physics standard level paper 3 · specimen paper physics standard level paper 3 instructions to...

27 pages

SPEC/4/PHYSI/SP3/ENG/TZ0/XX

SPECIMEN PAPER

PHYSICSSTANDARD LEVELPAPER 3

INSTRUCTIONS TO CANDIDATES

�� Write your session number in the boxes above.�� Do not open this examination paper until instructed to do so.�� Section A: answer all questions.�� Section B:� answer all of the questions from one of the options.�� Write your answers in the boxes provided. �� A calculator is required for this paper.�� A clean copy of the Physics Data Booklet is required for this paper.�� The maximum mark for this examination paper is [35 marks].

Option Questions

Option A — Relativity 4 – 5

Option B — Engineering physics 6 – 7

Option C — Imaging 8 – 9

Option D — Astrophysics 10 – 11

© International Baccalaureate Organization 2014

Candidate session number

1 hour

Examination code

28EP01

– 2 – SPEC/4/PHYSI/SP3/ENG/TZ0/XX

28EP02

SECTION A

Answer all questions. Write your answers in the boxes provided.

1. The speed of sound in air, v, was measured at temperatures near 0 Cq . The graph shows the data DQG�WKH�OLQH�RI�EHVW�¿W��7KH�HUURU�EDUV�IRU�WHPSHUDWXUH�DUH�WRR�VPDOO�WR�EH�VKRZQ�

–20 –10 0 10 20

320

310

330

340

350v / m s–1

� / 0 Cq

A student suggests that the speed of sound v is related to the temperature � in degrees Celsius by the equation

v a bT �

where a and b are constants.

(a) (i) Determine the value of the constant a��FRUUHFW�WR�WZR�VLJQL¿FDQW�¿JXUHV� [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(This question continues on the following page)

– 3 –

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28EP03

(Question 1 continued)

(ii) Estimate the absolute uncertainty in b. [3]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(iii) A student calculates that 1 10.593ms Cb � �q . State, using your answer to (a)(ii), the value of b�WR�WKH�FRUUHFW�QXPEHU�RI�VLJQL¿FDQW�¿JXUHV� [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) (i) Estimate the temperature at which the speed of sound is zero. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) Explain, with reference to your answer in (b)(i), why the student’s suggestion is not valid. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


28EP04

2. A student uses an electronic timer in an attempt to estimate the acceleration of free-fall g. She measures the time t taken for a small metal ball to fall through a height h of 0.50 m. The percentage uncertainty in the measurement of time is 0.3 % and the percentage uncertainty height is 0.6 %.

(a) Using 212

h gt , calculate the expected percentage uncertainty in the value of g. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) State and explain how the student could obtain a more reliable value for g. [3]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

– 5 –

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28EP05

3.� ,Q�DQ�H[SHULPHQW�WR�PHDVXUH�WKH�VSHFL¿F�KHDW�FDSDFLW\�RI�D�PHWDO��D�SLHFH�RI�PHWDO�LV�SODFHG�inside a container of boiling water at 100 100 Cq . The metal is then transferred into a calorimeter containing water at a temperature of 10 100 Cq ��7KH�¿QDO�HTXLOLEULXP�WHPSHUDWXUH�RI�WKH�ZDWHU�ZDV�measured. One source of error in this experiment is that a small mass of boiling water will be transferred to the calorimeter along with the metal.

(D�� 6XJJHVW� WKH� HIIHFW� RI� WKH� HUURU� RQ� WKH�PHDVXUHG�YDOXH�RI� WKH� VSHFL¿F�KHDW� FDSDFLW\�RI� the metal. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) State one other source of error for this experiment. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


28EP06

SECTION B

Answer all of the questions from one of the options. Write your answers in the boxes provided.

Option A — Relativity

4. (a) Einstein discovered a discrepancy, related to the speed of light, between Maxwell’s equations of electromagnetism and Newtonian mechanics. Outline the discrepancy and how Einstein dealt with it. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Option A continues on the following page)

– 7 –

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28EP07

(Option A, question 4 continued)

(E�� $�SURWRQ�HQWHUV�D�UHJLRQ�RI�XQLIRUP�PDJQHWLF�¿HOG�ZKLFK�LV�GLUHFWHG�LQWR� WKH�SODQH�RI� the page as shown.

proton

XQLIRUP�PDJQHWLF�¿HOG

5HIHUHQFH�IUDPH�6�LV�DW�UHVW�ZLWK�UHVSHFW�WR�WKH�PDJQHWLF�¿HOG��7KH�VSHHG�RI�WKH�SURWRQ�LV�measured to be v in S.

(i) State the nature of the force on the proton according to an observer in S. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) Sc is a reference frame in which the proton is at rest. State and explain whether, according to an observer in Sc, there is a force on the proton. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



28EP08

(Option A continued)

5. A rocket of proper length 900 m is moving at speed 0.80c relative to the Earth. E is a reference frame in which the Earth is at rest. R is a reference frame in which the rocket is at rest. The diagram is from the point of view of E.

rocket

rocket

emission

reception

Earth

light 0.80c

0.80clight

Earth

(a) A light signal is emitted from the back of the rocket and is received at the front of the rocket.

Determine the

(i) time interval between the emission and reception of the light signal according to an observer in R. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) time interval between the emission and reception of the light signal according to an observer in E. [3]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


– 9 –

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28EP09


(iii) distance separating the emission and reception of the light signal according to an observer in E. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



28EP10


(b) One photon is emitted from the back B of the rocket and another photon is emitted from the front F of the rocket, as shown.

B

photon

R

photon

F

The emissions are simultaneous according to observers in R. The photons are received by an observer at rest in the middle of the rocket.

The spacetime diagram represents the reference frame of the Earth E and the rocket frame R. The coordinates in frame E are x and ct and in frame R they are xc and ctc. The position of the back B and of the front F of the rocket at 0tc are labelled. The origin of the axes corresponds to the middle of the rocket.

ctc

B

ct

0 0

F

rocket frame

x

xc

Earth frame

(i) On the spacetime diagram, draw lines to show the worldlines of the photons from when they were emitted to when they were received. [3]


– 11 –

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28EP11


(LL�� 8VLQJ�WKH�VSDFHWLPH�GLDJUDP��GHWHUPLQH�ZKLFK�SKRWRQ�ZDV�HPLWWHG�¿UVW�DFFRUGLQJ�to observers in E. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(iii) Determine the time separating the emissions of the two photons according to observers in E. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) A missile is launched from the rocket. The velocity of the missile is – 0.62c relative to the rocket. Calculate the velocity of the rocket relative to the Earth. [3]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

End of Option A


28EP12

Option B — Engineering physics

6. A bucket of mass m is held above a water well by a rope of negligible mass, as shown. The rope is wound around a cylinder of mass M and radius R. The moment of inertia of the cylinder about its axis is 21

2I MR .

horizontalaxis R

cylinder mass M

rope

bucket mass m(not to scale)

The bucket is released from rest. Resistance forces may be ignored.

(a) Show that the acceleration a of the bucket is given by the following equation.

2

mga Mm

�. [4]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Option B continues on the following page)

– 13 –

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28EP13

(Option B, question 6 continued)

(b) The following data are available.

Bucket mass m 24 kg Cylinder mass M 36 kg Radius R 0.20 m

(i) Calculate the speed of the bucket when it has fallen a distance of 16 m from rest. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) Calculate the rate of change of the angular momentum of the cylinder. [3]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(F�� 7KH� EXFNHW� LQ� �E�� LV� ¿OOHG�ZLWK�ZDWHU� VR� LWV� WRWDO�PDVV� LV� QRZ� ��NJ�� 7KH� EXFNHW� LV�raised at a constant speed of 2.0 m s–1 using an electric motor attached to the cylinder. Calculate the power output of the motor. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



28EP14

(Option B continued)

7. The pressure volume (pV) diagram shows a cycle ABCA of a heat engine. The working VXEVWDQFH�RI�WKH�HQJLQH�LV�D�¿[HG�PDVV�RI�DQ�LGHDO�JDV�

p / 105 Pa

6

5

4

3

2

1

0

A B

C

0 2 4 6 8 10 V / 10–3 m3

The temperature of the gas at A is 400 K.

(a) Calculate the maximum temperature of the gas during the cycle. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


– 15 –

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28EP15


(b) For the isobaric expansion AB, calculate the

(i) work done by the gas. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) change in the internal energy of the gas. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(iii) thermal energy transferred to the gas. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



28EP16


(c) The work done on the gas during the isothermal compression is 1390 J. Determine the change in entropy of the gas for this compression. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(G�� 'HWHUPLQH�WKH�HI¿FLHQF\�RI�WKH�F\FOH�$%&$� [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(H�� 6WDWH�ZKHWKHU�WKH�HI¿FLHQF\�RI�D�&DUQRW�HQJLQH�RSHUDWLQJ�EHWZHHQ�WKH�VDPH�WHPSHUDWXUHV�as those operating in cycle ABCA on page 14, would be greater than, equal to, or less than WKH�HI¿FLHQF\�LQ��G�� [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

End of Option B

– 17 –

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28EP17

Please do not write on this page.

Answers written on this page will not be marked.


28EP18

Option C — Imaging

8.� �D�� 7KH� GLDJUDP� VKRZV� D� &DVVHJUDLQ� UHÀHFWLQJ� WHOHVFRSH� FRQVLVWLQJ� RI� D� VPDOO� GLYHUJLQJ�mirror M�, a large converging mirror M�, and a converging lens L. The focal point of M2 is at F.

M2

light from a distant planet

F M1

L

(not to scale)

The telescope is used to view a planet. The diameter of the planet subtends an angle of 1.40 u10–4 rad at M�. The focal length of M2 is 9.50 m.

(i) Show that the diameter of the image of the planet that would be formed by M2 alone is 1.33 mm. [3]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Option C continues on the following page)

– 19 –

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28EP19

(Option C, question 8 continued)

(ii) M1 is at a distance of 8.57 m from the aperture of M�. The image in (a)(i) now serves as a virtual object for M1. A real image is formed at the opening of M�. Show that the diameter of this image is 12.0 mm. [3]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(LLL�� 7KH�UHDO�LPDJH�LQ��D��LL��LV�QRZ�YLHZHG�E\�/�RI�IRFDO�OHQJWK��PP��7KH�¿QDO�LPDJH�RI� WKH�SODQHW� LV� IRUPHG�DW� LQ¿QLW\�� &DOFXODWH� WKH�RYHUDOO�PDJQL¿FDWLRQ�RI� the telescope. [3]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



28EP20


(E�� L�� 7KH� ODUJH� FRQFDYH� PLUURU� LQ� PRVW� UHÀHFWLQJ� WHOHVFRSHV� LV� SDUDEROLF� UDWKHU� WKDQ�spherical. Suggest one reason for this. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) State one�DGYDQWDJH�RI�UHÀHFWLQJ�WHOHVFRSHV�FRPSDUHG�WR�UHIUDFWLQJ�WHOHVFRSHV� [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) Telescopes available today include, in addition to optical telescopes, infrared, radio, ultraviolet and X-ray telescopes. Outline how the introduction of these telescopes has changed our view of the universe. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


– 21 –

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28EP21

(Option C continued)

9. (a) A compound microscope has an objective lens of focal length 0.40 cm and an eyepiece lens of focal length 3.20 cm. The image formed by the objective is 0.20 m from the REMHFWLYH�OHQV��7KH�¿QDO�LPDJH�LV�IRUPHG�DW�D�GLVWDQFH�RI��FP�IURP�WKH�H\HSLHFH�OHQV�

(i) Show that the position of the object is 4.1 u10–3 m from the objective lens. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(LL�� 'HWHUPLQH�WKH�DQJXODU�PDJQL¿FDWLRQ�RI�WKH�PLFURVFRSH� [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(iii) The smallest distance between two points that can be distinguished by an unaided human eye from a distance of 25 cm is approximately 0.1 mm. Calculate the smallest distance between two points that can be distinguished using this microscope. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



28EP22


(E�� 7KH� LPDJHV� IURP� WKH� PLFURVFRSH� DUH� GLJLWL]HG� DQG� WUDQVPLWWHG� DORQJ� DQ� RSWLF� ¿EUH�� The input power of the signal is 120 mW and the attenuation per unit length of the RSWLF�¿EUH�LV��G%�NP–1��7KH�OHQJWK�RI�WKH�¿EUH�LV��NP��&DOFXODWH�WKH�RXWSXW�SRZHU�of the signal. [3]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

End of Option C

– 23 –

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28EP23

Option D — Astrophysics

10. (a) State the element which is the end product of nuclear reactions taking place inside main sequence stars. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) A main sequence star has apparent brightness 7.6 u10–14 W m–2 and luminosity 3.8 u1027 W.

(i) Calculate, in pc, the distance of the star from Earth. [3]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) Suggest whether the stellar parallax method is appropriate for measuring the distance to this star. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(iii) The luminosity of the star in (b) is ten times the luminosity of our Sun.

Determine the ratio MM:

where M: is the mass of the Sun. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Option D continues on the following page)


28EP24

(Option D, question 10 continued)

(c) The image shows a Hertzsprung–Russell (HR) diagram.

luminosity(Sun = 1)

30000K 10000K 7500K 6000K 5000K 4000K 3000K

main sequence

white dwarfs

temperature

100 000

10 000

1000

100

10

0.1

0.01

0.001

0.0001

0.00001

1


– 25 –

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28EP25


(i) Estimate, using the HR diagram, the ratio RR:

where R is the radius of the star in (b) and R: is the radius of the Sun. [3]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) Sketch a line on the HR diagram to show the evolutionary path of this star. [2]

(iii) Describe, with reference to the Chandrasekhar limit, the equilibrium state of this VWDU�LQ�LWV�¿QDO�HYROXWLRQDU\�VWDJH� [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



28EP26

(Option D continued)

11. (a) The hydrogen spectrum from a laboratory source includes a line of wavelength 434 nm. The same line emitted from a distant galaxy has wavelength 502 nm when observed on Earth.

(i) Suggest why the two wavelengths are different. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) Determine the distance, in Mpc, from this galaxy to Earth using a Hubble constant of 71 km s–1 Mpc–1. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


– 27 –

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28EP27


(b) In the 1990s, two research groups started projects involving observations of distant supernovae. They aimed to show that distant galaxies were slowing down.

(i) Suggest why it was expected that distant galaxies would be slowing down. [1]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) Describe how it was deduced that the universe is expanding at an accelerated rate. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

End of Option D

Please do not write on this page.

Answers written on this page will not be marked.

28EP28

SP

EC

/4/P

HY

SI/S

P3/

ENG

/TZ0

/XX

/M

15 p

ages

MA

RK

SCH

EME

SPEC

IMEN

PA

PER

PHYS

ICS

Stan

dard

Lev

el

Pape

r 3

–

2 –

SPEC

/4/P

HY

SI/S

P3/E

NG

/TZ0

/XX

/M

Gen

eral

Mar

king

Inst

ruct

ions

Su

bjec

t Det

ails:

Phy

sics S

L P

aper

3 M

arks

chem

e M

ark

Allo

catio

n C

andi

date

s ar

e re

quire

d to

ans

wer

AL

L q

uest

ions

in S

ectio

n A

[15

mar

ks] a

nd a

ll qu

estio

ns fr

om O

NE

opt

ion

in S

ectio

n B

[20

mar

ks].

Max

imum

tota

l

[35

mar

ks].

Mar

ksch

eme

form

at e

xam

ple:

Que

stio

n A

nsw

ers

Not

es

Tot

al

4.

b ii

the

disp

lace

men

t and

acc

eler

atio

n 9

ar

e in

opp

osite

dire

ctio

ns9

Acce

pt fo

rce

for a

ccel

erat

ion.

2

1.

Each

row

in th

e “Q

uest

ion”

col

umn

rela

tes t

o th

e sm

alle

st su

bpar

t of t

he q

uest

ion.

2.

Th

e m

axim

um m

ark

for e

ach

ques

tion

subp

art i

s ind

icat

ed in

the

“Tot

al”

colu

mn.

3.

Ea

ch m

arki

ng p

oint

in th

e “A

nsw

ers”

col

umn

is sh

own

by m

eans

of a

tick

(9) a

t the

end

of t

he m

arki

ng p

oint

. 4.

A

que

stio

n su

bpar

t may

hav

e m

ore

mar

king

poi

nts

than

the

tota

l allo

ws.

Thi

s w

ill b

e in

dica

ted

by “

max

” w

ritte

n af

ter t

he m

ark

in th

e “T

otal

” co

lum

n. T

he re

late

d ru

bric

, if n

eces

sary

, will

be

outli

ned

in th

e “N

otes

” co

lum

n.

5.

An

alte

rnat

ive

wor

ding

is in

dica

ted

in th

e “A

nsw

ers”

col

umn

by a

slas

h (/)

. Ei

ther

wor

ding

can

be

acce

pted

. 6.

A

n al

tern

ativ

e an

swer

is in

dica

ted

in th

e “A

nsw

ers”

col

umn

by “

OR

” on

the

line

betw

een

the

alte

rnat

ives

. Ei

ther

ans

wer

can

be

acce

pted

. 7.

W

ords

in a

ngle

d br

acke

ts ‹

› in

the

“Ans

wer

s” c

olum

n ar

e no

t nec

essa

ry to

gai

n th

e m

ark.

8.

W

ords

that

are

und

erlin

ed a

re e

ssen

tial f

or th

e m

ark.

9.

Th

e or

der o

f mar

king

poi

nts d

oes n

ot h

ave

to b

e as

in th

e “A

nsw

ers”

col

umn,

unl

ess s

tate

d ot

herw

ise

in th

e “N

otes

” co

lum

n.

10.

If th

e ca

ndid

ate’

s an

swer

has

the

sam

e “m

eani

ng”

or c

an b

e cl

early

inte

rpre

ted

as b

eing

of e

quiv

alen

t sig

nific

ance

, det

ail a

nd v

alid

ity a

s th

at in

the

“Ans

wer

s”

colu

mn

then

aw

ard

the

mar

k. W

here

this

poi

nt is

con

side

red

to b

e pa

rticu

larly

rele

vant

in a

que

stio

n it

is e

mph

asiz

ed b

y O

WTT

E (o

r wor

ds to

that

eff

ect)

in

the

“Not

es”

colu

mn.

11

. R

emem

ber t

hat m

any

cand

idat

es a

re w

ritin

g in

a se

cond

lang

uage

. Ef

fect

ive

com

mun

icat

ion

is m

ore

impo

rtant

than

gra

mm

atic

al a

ccur

acy.

–

3 –

SPEC

/4/P

HY

SI/S

P3/E

NG

/TZ0

/XX

/M

12.

Occ

asio

nally

, a p

art o

f a q

uest

ion

may

requ

ire a

n an

swer

that

is re

quire

d fo

r sub

sequ

ent m

arki

ng p

oint

s. If

an

erro

r is

mad

e in

the

first

mar

king

poi

nt th

en it

sho

uld

be p

enal

ized

. H

owev

er, i

f th

e in

corr

ect a

nsw

er is

use

d co

rrec

tly in

sub

sequ

ent m

arki

ng p

oint

s th

en f

ollo

w t

hrou

gh m

arks

sho

uld

be a

war

ded.

W

hen

mar

king

, in

dica

te th

is b

y ad

ding

EC

F (e

rror

car

ried

forw

ard)

on

the

scrip

t. “E

CF

acce

ptab

le”

will

be

disp

laye

d in

the

“Not

es”

colu

mn.

13

. D

o no

t pen

aliz

e ca

ndid

ates

for e

rror

s in

units

or s

igni

fican

t fig

ures

, unl

ess i

t is s

peci

fical

ly re

ferr

ed to

in th

e “N

otes

” co

lum

n.

–

4 –

SPEC

/4/P

HY

SI/S

P3/E

NG

/TZ0

/XX

/M

SEC

TIO

N A

Que

stio

n A

nsw

ers

Not

es

Tot

al

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bel

ow

273

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R

this

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pera

ture

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ht 9

it

appe

ars t

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near

fit m

odel

can

not b

e ex

trapo

late

d fa

r fro

m 0

Cq 9

2

–

5 –

SPEC

/4/P

HY

SI/S

P3/E

NG

/TZ0

/XX

/M

Que

stio

n A

nsw

ers

Not

es

Tot

al

2.

a

the

estim

ated

per

cent

age

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rtain

ty in

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u�

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cept

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ne h

eigh

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from

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itabl

e gr

aph ‹of

hei

ght

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rsus

ht

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g is

twic

e th

e gr

adie

nt 9

O

R

use

a sm

alle

r bal

l ‹to

redu

ce a

ir re

sist

ance

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use

a ‹m

uch›

larg

er h

eigh

t 9

repe

at m

any

times

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get a

n av

erag

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tim

e› 9

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w

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vers

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alys

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oted

gr

aph.

3

3.

a

the

actu

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ecifi

c he

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e le

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alcu

late

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lue 9

m

ore

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ansf

erre

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the

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rimet

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onte

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han

acco

unte

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r 9

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not a

llow

a ba

ld a

nswe

r. 2

b

m

etal

may

not

hav

e be

en h

eate

d un

iform

ly

OR

m

etal

may

not

all

be a

t 100

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en

ergy

was

lost

to a

ir du

ring

the

trans

fer 9

en

ergy

may

hav

e be

en lo

st to

the

air t

hrou

gh th

e ca

lorim

eter

9

wat

er m

ay n

ot b

e at

uni

form

tem

pera

ture

9

1 m

ax

–

6 –

SPEC

/4/P

HY

SI/S

P3/E

NG

/TZ0

/XX

/M

SEC

TIO

N B

O

ptio

n A

— R

elat

ivity

Que

stio

n A

nsw

ers

Not

es

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al

4.

a

Max

wel

l’s e

quat

ions

impl

ied

a sp

eed

of li

ght i

ndep

ende

nt o

f its

sour

ce

OR

in

New

toni

an m

echa

nics

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ed o

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ht d

epen

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n ve

loci

ty o

f sou

rce 9

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nste

in tr

uste

d M

axw

ell’s

equ

atio

ns

OR

Ei

nste

in m

odifi

ed N

ewto

nian

mec

hani

cs 9

2

b

i m

agne

tic 9

1

b ii

if a

forc

e ex

ists

in o

ne ‹i

nerti

al› f

ram

e a

forc

e m

ust e

xist

in a

ny o

ther

‹ine

rtial› f

ram

e 9

ca

nnot

be

mag

netic

bec

ause

the

prot

on is

at r

est i

n Sc

9

Acce

pt d

iscu

ssio

n in

term

s of

acce

lera

tion

as e

quiv

alen

t to

forc

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pt a

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uest

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2

9.

a i

22

11

11

10.

4010

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