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PhysicsCourse Questions

Advanced Higher

8097

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.

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November 2000

PhysicsCourse Quest ions

Adva nced H igher

S upport Ma t eria ls

HIGHER STILL

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Physics: Course Questions (Advanced Higher) 1

INTRODUCTION

Course assessment will require candidates to respond to questions which integrate the

work studied across the component units as well as to questions which are less

structured and set in less familiar and more complex contexts (Advanced Higher

Physics, National Course Specification page 19, Second edition - December 1999).

A unit assessment in Advanced Higher Physics contains questions designed to assessachievement of the performance criteria associated with that unit and is not intended

to grade or rank the candidates. The course assessment is designed to grade, hencecertain questions, or parts of questions, are designed to assess the attainment of the

candidate against the Grade descriptions for the award at A.

Generating evidence for estimates of performance and for appeals

The unit assessments cannot be used on their own to provide an estimate of

performance or as evidence for appeals. Course type questions are required for these

purposes. These questions must emulate the demands of the external courseassessment. This pack provides examples of this type of question. The questions,

provided in the specimen question paper, are further sources.

A prelim paper attempted after the completion of two units can provide useful

evidence for appeals. Such a paper might reflect the format and duration of the final

examination paper and provide useful practice of examination technique. For this

paper to be a suitable basis on which to submit an appeal, it must be able to persuade

the Principal Assessor that it:

has not been seen by the candidate offers a suitable level of demand

allows for a demonstration of the criteria associated with the Gradedescriptions for the C and A awards.

The test paper can contain questions which are in the public domain. It is not

intended that all staff across Scotland should construct new questions when there are

valid past paper questions available from previous years. However the use of a

complete paper e.g. that of the previous year or so, is unlikely to prove acceptable to

SQA in that there is a high probability that the candidate has seen these questions.

A prelim paper consisting of a variety of questions of suitable demand from a range of

sources should be set. The paper should include questions that require candidates tointegrate across at least two units. Such a prelim would be supplemented by evidence

of attainment in the remaining unit, for example, by a short test of course typequestions on that unit.

Although the prelim is a preferred method in many centres, this is not a requirement

of SQA and a number of appropriate shorter tests of suitable demand makes a possible

alternative.

The questions

Many of the questions in this pack are based on previous CSYS questions. These

have been selected and adapted to reflect the demands of the Advanced Higher

syllabus.

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Solutions and marking scheme

Brief solutions to all questions have been provided at the end of this pack. These

solutions are designed to be of assistance to staff in marking students scripts.

The general instructions for markers issued by SQA in 1999 should be used as an

additional guide for awarding marks. Comments have been made to assist markingand highlight specific points.

For questions involving calculations where two marks are allocated, the followinggeneral rule for the award of partial marks should be applied:

{} for the formula, {} for substitution,

{1} for final answer. If the unit in final answer is wrong or missing deduct {}.

This is denoted in the marking scheme as [standard marking].

Where a question involving a calculation has more than two marks allocated,

comment is provided to assist in awarding marks. In some cases alternative methods

of responding to the question have been identified.

For questions calling for a description or an explanation a brief solution has been

provided. Professional judgement should be applied in giving credit for alternative

correct answers.

Credit should be given for correct physics. Wrong physics is always penalised.

It is appropriate to emphasise that in any external examination paper, markers attend a

markers meeting where marking of the individual questions are discussed.Decisions are then made on any finer points and markers all agree to apply these

decisions in their individual marking in order to ensure uniformity across the scripts.

In addition at the standardisation the examining team cross mark a selection of

scripts from each marker to ensure that there is a uniformity of marking. Any

excessive strict or excessive lenient marking is adjusted accordingly.

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MECHANICS

1. A child of mass 40 kg swings in a horizontal circle of radius 2.0 m by holding

the end of a rope attached to a vertical post as shown in the figure below.

The child completes one revolution in 4.0 s

(a) Find:

(i) the speed of the child

(ii) the horizontal component of tension in the rope

(iii) the vertical component of tension in the rope

(iv) the angle made by the rope with the pole. 8

(b) The child lets go when his feet are 0.50 m above the ground. Calculate

how far from the post he lands. State any assumption you made. 4

(12)

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2. A solid wheel and axle is allowed to roll from rest at AA/down an inclined

set of rails as shown in Figure 1.

Figure 1

The following information is given:

Mass of wheel and axle assembly = 1.4 kg

Height of AA/ above BB/ = 0.40m

Distance between AA/ and BB/ = 2.0 m

Diameter of axle = 1.0 cm

Time to travel from AA/ to BB/ = 30 s

(a) Calculate the speed of the solid wheel when it reaches BB/. 2

(b) Calculate the angular velocity of the solid wheel at BB/. 2

(c) (i) Write down an expression for the total rotational and translational

kinetic energy of the wheel at BB/.

(ii) Find the moment of inertia of the wheel. 3

(d) The experiment is repeated with a spoked wheel as shown in Figure 2.

The spoked wheel is mounted on an identical axle and has the same mass

as the solid wheel. The radius of the spoked wheel is greater than that of

the solid wheel.

Figure 2

(i) State and explain how the moment of inertia of the spoked wheel

compares with the moment of inertia of the solid wheel.

(ii) State and explain how the time taken for the spoked wheel to reach

BB

/

compares with the time taken for the solid wheel to reach BB

/

. 4(11)

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3. (a) State the mathematical expression of the inverse square law of gravitation 1

(b) (i) Show that the speed, v, of a satellite in orbit around the Earth is

given by

vGM

r

E= .

(ii) In the above expression state the meaning of the symbols G, MEand r. 3

(c) A satellite of mass 120 kg is placed in orbit 600 km above the Earth.

(i) Calculate the kinetic energy of the satellite

(ii) State the expression for the gravitational potential at a distance rfrom a mass M.

(iii) Due to the work done by friction the orbit of the satellite decreases to

580 km above the Earth. Calculate the loss of potential energy of thesatellite.

(iv) State and explain what happens to the kinetic energy of the satellite

when the orbit decreases. 7

(11)

4. (a) State what is meant by the moment of inertia of a rigid oject about an

axis of rotation. 1

(b) The rotor of an electricity generator in a power station can be consideredas a uniform cylinder rotating about its axis. The manufacturer quotes thefollowing data for such a rotor:

Rotor diameter = 3.6 m

Rotor mass = 210 103 kgMoment of inertia of rotor = 3.4 105 kg m2

Running Speed = 600 revolutions per minute

Time to reach running speed from rest = 30 s

(i) Calculate the angular acceleration of the rotor as it is brought from

rest to its running speed. You may assume that the acceleration is

uniform.

(ii) Calculate the torque exerted on the rotor.

(iii) What is the kinetic energy of the rotor at its running speed?

(iv) Due to the motion of the rotor, a nut on the surface of the rotor

experiences a force. The mass of the nut is 0.80 kg. The rotor is

turning at its designed running speed. Calculate the size of the force

experienced by the nut.

(v) Explain why there is a limit to the safe running speed of the rotor. 9

(10)

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5. When a car is moving at a steady speed, it may be assumed that each piston in

the engine moves with simple harmonic motion.

(a) A piston has a mass of 0.35 kg and a stroke (twice the amplitude) of

7.6 cm. When the engine is turning at 3000 revolutions per minute, find:

(i) the maximum acceleration of the piston(ii) the position or positions where the maximum acceleration occurs

(iii) the maximum force exerted on the piston

(iv) the maximum speed of the piston

(v) the maximum kinetic energy of the piston. 9

(b) Explain, in terms of the physical principles involved, the effects of over

revving the engine. 2

(11)

6. (a) In a particle accelerator, protons can be made to travel at speeds

approaching the speed of light. Using the relationship:

mm

v

c

=

0

2

21

12

(i) determine the speed of a proton, when its relativistic mass is double

its rest mass

(ii) calculate the relativistic energy of a proton travelling at this speed. 4

(b) In a hydrogen atom, the angular momentum of the electron is quantised.

(i) Calculate the lowest value for the angular momentum of the

electron.

(ii) When the electron has its lowest angular momentum, the orbital

radius of the electron is 5.3 10-11 m. Calculate the linearmomentum of the electron in this case.

(iii) Calculate the de Broglie wavelength of the electron in a hydrogen

atom when it has its lowest angular momentum. 6(10)

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7. The figure below shows a Ferris wheel, at a fun fair, which rotates in a

vertical plane about a horizontal axis.

Data for the Ferris wheel is given below.

Moment of inertia of the wheel empty = 8.8 105 kg m2

Maximum passenger mass per chair = 200 kgNumber of chairs = 16

Radius of the wheel = 10 m

The Ferris wheel is loaded to a maximum. When rotating at its maximum

angular speed, the period of rotation of the wheel is 30 s(a) Calculate the moment of inertia of the fully loaded Ferris wheel. 2

(b) Calculate the rotational kinetic energy of the loaded wheel at thismaximum angular speed. 2

(c) With the driver motor switched off and no application of the brakes, the

system decelerates uniformly to rest from its maximum speed. The

wheel takes 20 revolutions to come to rest.

(i) Calculate the angular deceleration of the wheel.

(ii) Calculate the frictional torque which causes this deceleration. 4

(d) A passenger will experience a force exerted by the seat. When the seat is

at the highest position, this force is a minimum.

(i) Explain why this is the case.

(ii) Calculate the value of this force experienced by a 50 kg passenger. 4

(12)

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8. (a) An ice skater changes her angular velocity in a spin by pulling in her

outstretched arms (Figure 1(a)) until they are close to her body (Figure

1(b)).

Figure 1(a) Figure 1(b)

(i) State what happens to her angular velocity

(ii) Explain the change produced, taking into account that her body mass

does not alter and that no external torque is applied. 3

(b) A turntable is in the form of a disc with a moment of inertia about the

central vertical axis of 0.024 kg m2. The turntable rotates in the

horizontal plane on very low friction bearings about its centre. The

angular velocity of the turntable is 8.0 rad s-1.

A small dart of mass 0.15 kg is now dropped from rest just above the

turntable. The dart sticks into the turntable at a distance of 0.14 m fromits centre as shown in Figure 2.

Figure 2

(i) Calculate the moment of inertia of the dart and turntable together.(ii) Calculate the new angular velocity of the system.

(iii) Calculate:

(A) the kinetic energy of the turntable before the dart is dropped

(B) the kinetic energy of the turntable and dart after the dart hasbeen dropped.

(iv) Account for the change in kinetic energy. 8

(11)

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9. In an experiment to measure the gravitational acceleration g, a mass was

suspended from a spiral spring. The resulting extension of the spring was

measured. The mass was then pulled down a little further, released, and

allowed to oscillate. The periodic time of the oscillations was measured.

This was repeated for a number of different masses.

The graph of extension against mass from the readings obtained is shown

below.

0

40

80

120

160

0 0.1 0.2 0.3 0.4 0.5

Mass/kg

Extension/mm

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(a) From the graph:

(i) obtain a value for the spring extension per unit mass

(ii) find the uncertainty in this value

(iii) what mass would produce an extension of 1 m? 5

(b) When the mass is displaced from its equilibrium position, the restoring

force is given by:

F ky=

where kis the force per unit extension or spring constantmeasured in

N m-1.

(i) Show that the periodic time T of the oscillation is given by:

TM

k=2

where M is the mass suspended from the spring.

(ii) The values obtained for the periodic time of the oscillations fordifferent masses are shown below.

Mass M / kg Periodic time T / s

0.10 0.380.20 0.53

0.30 0.63

0.40 0.740.50 0.82

(A) Plot a straight line graph to verify the relationship between T

andM.

(B) Use the gradient of your graph to find a value for k.

(C) From your value for kand your answer to (a) (iii), obtain a

value for g, the gravitational acceleration. 8

(12)

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10. (a) (i) State what is meant by escape velocity.

(ii) Show that the expression for the escape velocity from a planet ofmassMis given by:

v GMr

= 2

where the symbols have their usual meaning.

(iii) Calculate the escape velocity from the Moon. The radius of the

Moon is 2.6 106 m. 5

(b) It is believed that stars which are sufficiently massive may collapse toform a black hole when their nuclear fuel is exhausted at the end of their

life. A star with a mass three times the mass of the Sun could collapse to

form a black hole of radius less than 10 km.

What is meant by a black hole? 1

(6)

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11. A disc is mounted on a bearing as shown in the figure below.

The hanging weight produces a constant torque on the disc. The disc rotates

with a uniform angular acceleration, .

The disc is released from rest and the time taken for five complete rotations

while accelerating is measured with a stopclock. The experiment is repeatedseven times and the readings are shown below.

Experiment Time tfor five rotations / s1 9.80

2 9.42

3 9.66

4 9.935 9.92

6 9.35

7 9.63

(a) Find the mean time tand the approximate random uncertainty in the

mean. 3

(b) The equation for the angular displacement of an object accelerating

uniformly from rest is given by

= 122

t .

(i) Use the mean time tto calculate the angular acceleration .

(ii) Calculate the uncertainty in from the uncertainty in t. 4

(c) The moment of inertiaIof the disc is given by

( )

Imgr

d

=

+

.

where m is the mass of the hanging weight, g is the acceleration due to

gravity, ris the radial arm of the accelerating torque, and d is theangular deceleration of the moving disc due to the frictional torque after

the hanging mass is removed.

Calculate the value ofIand the uncertainty inIgiven that:

m = 0.011 0.001 kgr = 0.012 0.002 md = 0.050 0.003 rad s-2

g = 9.81 0.01 m s-2

. 4(11)

Hanging weight

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ELECTRICAL PHENOMENA

12. (a) Air ceases to be an effective insulator at an electric field strength of

3.0 106 V m-1.

(i) Write down an expression for the electric field strengthEbetweenparallel plates separated by a distance dwhen the potential

difference between the plates is V.

(ii) Two parallel plates are separated by a distance of 1.5 mm. Calculate

the p.d. between the plates when insulation of the air between plates

breaks down. 2

(b) An uncharged spherical conducting sphere is placed in the regionbetween two charged plates as shown in the figure below.

(i) State the nature of the electric field inside the sphere.

(ii) Copy the diagram.

(A) Show the distribution of charge on the sphere.

(B) Sketch the electric field in the region between the plates. 4

(c) (i) The electrostatic potential Vat a distance rfrom a point charge Q is

VQ

ro=

4.

Write down an expression for the potential at the surface of aconducting sphere of radiusR and charge Q.

(ii) Calculate the charge on a conducting sphere of diameter 100 mm

when the potential of the sphere is 1.8 kV. 3

(9)

+

_

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13. (a) (i) Draw an arrangement of point charges which gives a point in space

where the electrostatic potential is zero and the electric field strengthis non zero. Indicate the point concerned.

(ii) Draw an arrangement of point charges which gives a point in space

where the electrostatic potential is non zero and the electric field

intensity is zero. Indicate the point concerned. 4

(b) Two protons are separated by a very large distance. They are projected

towards each other along the same straight line with equal speeds.

(i) The protons are momentarily at rest at a minimum separation rmin .

Write down an expression for the electrostatic potential at one

proton due to the field of the other.

(ii) Hence write down an expression for the electrostatic potentialenergy when the separation is rmin

(iii) Given that rmin is 5.0 10-15 m find the initial speed of the protons,stating any principle that you use in your calculation.

(iv) Calculate the potential difference required to accelerate protons in a

linear electrostatic accelerator in order to achieve the speed

determined in (b) (iii). 7

(11)

14. (a) An electron moving with a constant speed of 2.0 106 m s-1 enters aregion of space where there is a uniform magnetic field. The magnetic

induction of the magnetic field is 0.50 mT. The path of the electron

makes an angle of 30 with the direction of the magnetic field as shownin the figure below.

(i) Explain why the resultant movement of the electron must be helical.

(ii) Calculate the component of the electrons velocity perpendicular to

the field.

(iii) Write down an expression equating the force on the electron with the

central force required for circular motion.

(iv) Find the time for the electron to complete one turn of the helical

path. 7

(b) The speed of the electron is doubled. Explain the effect on the time

calculated in (a) (iv)? 2

(9)

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15. (a) The force Fon a current carrying conductor in a magnetic field is given

by:

F IlB= sin .

Derive the relationship for the magnitude of the force acting on a charge

q moving with speed v perpendicular to a magnetic fieldB. 2

(b) A beam of positively charged particles enters through slit X into a regionwhere there is a uniform magnetic inductionB and uniform electric field

strengthE.

Each particle has a mass m, charge q and speed v.Plate Z is made positive with respect to the earthed plate.

(i) State the directions of the electric and magnetic fields when the

particles pass through the region undeflected to leave by slit Y.

(ii) Write down an expression equating the forces due to the electric andmagnetic fields.

(iii) Derive an expression which shows the relationship between v, E,

andB.

(iv) The potential difference between the plates is 550 V. The plate

separation is 0.12 m.

(A) Calculate the electric field strength between the plates.

(B) The charged particles travelling undeflected between X and Y

have a speed of 1.2 103 m s-1.Calculate the magnetic induction of the magnetic field. 7

(9)

YX

Z

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16. (a) (i) State what is meant by electric field strengthEat a point.

(ii) Write down an expression for the force Fwhich acts on a charge q in

an electric field of strengthE. 2

(b) In an oscilloscope, electrons travelling at a speed of 1.5 107 m s-1 enter

midway between the y-plates as shown in the figure below. The lengthand separation of the plates are shown. The potential difference between

the plates is 40 V.

(i) Describe the motion of the electrons as they pass between the plates.

(ii) Calculate the vertical displacementy of the electrons as they leave

the region between the plates.

(iii) By considering horizontal and vertical components of velocity, or

otherwise, calculate the angle between the horizontal and the pathof the electrons as they emerge from the field between the plates. 7

(9)

17. (a) A solenoid is connected to a d.c. supply as shown in the diagram below.

The switch S is closed.

(i) Draw a graph to show how the current varies with time.

(ii) Explain the shape of the graph. 3

(b) A coil of inductance 6.0 H and resistance 4.0 is connected to a 24 Vd.c. supply of negligible internal resistance.

Calculate:

(i) the maximum current in the circuit

(ii) the maximum potential difference across the coil

(iii) the maximum rate of change of current in the coil. 5

(8)

S

0.050 m

0.020 m

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18. In the apparatus shown in the figure below, a beam of singly charged positive

ions enters an evacuated chamber at A. The ions travel between plates P1 andP2 before passing through slit S, normal to XY.

The whole apparatus is in a uniform magnetic field of magnetic induction

0.60 T. The potential difference between plates P1 and P2 is 3000 V. The

distance between P1 and P2 is 20 mm. The deflected ions form lines on aphotographic plate W.

(a) Show in a sketch, the polarity of plates P1 and P2 and the direction of the

magnetic field which will make the ions follow the path shown. 2

(b) (i) Show that ions passing through the slit S have a velocity v given by

vE

B=


(ii) Explain what will happen to ions which have a speed greater than

this value. 2

(c) Calculate the velocity of ions passing through S. 2

(d) Describe and account for the shape of the path of the ions after passingthrough S. 2

(e) Some ions form a trace on W at a point R. R is 190 mm from S.

Calculate the mass of one of these ions. 3

(11)

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19. A battery of e.m.f. 10V and negligible internal resistance is connected to a

data capturing device and a coil of wire as shown in the circuit diagram

below.

When the switch is closed, the data capturing device measures the current at

intervals of 0.1 ms.

The current in the circuit is found to vary over the first millisecond as shown

in the graph below.

data capture device to

measure the current

S

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19. continued

(a) Switch S is closed. The coil produces a back e.m.f.

(i) State the size of the back e.m.f. at this time.

(ii) Explain why the back e.m.f. opposes the battery e.m.f. 2

(b) Use the graph to determine:

(i) the initial rate of change of current

(ii) the self inductance of the coil 4

(c) The final steady current in the circuit is 25 mA.

(i) Find the resistance of the coil.

(ii) Calculate the energy stored in the inductor when the current is at its

maximum. 4

(d) A coil of negligible resistance is connected to a variable frequency

sinusoidal a.c. supply. Sketch a graph showing how the current in thecoil varies with frequency. The amplitude of the output voltage from the

supply is constant. 1

(11)

20. (a) The magnetic inductionB at a distance rfrom an infinitely long straightwire carrying a currentIis given by

BI

r=

0

2

Derive the expression for the force per unit length between two long

parallel wires carrying currentsI1 andI2 at a distance rapart. 2

(b) A long horizontal cable P lying in a North-South direction provides the

electricity supply to an industrial process. The cable carries a current of

200 A in the direction from North to South. The vertical component of

the Earths magnetic field is 4.36 10-5 T.

(i) What is the size and direction of the force per unit length acting on

the wire due to the vertical component of the Earths magnetic field?

(ii) A second identical cable Q is laid parallel to and at a distance of

1.5 m from cable P in the same horizontal plane. Cable Q carries acurrent of the same size and in the same direction as the current in P.

What is the size and direction of the force per unit length acting on P

due to Q? 6

(8)

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21. (a) Two point charges Q1 and Q2 are separated in air by a distance r.

Write down an expression for the force acting on charge Q2. 1

(b) A negative pion is made up of a d quark and a u antiquark. The electric

charge on the d quark is 1/3 e and that on the u antiquark is 2/3 e where e

is the charge on an electron.

(i) The distance between the quark-antiquark pair is 1.0 10-15 m.Calculate the electric force between the quark-antiquark pair in the

pion.

(ii) Name the force which holds this quark-antiquark pair together. 3

(c) The figure below shows a charge q travelling directly towards a fixedstationary charge Q. Charge q is initially travelling with a velocity v.

Show that, for a head on collision, the distance of closest approach, rc is

given by

rqQ

mvc =

2 02

where m is the mass of charge q and 0 is the permittivity of free space. 2

(d) An alpha particle of mass 6.7 10-27 kg is moving with an initial velocityof 1.0 107 m s-1 directly towards a fixed stationary gold nucleus. Theatomic number of gold is 79.

Find the distance of closest approach of the alpha particle to the gold

nucleus. 2

(e) (i) Explain why the radii of all atomic nuclei are very tiny.

(ii) Name the force associated with beta decay in radioactive nuclei. 3

(11)

+ +v

qQ

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WAVE PHENOMENA

22. (a) (i) Explain what is meant by a stationary wave.

(ii) State the differences between a travelling wave and a stationary

wave. 3

(b) (i) Explain why the relationship

y a ftx

=

sin2

represents a travelling wave.

(ii) A travelling sound wave is represented by the expression

( )p t x= 2 330sin

wherep is the pressure variation in pascals and the other symbols

have their usual meanings.

Find

(A) the wave frequency(B) the wavelength

(C) the wave speed. 6

(10)

23. (a) A source of sound waves of frequencyfis moving towards a stationary

observer. Show that the frequency detected by the stationary observer is

given by

=

f fv

v vs.

where v is the speed of sound in the medium and vs is the speed of thesource of sound waves relative to the observer. 2

(b) A car has a siren emitting a note of frequency 550 Hz. The car is

travelling at 45 m s-1 towards a stationary observer.

(i) Calculate the frequency of the sound heard by the observer as the car

approaches.

(ii) What frequency will be heard by the observer after the car has

passed the observer? 4

(c) In a gas discharge tube, moving gas atoms emit light after being put into

an excited state by passing a current through the gas.

(i) State the effect on the frequency of the light observed by a stationary

observer in

(A) the direction in which the atom producing the light is moving

(B) the direction opposite to that in which the atom producing the

light is moving.

(ii) Explain briefly why cooling the discharge tube would have the effect

of making the light emitted more monochromatic. 3

(9)

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24. (a) (i) State the conditions for two light beams to be coherent.

(ii) The conditions for coherence are usually more difficult to satisfy forlight than for sound.

Explain why this is so. 2

(b) Interference fringes may be formed by division of amplitude when light

from an extended source is incident normally on a thin wedge shapedfilm.

(i) State what is meant by division of amplitude.

(ii) There is no coherence between light waves originating from

different points on an extended source. Explain why an extended

source can be used to produce interference fringes.

(iii) Show that the distance x between fringes formed by a thin film

whose thickness increases by an amountD over a lengthL is givenby

xL

nD=

2

where is the wavelength of the light in a vacuum (or air) and n isthe refractive index of the medium of the film. 5

(c) Two optically flat glass plates of length 125 mm are separated at one end

by a hair as shown in the figure below. This forms a thin air wedge.

Light of wavelength 589 nm illuminates the plates from above.

At the line of contact of the glass plates there is a dark fringe.A further 55 dark fringes are counted in a distance of 50.3 mm.

(i) Explain why there is a dark fringe at the point of contact of the glass

plates.

(ii) Calculate the thickness of the hair.

(iii) State what would happen to the fringes if the space between the

glass plates was filled with water, rather than air. 5

(12)

hair

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25. White light is reflected normally from one part of a soap film with

surfaces A and B as shown in Figure 1. The refractive index of the soapfilm is 1.38.

Figure 1

The light is then focussed on to the slit of a spectrometer as shown in

Figure 2.

Figure 2

The first order spectrum observed has a dark band with a minimum intensity

at an angle corresponding to a wavelength (in air) of 578 nm.

(a) (i) State what is meant by the optical path difference between wavesreflected from the two surfaces A and B of the film.

(ii) Explain how the absence of light at 578 nm can be accounted for by

interference effects in the thin film.

(iii) Calculate the minimum thickness of soap film consistent with a dark

band at 578 nm. 5

(b) White light is reflected normally from a different part of the film and the

position of the dark band in the first order spectrum is found to be closer

to the red end of the spectrum.

Explain what information this gives about the difference in filmthickness between the two positions used for reflection. 2

(e) After the conclusion of the experiment it was noticed that a black bandformed across the film at the top of the film and increased in width until

it extended over most of the film just before the film broke.

Explain this observation. 2

(9)

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26. The figure below shows a non reflective coating for a lens. This coating

produces destructive interference of the reflected beams at normalincidence.

(a) Derive a relationship between the minimum thickness dof the coating,the wavelength of the light in air and the refractive index n of thiscoating. 2

(b) Magnesium fluoride is used as a non reflective coating for a lens. The

refractive index of magnesium fluoride for a wavelength of 550 nm is

1.38. Calculate the thickness of magnesium fluoride required to produce

destructive interference for light of wavelength 550 nm. 2

(c) Explain what effect the coating will have on the intensity of transmitted

light. 2

(d) The lens is illuminated with white light and viewed in the reflected light.

Describe and explain the appearance of the lens 2

(8)

27. When unpolarised light is incident on the surface of water at the Brewster

angle, the reflected light is polarised.

(a) Explain what is meant by light is polarised. 1

(b) Explain why sound is not polarised by reflection. 1

(c) Calculate Brewsters angle for monochromatic light reflected from water.The refractive index of water is 1.33 for this light. 2

(d) Suggest why polarising sunglasses might be of use to a trout fisherman. 1

(5)

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28. A source of monochromatic light is placed behind two narrow slits

separated by 0.25 mm. A light detector, 2.5 m in front of the slits, ismoved from X to Y as shown in the figure below.

As the detector moves from X to Y, a series of maximum and minimum

readings is observed.

The distance of the detector from X for each maximum reading is recorded

in Table I.Table 1

Order of maximum reading 0th 1st 2nd 3rd 4th 5th

Distance from X/mm 0 6.9 14.1 21.0 27.9 35.0

(a) (i) Show that the fringe spacing x for an experimental arrangementof this type is given by the expression

xD

d=


(ii) Calculate the wavelength of light used in the experiment. 4

(b) The experiment is repeated using a different colour of light and the

results are shown in Table 2.

Table 2

Order of maximum reading 0th 1st 2nd 3rd 4th 5th

Distance from X/mm 0 6.0 12.0 17.9 24.0 30.1

(i) State how the wavelength of this light compares with that used in

the original experiment.

(ii) Suggest one way in which the experimental arrangement could be

changed so that the separation of the maximum readings returned

to those in Table I. 2

(6)

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Solutions and notes to assist marking

Marks are shown bold inside curly brackets e.g. {2} or {1/2}.Where necessary guidance in the award of partial marks is shown.

MECHANICS

1. (a) (i) 3.1 m s-1{2} [standard marking](ii) 197 N (allow 192 N) {2} [standard marking](iii) 392 N {2} [standard marking](iv) 26.7 {2} [standard marking]

(b) horizontal distance 0.99 m {2} [standard marking]distance from post (using Pythagoras) 2.2 m {1}assumption - initial movement at a tangent {1}

2. (a) 0.13 m s-1 {2}(b) 26 rad s-1 {2}(c) (i) Total Ek = mv

2 {1/2} + I2 {1/2}(ii) I = 0.016 kg m2 {2} [standard marking]

(d) (i) Will be greater {1}, since mass on average further from the axis. {1}(ii) Longer {1} since more rotational Ek, less translational Ek at the bottom so

average speed smaller. {1}3. (a) F

Gm m

r= 1 2

2{1}

(b)mv

r

GM m

r

E

2

2= {1/2} + {1/2}

v2 =

r

GME [{1/2} for evidence that v GMr

E= is obtained]

Where G is the universal gravitational constant, ME is the mass of the Earth

and r is the distance between the satellite and the centre of the Earth {1/2}.(c) (i) Ek= mv

2 {1/2} Ek =

12

11 24

61206 67 10 6 0 10

7 0 10

. .

.

{1/2} + {1/2} + {1/2} for correct data in numerator and denominator Ek= 3.4 109 J {1} [deduct {1/2}if unit wrong or missing](ii) E

GM

rp= {1}

(iii) 2.0 107 J {2} [no mark for formula, since above used][{1/2} + {1/2} for correct substitutions for GMm + both rs][{1} for final answer, deduct {1/2} if wrong or missing unit]

(iv) Ek increases {1},since v increases as rdecreases {1}

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4. (a) Moment of inertia is a measure of the reluctance of a body to accelerate

rotationally in response to a torque {1/2}, takes account of distribution ofmass as well as mass. {1/2}

(b) (i) 2.1 rad s-2 {2} [standard marking](ii) 7.1 105 N m {2} [standard marking](iii) 6.7 108 J {2} [standard marking](iv) 5.7 103 N {2} [standard marking](v) Nut might shear {1}

5. (a) (i) 3.75 103 m s-2 {2} [standard marking]at the extreme positions {1}

(iii) 1.3 103 N {2} [standard marking](iv) 11.9 m s-1 {2} [standard marking](v) 24.9 J {2} [standard marking]

(b) Increases the max acceleration {1}, increases the max force on piston {1}6. (a) (i) 2.6 x 108 m s-1 {2} [formula given, {1/2}+ {1/2}for correct substitutions]

(ii) 3.0 10-10 J {2} [standard marking](b) (i) 1.1 10-34 kg m2 s-1 ( or Js) {2} [standard marking]

(ii) 2.0 10-24 kg m s-1 {2} [standard marking](iii) 3.3 10-10 m {2} [standard marking]

7. (a) 1.2 106 kg m2 {2} [standard marking](b) 2.6 104 J {2} [standard marking]

(i) 1.7 10-4 rad s-2 {2}[standard marking](ii) 204 Nm {2} [standard marking]

(c) (i) At the top of the motion the force upwards from the seat has to equal the

weight less the central force required for circular motion. {1}At the bottom the force upwards from the seat has to equal the weight plus

the central force. {1}(ii) 468 N {2} [standard marking]

8. (a) (i) Increases {1}(ii) Mass brought in towards the axis {1/2}, moment of inertia decreases {1/2}

angular momentum remains unchanged {1/2}, hence angular velocity

increases {

1

/2}(b) (i) 0.027 kg m2 {2} [standard marking](ii) 7.1 rad s-1 {2} [standard marking](iii) (A) 0.77 J {2} [standard marking]

(B) 0.68 J {1} [same calculation as (A) hence 1 mark for answer only](iv) Lateral friction and slight lateral movement produce heat [allow: heat

produced due to friction between dart and disc] {1}

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9. (a) (i) 360 mm kg-1 {2} (allow 10)(ii) 20 mm kg-1 {2} (allow between 15 and 25 )(iii) 2.8 kg {1}

(b) (i) F= -ky and F= ma hence a =Mk y- {1/2}

a = - 2y {1/2} 2 = k

M{1/2} [notice that a is acceleration]

TM

k= =

22

[{1/2} for evidence that

kMT 2= is obtained]

(ii) (A) plot T2

againstMwith: both axes correctly labelled {1/2}points plotted correctly {1}best straight line drawn {1/2}

(B) 29.7 N m-1 {2}(C) 10.6 m s-2 {2} [for answers to B and C allow appropriate range]

[answers to B and C should be given to two significant figures,

above answers are given to three significant figures to assist

marking]

10. (a) (i) Minimum velocity required at the surface of a planet to remove an object

to infinity. {1}(ii) To escape total energy Ek + Ep(at infinity) = 0

hence total energy on surface of planet Ek + Ep (surface) = 0 {1/2}

mv2 {1/2} +

rGMm {1/2} = 0

v

2

= r

GM

[{

1

/2} for evidence that v = rGM2

is obtained](iii) 1.9 103 m s-1 {2} [standard marking]

(b) The escape velocity is greater than the speed of light so nothing including

light can escape from the star. {1}ORThe collapsed star has a very large gravitational field. Light is affected by

gravitational fields and does not escape. {1}

11. (a) 9.67 s {2} [standard marking]

uncertainty = readingsofnumber min-max {1/2} = = 0.08 s {1/2}(b) (i) 0.67 rad s-2 {2} [standard marking]

(ii) % uncertainty in is 0.8% {1/2}% uncertainty in tis 1.6% {1/2} of 0.67 = 0.01 rad s-2 {1}

(c) I = 1.8 x 10-3 kg m2 {2} [formula given but give {1}for substitutions]percentage uncertainty in denominator = 1.4% {1/2}percentage uncertainty in numerator = 19% {1/2}overall uncertainty = 19% {1/2} = 0.3 x 10-3 kg m2 {1/2}

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ELECTRICAL PHENOMENA

12. (a) (i) E Vd= {1/2}

(ii) 4.5 kV {11/2} [{1/2} for substitutions {1} for answer](b) (i) Zero

(ii) (A) correct charges on the outside surface {1}(B) direction of lines shown correctly {1}

lines terminate at 90o to plates and to surface of sphere{1}(c) (i) V Q R= 4 0 {1}

(ii) 1.0 nC {2} [formula given above [{1/2} + [{1/2} for substitutions/data]

13. (a) (i) Arrangement {1} [e.g. one positive, one negative]Position {1} [e.g. mid way between equal + and - charges]

(ii) Arrangement {1} [e.g. two positive charges]Position {1} [e.g. mid way between equal positive charges]

(b) (i) V q r= 4 0 min {1}(ii) E q rp =

2

04 min {1}

(iii) Change in Ep = change in Ek OR all initialEkconverted toEp {1/2}[Correct data substitutions for q {1/2}, for 0 {1/2}, and for m {1/2}]5.2 106 m s-1 {1} for answer (note: min0

22

21 42 rqmv = )

(iv) 1.4 105 V {2} [standard marking]

14. (a) (i) Component of initial velocity parallel to the field remains unchanged. {1}Component of velocity perpendicular to field results in circular motion {1}

(ii) 1.0 106

m s

-1

{1}(iii) ( )Bqv m v rsin sin = 2 {1} [ORBqv = mv2/r]

(iv) 7.15 10-8 s {3} [T=v

r2 {1/2} andm

Bq

r

v= {1/2} hence T=

qBm2 {1/2}]

[substitutions {1/2} and final answer {1} as for standard marking](b) No change in time for one rotation {1}

since doubling speed doubles r{1/2}and distance travelled is doubled {1/2}

15. (a) I Nqv= {1/2} and F BNqvl= {1/2}

force per unit charge = =BNqvl Nl Bqv {1}[OR other equivalent derivation]

(b) (i) Electric field from top plate to bottom {1}Magnetic field at right angles {1/2}, into the paper{1/2}

(ii) Bqv Eq= {1}(iii) v E B= {1}(iv) (A) 4.6 103 V m-1 {2} [standard marking]

(B) 3.8 T {1}[no partial mark for formula or substitutions, but allowcredit if wrong answer for (A) correctly used here]

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16. (a) (i) The force per unit charge at the point (acting on a small test charge) {1}(ii) F Eq= {1}

(b) (i) Parabola {1}(ii) horizontally t= (length of plates)/vH = 0.05/(1.5 107) {1/2}

vertically E = V/d {1/2} a = Eq/m {1/2} s = at2 {1/2}2.0 mm {1}

(iii) vertical velocity tm

Eq= {1}

tan= v vV H {1/2} substitutions {1/2} = 4.5o {1}

17. (a) (i) Shape of graph correct {1/2}Axes labelled correctly{1/2}

(ii) Increasing current produces back e.m.f. {1/2}Initial back e.m.f. equal to supply voltage {1/2}Hence initial rate of current increase is limited

{

1/

2}Rate of current increase gets less asIrises and voltage across resistorincreases. {1/2}

(b) (i) 6 A {2} [standard marking](ii) 24 V {1}(iii) 4 A s-1 {2} [standard marking]

18. (a) P1 positive, P2 negative {1}B field out of paper {1}

(b) (i) Bqv Eq= {1} [hence answer given](ii) Deflected (towards X) hence do not pass through S. {1}

(c) E = V/d {1/2}; for substitutions {1/2} 2.5 105 m s-1 {1}(d) Circular path {1/2}

Force on ion due to motion through B field is constant {1/2}and perpendicularto direction of motion {1/2}and acts as a central force. {1/2}

(e) 3.6 10-26 kg {2} [standard marking]

19. (a) (i) 10 V {1}(ii) Induced e.m.f. opposes the change of current, the battery must supply

energy in overcoming the back e.m.f. {1}(b) (i) 5 A s-1 {2} [readings from graph at t= 0 and calculation of gradient]

(ii) 2 H {2} [standard marking](c) (i) 400 {2} [standard marking]

(ii) 6.25 10-4 J {2} [standard marking](d) Axes labelled {1/2}

Shape correct {1/2}

20. (a) B atI2 due toI1 = 0 1 2I r {1/2}

force on length l carrying currentI2 =BI l2 {1/2} = 0 1 2 2I I l r {

1/2}force per unit length = 0 1 2 2I I r {

1/2}(b) (i) 8.72

10-3 N

{2

}, East

{1

}(ii) 5.3 10-3 N (or N m-1) {2} towards Q {1}

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21. (a) F Q Q r = 1 2 024 {1}

(b) (i) correct substitution for charge (1.6 10-19) {1/2}correct substitution for 0 or 1 /4o{1/2}51 N {1}

(ii) Strong force {1}(c) Change in Ek= change in Ep {1/2}

040 02

21 =+ crqQmv {1}{1/2} for evidence that final expression is obtained

(d) (i) 1.1 10-13 m {2}[formula given, {1/2} + {1/2} for substitutions](e) (i) The strong force which holds the nucleons together has a very short

range (about 10-14 m) {1}(ii) Weak force {1}

WAVE PHENOMENA

22. (a) (i) A wave formed by two waves of same wavelength and frequency {1

/2},travelling in opposite directions. {1/2}(ii)

Travelling wave Stationary wave

Energy is transported {1/2} Energy is stored {1/2}Phase difference between adjacent

oscillating points. {1/2}No phase difference between

adjacent oscillating points

(between nodes).

Adjacent points have same

amplitude (1D wave).

Adjacent points oscillate with

different amplitude. {1/2}

(Use professional judgement. - {1/2} for each relevant independent difference)

(b) (i) For a displacementy to be constant

xft must remain constant {1}

but as tincreasesx must increase {1} (and the equation represents atravelling wave)

[Use professional judgement with respect to detail]

(ii) (A) 165 Hz {1}(B) 2 m {1}(C) 330 m s-1 {2} [standard marking]

23. (a) = vf

S

1{1}

v

f

v

f

v

f

S

= {1/2} hence

svv

fvf

= {1/2}

(i) 634 Hz {2}[no partial mark for formula since given ]{{1/2} for vs and {1/2} for other substitutions]

(ii) 486 Hz {2} [standard marking](b) (i) (A) Will increase (very slightly) {1}

(B) Will decrease (very slightly) {1}(ii) Cooling would reduce the speed of the atoms. {1}

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24. (a) (i) They must have the same wavelength {1/2} and have a constant phaserelationship. {1/2} - i.e. in general they must be from the source and thesame part of the source, and have a very small path difference.

(laser light a special case)

(ii) Two light sources cannot maintain a constant phase relationship

(whereas two loudspeakers can be driven from the same signalgenerator).{1/2}Light wavetrains are short (whereas continuous waves from a

loudspeaker can be very long) {1/2} (use professional judgement foralternatives)

(b) (i) A wave is split into two waves by partial reflection {1} and partialtransmission {1} at a surface.

(ii) Each point on the source produces two waves by division of amplitude

which are recombined having a path difference determined only by the

film thickness (and refractive index). {1}

(iii) for a dark fringe, m ny= 2 {1

/2}for the next dark fringe, ( )m n y

xD

L+ = +

1 2

{1}and =

2xDnL

{1/2} hencenDLx

2= [as given]

(c) (i) Phase change of at the lower surface. {1}(ii) 4.03 10-2 mm {2}[no partial mark for formula since given]

[{1/2} + {1/2} for correct substitutions instead](iii) Spacing would decrease. {1}

25. (a) The equivalent path difference in a vacuum (or air) for two waves, whichwould produce the same phase difference between the waves. {1}OR

optical path = geometrical path difference refractive index {1/2}the optical path difference is the difference between the two optical paths {1/2}

(b) Light reflected from the two surfaces has an optical path difference equal to a

whole number of wavelengths. {1} This produces destructive interference{1/2} since there is a phase change for one of the reflections. {1/2}

(c) 209 nm {2} [standard marking](d) The film is thicker {1}, since the wavelength is larger being closer to the red

end {1

/2} and nd 2= hence dis larger. {1

/2}(e) When the film is very thin and about to break{1/2}, light reflected from both

surfaces has nearly zero optical path difference {1/2}, and since there is aphase change of for light reflected from one surface {1/2}, destructiveinterference occurs{1/2}.

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26. (a) Optical path difference = 2nd{1/2}For destructive interference 2 2nd= {1/2}since there is a phase change at both surfaces {1/2}Hence nd 4= {1/2}

(b) 100 nm {2}[no partial marks for formula since given][allow {1/2} + {1/2} for correct substitutions](c) Intensity of transmitted light is increased. {1}

Since less light is reflected and energy is conserved. {1}(OR constructive interference between transmitted rays)

(d) Destructive interference occurs at 550 nm (at this one wavelength) {1/2}At larger (red) and smaller (blue) wavelengths interference is incomplete. {1/2}The combination of some reflected red and blue gives purple hue. {1}

27. (a) Electric (or magnetic) field vector oscillates in a single fixed plane. {1}(b) Sound is a longitudinal wave. {1}(c) 53 {2} [standard marking](d) Reflected light is partially polarised. {1/2}

Polarising sunglasses can cut this out allowing trout beneath the surface to be

seen. {1/2}

28. (a) (i) For the first fringe path difference dsin D

xd {1/2} for small {1/2}

Since first bright fringe, path difference = {1/2}

Hence =D

xd {1/2}

(ii) 7.0 10-7 m {2}}[no partial marks for formula since given][allow {1/2} + {1/2} for correct substitutions]

(b) (i) x smaller hence smaller {1}(ii) increaseD (or decrease d) {1}

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DATA

Common Physical quantities

QUANTITY SYMBOL VALUE

Gravitational acceleration g 9.8 m s-2

Radius of Earth RE 6.4 x 106 m

Mass of Earth ME 6.0 x 1024 kg

Mass of Moon MM 7.3 x 1022 kg

Mean radius of Moon orbit 3.84 x 108 m

Universal constant of gravitation G6.67 x 10

-11

m

3

kg

-1

s

-2

Speed of light in vacuum c 3.0 x 108 m s-1

Speed of sound in air v 3.4 x 102 m s-1

Mass of electron me 9.11 x 10-31 kg

Charge on electron e -1.60 x 10-19 C

Mass of neutron mn 1.675 x 10-27 kg

Mass of proton mp 1.673 x 10-27 kg

Plancks constant h 6.63 x 10-34 J s

Permittivity of free space 0 8.85 x 10-12 F m-1

Permeability of free space 0 4 x 10-7 H m-1

Refractive index of water

of perspex

n

n

1.33

1.5

The solutions to the questions use the data values given above.

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