arrow to show the direction of movement of electrons as the two

slices are brought into contact. [1]

(b) Explain the origin of the depletion region at the junction.

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

……………………...………………………………………………………………………………...[4]

p-type

material

n-type

material

Fig. 6.1

11

(c) In the figure below, show how a battery is connected so as to increase the width of the

depletion region. [1]

7. This question is about harvesting offshore wind power.

Hywind, the world’s first floating wind turbine that combines technologies from both the wind

farming industry and the oil and gas sectors was recently commissioned off the coast of

Norway. The Hywind are towed out to the open sea and then the floating Hywind is

anchored to the seabed by 3 long cables. The high-speed wind turbine is then used to

generate electricity. One of the reasons for operating the Hywind offshore is the continuous

presence of high speed wind from 8 m s-1 to 30 m s-1.

gearbox generator

Internal structure

of the Wind

turbine

Sea bed

Fig. 7a

Some of the Hywind Data:

Turbine mass: 138 000 kg

Turbine height above the sea surface: 65 m

Rotor blade diameter: 82.4 m

Displacement of water by Hywind: 5300 m3

Diameter submerged body: 8.3 m

Water depths: 120 - 700 m

12

(a) Determine the weight of the entire Hywind structure. (Assume there is no tension in the 3

long cables.) [Given density of seawater = 1025 kg m–3]

Weight = ……………………….. N [2]

(b) (i) The turbine is designed so that it faces the wind. As the rotor blades are set at an angle

to the plane in which they rotate, they deflect the wind.

Explain why the rotor blades rotate when subjected to the wind.

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

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

(ii) By outlining the energy conversions, explain how the electric power is generated using

the energy from the wind.

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

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

Fig. 7b shows how the output power, P, from a wind turbine varies with the speed, v, of the

wind.

13

Fig. 7b

It is thought that, for a given fixed size of the rotor blade, the electrical power output, P,

varies with the wind speed v according to the expression 3kvP

(c) Using the graph of Fig. 7b, show that k is a constant.

[2]

14

(d) Some corresponding values of lg P and lg v for the data in Fig. 7b are subsequently

plotted on the graph of Fig. 7c.

(i) On Fig. 7c,

1. plot the point corresponding to v = 11.0 m s–1,

2. draw the best-fit line for all the plotted points. [2]

(ii) Determine the gradient of the best-fit line drawn in (i) part 2.

Gradient = …………………….. [2]

Fig. 7c

15

(iii) Hence comment on the validity of the relation given in 7(c). Explain your answer.

………………………………………………………………………………………………………......

………………………………………………………………………………………………………......

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

8. As a bar magnet is dropped through a coil, an e.m.f. is induced in the coil. The maximum

e.m.f. E is induced as the magnet leaves the coil with speed v.

It is suggested that E is directly proportional to v.

Design a laboratory experiment to test the relationship between E and v. You should draw a

diagram showing the arrangement of your equipment. In your account you should pay

particular attention to

(a) the procedure to be followed,

(b) the measurements to be taken,

(c) the control of variables,

(d) the analysis of the data,

(e) the safety precautions to be taken. [12] [12]

Diagram

………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………..

16

………………………………………………………………………………………………………………..

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17

Answers:

1(a) height = area under triangle = ½ x 0.90 x 8.8 [M1]

= 3.96 m [A1]

(b) The accelerations are equal [A1] as they are straight lines with the same gradient

[M1].

(c) The area under graph after rebound is smaller than area under graph when the girl

falls [M1], hence the girl reaches a lower height after rebound and has lower

potential energy at t = 1.85 s [A1].

(d) change of momentum = <F> t [C1]

50[8.8 –(- 4.4)] = <F> x 0.50 [M1]

<F> = 1.32 x 103 N [A1]

2)a) The first law of thermodynamics states that the internal energy is a function of state [B1] and that the increase in internal energy is equal to the

sum of the heat supplied to the system and the work done on the system [B1].

b)

(i) T α PV pV (= 170 J) evaluated correctly for 2 set of readings taken from BC [M1] Since nR are constants in pV=nRT, same pV values mean same hence it is isothermal (or not isothermal) [A1]

(ii) At constant pressure, V T: 1.7 × 105

𝑇𝐴=

3.4 × 105

385 [C1]

TA = 193 K [A1]

(iii) ΔU = zero [M1]

Net work done on system is +ve. [M1]

Since ΔU = Q + W,

net Q is negative, [C1]

so heat is extracted. [A1]

18

3 (a)

(b) Peak current = 1.7 x √2

Force = BIL sin 34o

= 2.6 x 10-3 X (1.7 x √2) x 0.047 x sin 34o [C1]

= 1.64 x 10-4 N [A1]

4 (a) into (plane of) paper [B1]

(b) mv2/r = Bqv v/rB = q/m

q/m = (8.2 × 106 ) / (23 × 10-2 × 0.74) [C1]

= 4.82 × 107 C kg-1 [A1]

(c) mass = (1.6 × 10-19 ) / (4.82 × 107 × 1.66 × 10

-27 ) [C1]

= 2 u [A1]

(d) one proton and one neutron [A1]

19

5

a)

(i) Explain what lines L1 to L6 represent and whether point A, as indicated in Fig. 3.1, is

a point of constructive or destructive interference.

There are lines joining points of constructive interference/maxima [B1]. Point A lies

on the line of constructive interference, hence constructive [B1].

(ii) State the relationship between the magnitude of the path difference S1P – S2P and

wavelength, for any point P on the lines L1 to L6.

Path difference S1P – S2P is equal to integer multiple of wavelength

i.e. S1P – S2P = n [A1] where n = 0, 1,2,3 …

(iii

)

Draw, on Fig. 3.1, a line to show one direction along which the waves have

minimum amplitude.

see

Line cannot cross constructive interference line.

(iv

)

If the separation of the sources is increased, state what would happen to the

spacing of the maxima?

Fig. 3.1

20

Spacing decreases (similar to double slit formula) [A1]

In a separate experiment using a ripple tank, two source interference of water

waves, using double-slit arrangement, were not be observed when the slits are

wide. However, narrowing the slits with the same previous separation produced

obvious interference patterns. Suggest why.

When slits are wide, there is little spreading (diffraction) of water waves

and hence 2 individual streams of waves cannot meet(interfere) to form

interference patterns.

When slits are narrow, significant spreading [B1] occurs which allows both

waves to meet/overlap (interfere) and therefore superpose. [M1]

Overlap allows constructive and destructive interference to form at various

places, which is the obvious interference pattern observed [A1]

6. A junction is formed between slices of p-type and n-type semiconductor material, as shown in Fig. 6.1.

(a) B1- correct direction of arrow to the left

(b) Describe the origin of the depletion region at the junction. [4]

The p-type semiconductor has an excess of holes and the n-type semiconductor has an excess of electrons. [B1]

When these two semiconductors are placed together to form a junction, mobile electrons diffuse from the n-type across the junction to fill up some of the positive holes at the p-type and holes diffuse from p-type to n-type to combine with the electrons. [B1- electrons and holes combine]

This diffusion results in a region of negative ions in the p-type and positive ions in the n-typeat the junction as shown in the figure below. [B1- ions formed]

p-type

material

n-type

material

Fig. 6.1

21

As these ions are locked in the crystal lattice structure and are immobile, they create an electric field that prevents further diffusion of charge carriers. [B1-Field formed to stop further diffusion]

The depletion region is so named because the region is depleted of mobile charge carriers.

(c) On Fig. 6.1, draw the symbol for a battery, connected so as to increase the width of the depletion

region. [1]

B1 for correct battery

7 (a) Weight of Hywind structure, W = 5300 x 1025 x 9.81 = 5.33 x 107 N [A1]

(b)(i) The blades exert a force on the wind to change the momentum of the wind [M1]

By Newton’s 3rd law, the wind exerts an equal and opposite force on the wind blades

[M1]

Since the blades are attached to a pivot (center of rotor), the force on each blade

causes a torque or moment [A1] which results in a rotation of the wind turbine.

(ii) The kinetic energy of the wind is converted to rotational kinetic energy of the wind

blade and gear box [B1] causing the coils in the generator to rotate and cut the

magnetic field inside the generator [B1] which produces electrical energy through

the effect of electromagnetic induction.

c) Using points:

(10.5, 1300000): k = (1300000)/ 10.53 = 1123

(11.5, 1700000): k = (1700000)/ 11.53 = 1118

(14.5, 3400000): k = (3400000)/ 14.53 = 1115

k is approximately 1120 for all the 3 points tested.

[2] -obtain 3 values of k correctly;

[1] – obtain 2 values of k correctly.

Hence we can conclude that k is a constant.

d) (i) When v= 11 ms-1, p = 1500000 W

lg (11/ ms-1) = 1.041 , lg (1500000/W) = 6.176 = 6.18 (3 sf)

22

(d) (ii) Using points from the graph: (0.93,5.84), (1.13,6.44)

Gradient = (6.44 – 5.84)/(1.13 – 0.93) [C1]

= 0.6/0.2

= 3.0 [A1]

(d) (iii) 3kvP

lg p = 3 lg v + lg k hence gradient of the line is expected to be 3.

Since the experiment data also shows a straight line graph with gradient equals 3.0

[M1], the relationship 3kvP is probably valid.[A1]

23

8. Diagram: [2]

D1 Labelled diagram explicitly showing magnet falling vertically through coil (dotted lines,

magnet initial and final position etc). [1]

D2 Voltmeter or c.r.o. connected directly to the coil. Allow voltage sensor connected to

datalogger. [1]

Procedure [3]

P3 Method to change speed e.g. change height. [1]

P4 Measurements to determine v. Use metre rule to measure distance magnet falls to

the bottom of the coil or metre rule/ruler to measure length of coil or ruler to measure

length of the magnet. [Allow timing instrument to measure the time of the fall from the

start to the bottom of the coil.] [1]

P5 Method of determining v corresponding to appropriate distance e.g. v = √2gh or

v=2h/t (for height method) or v = L/t for length of magnet or coil and by stopwatch, timer

or light gate(s) connected to datalogger. [Allow v = gt for timing fall to bottom of coil.] [1]

Analysis [2]

A1 Plot a graph of E against v. [Allow lg E against lg v]

A2 Relationship valid if straight line through origin.

[If lg-lg then straight line with gradient = (+)1 (ignore reference to y-intercept)]

Safety considerations [1]

use sand tray/cushion to catch magnet. [1]

Control of variables & accuracy enhancement [4]

Relevant points might include:

1. Use coil with large number of turns/drop magnet from large heights/strong

magnet

2. Detailed use of datalogger/storage oscilloscope to determine maximum E; allow

video

3. camera including slow motion play back

4. Use same magnet or magnet of same strength.

5. Keep the number of turns on the coil constant.

6. Use a short magnet so that v is (nearly) constant

7. Use short/thin coil so that v is (nearly) constant

8. Use a non-metallic vertical guide/tube

9. Method to support vertical coil or guide/tube

10. Repeat experiment for each v and average the respective E values (ie to find

average value of E for each v instead of repeating experiment to find the average

value of v )

Do not allow vague computer methods.

[Total: 12]


CANDIDATE

NAME

TUTOR

NAME 1 4

PHYSICS

Paper 3 Longer Structured Questions

17 September 2015

2 hours


Candidates answer on the Question Paper.

Write in dark blue or black pen.

You may use a soft pencil for any diagrams, graphs or

rough working.

Do not use paper clips, highlighters, glue or correction fluid.

Section A

Answer all questions.

Section B

Answer any two questions. Please circle, on the cover

page, the two questions chosen.

You are advised to spend about one hour on each section.

The number of marks is given in brackets [ ] at the end of

each question or part question.

For Examiner’s Use

1 8

2 8

3 8

4 8

5 8

6 / 7 / 8

20

20

Total / 80

CIVICS

GROUP


3

SECTION A

1. During the course of a billiard game, a billiard ball A of mass m1, strikes a billiard ball B of

mass m2. The momentum p of ball B varies with time t as shown in Fig 1.1.

Fig 1.1

(a) Sketch on Fig 1.2 the variation of the force on ball B vs t. [1]

Fig 1.2

(b) State Newton’s Third Law of motion.

…………………………………………………………………………………………………….

…………………………………………………………………………………………………… [1]

(c) Sketch on Fig 1.2 the variation of the force on ball A vs t. [1]

4

(d) Show how your answer for (a) and (c) can lead to the principle of conservation of

momentum.

[3]

(e) Billiard ball B then strikes the side of the billiard table at 5.0 m s-1 and rebounds with a

velocity of 4.0 m s-1 as shown in Fig 1.3. B has a mass of 160 g.

Fig 1.3

Calculate the magnitude of the change in momentum of the ball.

Change in momentum = ___________kg m s-1 [2]

5

2. Fig. 2.1 shows the equipotential lines around three charged particles, with the potential

values indicated in volts. The diagram is drawn to scale.

Fig 2.1

(a) State the sign of each charge. [1]

Q1:……………..….. Q2:………………….. Q3:…….…………..

(b) Use the expression for potential near a point charge to compare and explain the relative

magnitude of charge Q1 and Q2. [2]

……………………………………………………………………………………………………

…………………………………………………………………………………………………….

…………………………………………………………………………………………………… [2]

(c) Calculate the work done to move an electron from d to j.

Work done = ………………………. J [2]

-1

+1

0 volts

-5

-5

+5

6

(d) Determine the magnitude of the electric field strength at k.

Electric field strength = ………………. N C-1 [2]

(e) On Fig 2.1, draw a vector for the electric field strength at point f. [1]

3 (a) Some data for work function energy Φ and the threshold frequency fo of metal surfaces

are given in Fig 3.1.

Fig 3.1

(i) State what is meant by the threshold frequency.

…………………………………………………………………………………………………….

…………………………………………………………………………………………………… [1]

(ii) Calculate the threshold frequency for platinum.

threshold frequency = ………………………. Hz [2]

7

(b) Electromagnetic radiation having a continuous spectrum of wavelengths between 300

nm and 600 nm is incident, in turn, on each of the metals listed in Fig 3.1. Determine

which metals, if any, will give rise to the emission of electrons.

[2]

(c) When light of a particular intensity and frequency is incident on a metal surface,

electrons are emitted. State and explain the effect, if any, on the rate of emission of

electrons from this surface for light of the same intensity and higher frequency.

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………… [3]

4. (a) Fission and fusion are both nuclear processes that release energy. Singapore is also looking into the possibility of tapping on nuclear energy as an energy source. Intensive research continues to harness the energy released from the fusion of hydrogen.

8

(i) Complete the equation for the fission of uranium-235. [1]

Given the following data:

Mass / u 235U 235.0439 138Cs 137.9110 96Rb 95.9343 1n 1.0087

(ii) Calculate the energy released in a single fission.

Energy released = …………………. J [2]

(iii) Hence determine the rate of fission necessary to maintain a power output of 2.5 GW.

Fission rate = ............................................ s-1 [2] (b) (i) The nuclear reaction below represents the fusion of two deuterium nuclei. Complete

the equation and identify particle X.

Particle X is a .............................................. [1]

9

(ii) Despite the difficulties, the quest for a practical fusion reactor continues. State two advantages fusion power might have over fission power.

1 …………………………………………………………………………………………………

…………………………………………………………………………………………………….

2 …………………………………………………………………………………………………

…………………………………………………………………………………………………….

[2]

5 (a) Radium-224 has a half-life of 3.6 days.

(i) Define what is meant by half-life and decay constant.

Half-life:

…………………………………………………………………………………………………….

…………………………………………………………………………………………………… [1]

Decay constant:

…………………………………………………………………………………………………….

…………………………………………………………………………………………………… [1]

(ii) Show that the decay constant of Radium-224 is 2.23 x 10-6 s-1.

[1]

10

(iii) Hence, determine the activity of a sample of Radium-224 of mass 2.24 mg.

activity =........................................ Bq [3]

(iv) Calculate the number of half-lives that must elapse before the activity of a sample of

a radioactive isotope is reduced to one tenth of its initial value.

number of half-lives = [2]

11

Section B

6 (a) The Earth spins on its axis with a period of one day.

(i) Show that the angular velocity of a point on the Earth’s surface is 7.27 x 10 -5 rad s-1.

[1]

(ii) Calculate the centripetal acceleration of a point on the Earth’s equator given that the

radius of the Earth is 6.38 x 106 m.

Centripetal acceleration = ………………………… m s-2 [2]

(b) The acceleration of free fall g at the equator is not equal to the acceleration of free fall at

the poles. Explain

(i) why they are different

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………… [2]

(ii) why the difference is small

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………… [1]

12

(b) A satellite of mass 1500 kg orbits a planet of mass 6.0 x 1024 kg with an orbital radius r, of

3.0 x 107 m.

(i) Calculate the potential energy of the satellite.

Potential energy = ………………………….. J [2]

(ii) Calculate the kinetic energy, EK of the satellite.

EK = …………………. J [3]

When the satellite is at A, it is given a boost so that its kinetic energy increases suddenly

to 1.33EK. It goes into an elliptical orbit as shown in Fig 6.1. At its furthest point B, the

satellite is twice as far from the planet.

Fig 6.1

(iii) When the satellite is at Z, draw a vector to indicate its velocity v and a vector to

indicate its acceleration a. Label the vectors. [2]

13

(iv) Determine the kinetic energy EA of the satellite at A and its kinetic energy EB at B.

EA = ………..………….……. J

EB = ………..……………….. J [3]

(v) Using the grid below with an appropriate scale, sketch the variation of

1. the potential energy U, and

2. the kinetic energy E,

with distance of the satellite from the planet as it moves in this elliptical orbit,

indicating appropriate values on the axes. Label your graph. [4]

14

7. (a) Fig. 7.1 shows the variation with applied potential difference V of the current I in an

electrical component C.

Fig 7.1

(i) State, with a reason, whether the resistance of component C increases or decreases

with increasing potential difference. [2]

…………………………………………………………………………………………………….

……………………………………………………………………………………………………… [2]

(ii) Determine the resistance of component C at a potential difference of 4.0 V.

Resistance = …………………….. Ω [1]

15

(iii) Component C is connected in parallel with a resistor R of resistance 1200 Ω and a battery of e.m.f. E and negligible internal resistance, as shown in Fig. 7.2 below.

Determine the current in the battery for an e.m.f. of 2.0 V.

Fig. 7.2

Current = …………………….. A [3]

Component C is now connected in series with R as shown in Fig 7.3.

Fig 7.3

(iv) On Fig. 7.1, draw a line to show the variation with potential difference V of the

current I in resistor R. [2] [2]

E

C

R=1200 Ω

C R=1200 Ω E

16

(v) Hence, explain clearly how you may determine the current in the battery for an e.m.f.

of 2.0 V, with negligible internal resistance in this configuration, and state the value of

this current.

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………… [3]

(b) A potential divider circuit consists of two resistors of resistances P and Q, as shown in

Fig. 7.4. The battery has e.m.f. E and negligible internal resistance.

Fig 7.4

(i) Deduce that the potential difference V across the resistor of resistance P is given by

the expression [2]

[2]

17

The resistances P and Q are 2000 Ω and 5000 Ω respectively.

A voltmeter is connected in parallel with the 2000 Ω resistor and a thermistor is connected in

parallel with the 5000 Ω resistor, as shown in Fig. 7.5.

Fig 7.5

The battery has e.m.f. 6.0 V. The voltmeter is assumed to have infinite resistance.

(ii) State and explain qualitatively the change in the reading of the voltmeter as the

temperature of the thermistor is raised. [3]

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………… [3]

(iii) The voltmeter reads 3.6 V when the temperature of the thermistor is 19°C.

Calculate the resistance of the thermistor at 19°C.

Resistance = ………………………… Ω [2] [2]

18

(iv) If the voltmeter was discovered to be non-ideal, explain whether the actual answer to (iii)

would be higher or lower.

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………… [2]

19

8. (a) Define simple harmonic motion.

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………… [2]

(b) A mass, m of 0.80 kg, is suspended from a helical spring as shown in Fig 8.1. The spring

has a constant of 300 N m-1.

Fig 8.1

(i) Calculate the extension of the spring at equilibrium.

Extension = ………….. m [1]

The mass is pulled down from its equilibrium position by 1.5 cm and released.

(ii) Calculate the initial upwards acceleration of the mass.

acceleration = …………… m s-2 [2]

(iii) Determine the frequency of oscillation of the mass.

frequency = ……………… Hz [2]

20

(c) A bar magnet is now suspended from the spring and one end of the magnet is situated

in a coil of wire, as shown in Fig 8.2. The coil is connected in series with a switch and

a resistor. The switch is opened.

Fig 8.2

The bar magnet is displaced vertically and then released. As the magnet passes

through its rest position, a timer is started. The variation with time t of the vertical

displacement of the magnet from its rest position is shown in Fig 8.3. At t = 4.0 s, the

switch is closed.

Fig 8.3

(i) Use Fig 8.3 to determine the frequency of oscillation of the magnet.

Frequency = …………… Hz [2]

(ii) State Faraday’s Law of electromagnetic induction.

…………………………………………………………………………………………………….

………………………………………………………………………………………………… [1]

21

(iii) Use the laws of electromagnetic induction to explain why the amplitude of oscillation

decreases after the switch is closed.

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

……………………………………………………………………………………………………

………………………………………………………………………………………………….…

…………………………………………………………………………………………………… [4]

(iv) Use Fig 8.3 to determine the fraction of energy lost 6.0 s after the switch is closed.

Fraction = ……………… [2]

(d) The set-up in (c) is modified by suspending the magnet above the coil and adding an

alternating voltage supply source in series with the coil and resistor, as shown in Fig 8.4.

The frequency of the voltage source is set at 0.50 Hz. The magnet is at rest.

22

Fig 8.4

When the switch is closed, the magnet is observed to start oscillating.

(i) State the frequency of oscillation of the magnet.

Frequency of oscillation = ………….. Hz [1]

(ii) The frequency of the voltage source is gradually increased to 5.0 Hz. State

and explain what will be observed about the amplitude of oscillations of the

magnet.

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

…………………………………………………………………………………………………….

………………………………………………………………………………………………… [3]

THE END

23

Answers:

1

(d) (i)

o

p p pF

t t t t

[B1]

(d) (ii) If body A exerts a force (action) on body B, then body B exerts a force of equal magnitude but in the opposite direction on body A.

[B1]

(iii)

[A1]

t / s

p / kg m s-1

0

FB

t / s

F / N

0

FB

t / s

F / N

0

FA

24

2. (a) State the sign of each charge. [1]

Q1:negative. Q2: negative ….. Q3 positive

(b)

Since V = Q/4πεor, for the same V, r is larger for Q1. [M1]

Hence Q1 is larger in magnitude than Q2. [A1]

(c) Calculate the work done to move an electron from d to j.

Work done = q(Vf – Vi)

= -1.60 x 10-19[2 – (-3)] [C1]

= - 8.0 x 10-19 J [A1]

(d) Determine the magnitude of the electric field strength at k.

E = dV/dx = 2.0/0.012 [C1]

= 167 N C-1 [A1]

(e)

(iv) Area under the force-time graph equals to the change in momentum or its impulse

B A

B B B A A A

B B A A A A B B

f i

p p

m v u m v u

m v m v m u m u

p p

[C1] [M1] [A1]

(v) Variant 1 Momentum is conserved as the system is isolated system (billiard ball A & B). Friction is negligible. Variant 2 Momentum is not conserved as the system (billiard ball A & B) is under the influence of an external force, friction between the balls and the table top covering.

[A1] [M1] [A1] [M1]

5 (a) (i)

v v ua

t t

[B1]

(ii)

2 2

= Area under - graph

1

2

1

2

2

s v t

s v u t

v uv u

a

v u

a

[M1] [M1]

(b) 2 2

2 2-1

2

21 3 1.7 m s

1

v us

a

vv

[M1]

v us

a

vv

v ut

2 2

2

2

30.12 2.88

1

2.88 30.070 s

0.5 0.5

[M1] [A1]

(c) (i) The rate of change of momentum of a body is proportional to the

resultant force acting on it and the change takes place in the direction of the force

[B1]

(ii)

Average Force

0.16 12 0

0.1

19.2 N

p

t

m v u

t

[M1] [A1]

(iii)

2 2 2

-1

-1

2 cos70

25 16 40cos70

27.32

5.22 m s

0.84 kg m s

f i

i f i f

p m v m v v

v v v v v

v

p

* Can also solve using components along the x & y directions.

[M1] [M1] [A1]

70o

vf

-vi

vf -vi

25

vector is perpendicular to equipotential line, and points towards lower potential. [B1]

3.

ai)

lowest frequency of em radiation [M1] giving rise to emission of electrons (from the

surface) [A1]

ii)

E=hf

threshold frequency = (9.0 x 10-19)/(6.63 x 10-34) [C1]

=1.4 x 1015 Hz [A1]

b)

300nm photons frequency is 10 x 1015 Hz (M1)

Sodium and zinc will emit [A1]

(c)

Each photon has larger energy [M1] Fewer photons per unit time [M1] fewer electrons

per unit time [A1]

4.

a (i) U236

92 nCs 1

0

138

552 [B1]

(ii) energy released

= [235.0439 – (137.9110 + 95.9343+1.0087)] x 1.66 x 10-27x (3.00 x 108)2 [M1]

= 0.1899 x 1.66 x 10-27x (3.00 x 108)2

= 2.84 x 10-11 J [A1]

Number of fission per unit time = 2.5 x 109/ 2.84 x 10-11 [C1]

26

= 8.80 x 1019 s-1 [A1]

b(i) 11X

Particle X is a proton. [B1]

Any two of the three answers: [B1, B1]

(ii) 1. There is less radioactive waste produced from fusion and which has shorter half-life,

unlike fission. So there is less hazard arising from waste from fusion.

2. There is unlimited/abundant supply of deuterium from the sea (1 part in 5000 of the

hydrogen in seawater is deuterium) for fusion, while there is limited supply of uranium for fission.

3. More energy is produced per unit mass of reactants in fusion compared to fission.

5 (a) (i) 1half-life : average time taken for the activity of the Radium nuclide to fall to half its original value. [B1] OR average time taken for half the original number of Radium nuclei to decay. [B1] The decay constant of a radioactive material is the probability of decay of a nucleus per unit time. [B1] or it is the fraction of radioactive nuclei that will decay per unit time

(ii) = ln2/t1/2 = ln2 / 3.6= 0.193 day-1 = 2.23 10-6 s-1 [A1 for correct sub]

(iii) N = (2.24 10-3)/224 6.02 1023

= 6.02 1018 [M1]

Acitivity = N = 2.23 10-6 6.02 1018 [C1]

= 1.3 1013 Bq [A1]

(iv) A = A0e(-ln 2.t/T) 0.1 = exp(-ln2.n) [C1] n = 3.32 [A1]

6a)i) ω= 2π/T = 2π / (24 x 60 x 60) [M1] = 7.27 x 10 -5 rad s-1

ii) a = r ω2 = (6.38 x 106) (7.27 x 10 -5 )2 [C1] = 3.37 x 10-2 m s-2 [A1]

b)i) An object above the Earth’s equator undergoes circular motion while an object above the

poles doesn’t [M1]. Thus, part of the gravitational acceleration due to gravity is used to provide

the centripetal acceleration, leading to a smaller acceleration of free fall. [A1]

ii) as shown in a)ii), the centripetal acceleration of the equator is relatively much smaller than

the acceleration due to gravity [B1]. Hence the difference is small.

27

(b) (i) Calculate the potential energy of the satellite.

Potential energy = - GMm/r = - 6.67 x 10-11 x 6.0 x 1024 x 1500/3.0 x 107 [M1]

= -2.0 x 1010 J [A1]

Potential energy = ………………………….. J [2]

(ii) Calculate the kinetic energy, EK of the satellite.

mv2/r = GMm/r2

½mv2 = GMm/2r [C1]

EK = 6.67 x 10-11 x 6.0 x 1024 x 1500/2 x 3.0 x 107 [M1]

= 1.0 x 1010 J [A1]

Kinetic energy = …………………. J [3]

Fig 6.1

(iii)

Velocity vector tangential to curve (length between that at A and B). [B1]

acceleration vector directed towards centre of planet. [B1]

(iv)

EA = 1.33 x (1.0 x 1010 ) J = 1.33 x 1010 J [B1]

Applying COE,

1.33 x 1010 + (-2.0 x 1010) = (-2.0 x 1010/2) + EB [M1]

EB = (1.33 – 1.0) 1010 = 0.33 x 1010 J [A1]

(v)

28

Mark scheme:

Shape of graph for EK according to scale [M1]

Shape of graph for U according to scale [M1]

[for graph(s) that is not within 3.0 and 6.0 x 107 m (-1)]

Values for U, EK ,distance and constant total energy at 3.0

and 6.0 x 107 m [A2] [-½ for each missing value]

29

7.

(a) (i) State, with a reason, whether the resistance of component C increases or

decreases with increasing potential difference. [2] [2]

The gradient of a straight line joining the origin to a point on the curve increases, thus ratio of V/I

decreases. [M1]

Resistance decreases [A1]

(ii) Determine the resistance of component C at a potential difference of 4.0 V. [1]

Current is 2.00 mA, so R= 2000 Ω.

(iii)

Current for R = V/R= 2/1200 = 1.67 mA. [M1]

Current for C = 0.75 mA [M1]

Current from battery = 1.67 mA + 0.75 mA = 2.42 mA. [A1]

(iv) Straight line passing through zero [M1]

with the correct ratio [A1]

(v) Since there no internal resistance, the sum of pd across C and R must be 2V[M1], also the

two components have common current since they are in series[M1], hence use the graph to find

a point where the sum of pd across C and R is 2.0V and the current is the same, I=0.5 mA [A1]

(b) (i) [2]

V=IP [B1]

Current in circuit =E/(P+Q) [B1]

Hence V=EP/(P+Q)

(ii) As temperature rises, resistance of thermistor drops. [M1], overall resistance and hence p.d.

across 5000 Ω and thermistor drops. [M1] Therefore p.d. across 2000 Ω.resistor increases [A1]

(iii) 3.6 = (2*6) / (2+R)

R=1.33 kΩ [M1]

1/1.33=1/5 +1/T

T = 1.82 kΩ [A1]

(iv) Non ideal voltmeter has non-infinite resistance, hence p.d. read across voltmeter will be

bigger without the voltmeter or with ideal voltmeter [M1]. This means lower p.d. across the

thermistor which must mean a lower actual value for the resistance across the thermistor at

19°C . [A1]

30

8. (a)

Acceleration is always directed towards equilibrium point [B1]

And is proportional to displacement from equilibrium point [B1]

(b)

(i) F = ke

0.80 x 9.81 = 300x

e = 0.0262 m [A1]

(ii)

k(e + x) - mg = ma

300(0.026 + 0.015) - 0.80 x 9.81 = 0.80a OR kx = ma [C1]

a = 5.63 m s-2

[A1]

(iii) a = ω2 xo

5.63 = (2πf)2 (0.015) [C1]

f = 3.08 Hz [A1]

(c)

(i) Use Fig 8.3 to determine the frequency of oscillation of the magnet.

Period = 0.80 s [C1]

Frequency = 1/T = 1/0.80 = 1.25 Hz [A1]

Frequency = …………… Hz [2]

(ii) State Faraday’s Law of electromagnetic induction.

[1]

Magnitude of induced emf is proportional to the rate of change of flux linkage [1]

(iii) Use the laws of electromagnetic induction to explain why the amplitude of

oscillations decreases after the switch is closed. [4]

As magnet oscillates in the coil, the flux linkage with the coil changes and emf is

induced in the coil, from Faraday’s Law. [M1]

This causes an induced current to flow when the switch is closed. [M1]

The oscillating system loses energy as there is heat loss in the resistor. [M1]

Since energy of the system is proportional to the square of amplitude, amplitude

decreases. [A1]

Or

From Lenz Law, the flow of induced current produces a magnetic field which results

in a force opposing the motion of the magnet. [M1]

The maximum resultant force on the magnet decreases, and since amplitude is

proportional to the maximum resultant force, amplitude decreases. [A1]

31

(iv) Use Fig 8.3 to determine the fraction of energy lost 6.0 s after the switch is

closed.

Energy α amplitude2

Initial amplitude = 1.50 cm

After 6.0 s, amplitude = 0.50 cm

Fraction of energy lost = 1 – (0.50/1.50)2 [M1]

= 0.89 [A1]

Fraction = ………………….. [2]

(d)

(i) Frequency of oscillation = …0.50.. Hz [1]

(ii)

Amplitude increases then decreases [B1]

Amplitude is maximum at 1.25 Hz [B1] when resonance occurs. [B1]

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