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? M07/4/PHYSI/SP3/ENG/TZ1/XX+ IB DIPLOMA PROGRAMME PROGRAMME DU DIPLOME DU BI PROGRAMA DEL DIPLOMA DEL BI 22076512 physics sTANDARD level pApeR 3 Candidate session number Thursday 3 May 2007 (morning) 0 1 hour 0 INSTRUCTIONS TO CANDIDATES • • • • Write your session number in the boxes above. Do not open this examination paper until instructed to do so. Answer all of the questions from two of the Options in the spaces provided. At the end of the examination, indicate the letters of the Options answered in the candidate box on your cover sheet. 2207-6512 33 pages © IBO 2007 http://www. xtremepapers. net 0133 –2–M07/4/PHYSI/SP3/ENG/TZ1/XX+ Option A — Mechanics extension A1. Thisquestionisaboutgravitationalfieldstrengthnearthesurfaceofaplanet. (a) (i) Definegravitational field strength. [2] ………………………………………………………… ………………………………………………………… (ii) State why gravitational field strength at a point is numerically equal to the acceleration of free fall at that point. [1] ………………………………………………………… ………………………………………………………… ………………………………………………………… b) A certain planet is a uniform sphere of mass M and radius R of 5. 1 ? 106 m. (i) State an expression, in terms of M and R,forthegravitationalfieldstrengthatthe surface of the planet. State the name of any other symbol you may use. [1] ………………………………………………………… ………………………………………………………… ………………………………………………………… (ii) A mountain on the surface of the planet has a height of 2000 m. Suggest why the valueofthegravitationalfieldstrengthatthebaseofthemountainandatthetopof the mountain are almost equal. 2] ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… (This question continues on the following page) 2207-6512 0233 –3– M07/4/PHYSI/SP3/ENG/TZ1/XX+ (Question A1 continued) (c) A small sphere is projected horizontally near the surface of the planet in (b). Photographs of the sphere are taken at time intervals of 0. 20 s. The images of the sphere are placed on a grid and the result is shown below. point of elease 1. 00 cm represents 1. 00 m Thefirstphotographistakenattimet = 0. Each 1. 00 cm on the grid represents a distance of 1. 00 m in both the horizontal and the vertical directions. Use the diagram to (i) explain why lab report writing air resistance on the planet is negligible. [2] ………………………………………………………… ………………………………………………………… ………………………………………………………… (ii) calculate a value for the acceleration of free fall at the surface of the planet. [3] ………………………………………………………… ……………………………………………………….. ………………………………………………………… ………………………………………………………… (This question continues on the following page) Turn over 2207-6512 0333 –4– M07/4/PHYSI/SP3/ENG/TZ1/XX+ (Question A1 continued) (d) Use your answer to (c)(ii) and data from (b) to calculate the mass of the planet. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. ……………………………………………………………. 2207-6512 0433 [2] –5– M07/4/PHYSI/SP3/ENG/TZ1/XX+ A2. This question is about centre of gravity. (a) Describe what is meant by the centre of gravity of an object. [2] …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. (b) A sheet of cardboard is pivoted at point P and is held in the position shown in the diagram below. P C The centre of gravity of the sheet is at point C. i) (ii) On the diagram above, draw an arrow labelled W to represent the weight of the cardboard. [1] The cardboard sheet is now released. Explain why, using energy principles, the cardboard will eventually come to rest. [2] ………………………………………………………… ………………………………………………………… ………………………………………………………… (iii) Explain why, when the sheet comes to rest, point C will be below point P. [2] ………………………………………………………… ……………………………………………………….. ………………………………………………………… Turn over 2207-6512 0533 –6– M07/4/PHYSI/SP3/ENG/TZ1/XX+ Option B — Quantum physics and Nuclear physics B1. This question is about photoelectric emission. A piece of metal is placed in an evacuated container. Light of wavelength 444 nm is incident on the surface of the metal. The surface has a work function of 4. 60 eV. (a) (i) Calculate the energy, in joule, of a photon of light of wavelength 444 nm. [1] ………………………………………………………… ……………………………………………………….. ………………………………………………………… (ii) Deduce whether photoelectric emission of electrons will occur. [3] ………………………………………………………… ………………………………………………………… ………………………………………………………… (b) The wavelength of the light incident on the surface is now reduced to 222 nm. State and explain why electrons having a range of kinetic energy from zero to approximately 1. 0 eV will be emitted. ……………………………………………………………. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. 2207-6512 0633 [4] –7– M07/4/PHYSI/SP3/ENG/TZ1/XX+ B2. This question is about radioactive decay. A cobalt-60 nucleus decays with the emission of a -particle to form a nucleus of nickel-60. The nickel nucleus then decays with the emission of two ? ray photons of energies 1. 17 MeV and 1. 33 MeV. (a) Explain why the decay of nickel-60 leads to the conclusion that atomic nuclei have discrete energy levels. [2] …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. (b) A fresh sample of cobalt-60 contains N0 cobalt nuclei. Initially, there are no nickel-60 nuclei in the sample. After 3. 0 years, the ratio number of nickel-60 nuclei number of cobalt-60 nuclei is 1 . 2 (i) 2 N0 3 ……………………………………………………….. Deduce that the number of cobalt-60 nuclei remaining after 3. 0 years is [2] ………………………………………………………… (ii) Calculate the half-life of cobalt-60. [3] ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… Turn over 2207-6512 733 –– M07/4/PHYSI/SP3/ENG/TZ1/XX+ B3. This question is about fundamental particles. Particle production and annihilation are subject to conservation laws. Two of these laws are conservation of mass-energy and conservation of momentum. (a) State the names of three other conservation laws. 1. ………………………………………………………… 3. (b) ………………………………………………………… 2. [3] ………………………………………………………… Free neutrons are unstable. A neutron may decay to become a proton with the emission of an electron.A student represents the decay by the following equation. 1 0 (i) 0 n > 1 p + ? 1 e 1 State, by reference to conservation laws, why the student’s equation is not correct. [1] ………………………………………………………… (ii) Write down the correct decay equation. ………………………………………………………… 2207-6512 0833 [1] –– M07/4/PHYSI/SP3/ENG/TZ1/XX+ Option c — energy extension c1. Thisquestionisaboutthefirstlawofthermodynamics. (a) Describe what is meant by the internal energy of an ideal gas. [2] …………………………………………………………….. ……………………………………………………………. …………………………………………………………….. (b) The internal energy of an ideal gas increases by an amount ? U . During this process, an amount q of thermal energy is transferred to the gas and the gas does an amount w of external work. (i) Usethefirstlawofthermodynamicstostatearelationbetween? U , q and w. [1] ………………………………………………………… (ii) Suggest how the state of an ideal gas may be changed such that each of the following conditions is met separately. ?U = 0 ………………………………………………. w=0 ……………………………………………….. q=0 [3] ……………………………………………….. Turn over 2207-6512 0933 – 10 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ c2. This question is about heat pumps. The diagram illustrates an ideal heat pump that operates between a high-temperature region and a low-temperature region. high-temperature region T1 thermal energy transfer Q1 heat pump work done W thermal energy transfer Q2 low-temperature region T2 (a) (b) On the diagram above, draw arrows to indicate the directions of energy transfer for the heat pump. 1] The energy transfers between the heat pump and the high-temperature and the low-temperature regions are Q1 and Q2 respectively when an amount W of work is done. (i) State the relation between Q1, Q2 and W. [1] ………………………………………………………… (ii) State an expression, in terms of Q1 and Q2, for the ratio W . Q2 [1] ………………………………………………………… ………………………………………………………… (This question continues on the following page) 2207-6512 1033 – 11 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ Question C2 continued) (c) The kelvin temperatures of the high-temperature and low-temperature regions are T1 and T2 respectively. (i) Derive an expression, in terms of T1 and T2, for the ratio W . Q2 [2] ………………………………………………………… ………………………………………………………… ………………………………………………………… (ii) A refrigerator has an ice compartment at a temperature of ? 3 °C. Thermal energy is removed from the back of the refrigerator which is at a temperature of 37 °C.The rate of transfer of thermal energy from the ice compartment is 5 W. Using your expression in (i), calculate the input power to the refrigerator. [2] ………………………………………………………… ………………………………………………………… ………………………………………………………… (iii) State one reason why the actual input power for this refrigerator would have to be greater than that calculated in (c)(ii). [1] ………………………………………………………… Turn over 2207-6512 1133 – 12 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ 3. This question is about solar heaters. (a) An active solar heater (solar panel) is installed on the roof of a building in the southern hemisphere. Suggest why the panel should be facing northwards at noon. [2] …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. (b) At one particular location, the average power received from the Sun during a six-hour period each day is 40 W m–2. The solar heater has an overall efficiency of 35 %.It is required that, during the six-hour period, the solar heater raises the temperature of 140 kg of water by 25 K. The specific heat capacity of water is 4. 2 kJ kg–1 K–1. Calculate the minimum effective area of the solar heater. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. 207-6512 1233 [4] – 13 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ Blank page Turn over 2207-6512 1333 – 14 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ Option D — Biomedical physics D1. This question is about sound and hearing. The following graph shows the variation with frequency of the threshold of hearing for Frank and for Albert. sound intensity 100 level / dB 0 60 40 Albert 20 Frank 0 10 100 1000 10 000 frequency / Hz A sound source produces a note of frequency 70 Hz. The sound power output of the source is 0. 027 W. The sound is emitted uniformly in all directions. Frank and Albert both walk towards the source.Frank stops when he first hears the sound. Albert stops when he first hears the sound. (a) Use the graph to state and explain whether Albert or Frank stops closest to the source. [3] …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. (This question continues on the following page) 2207-6512 1433 – 15 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ (Question D1 continued) (b)Deduce that the distance from the speaker at which Frank first hears the sound is 46 m. You may assume there is no reflected sound. The surface area of a sphere of radius r is 4? r 2 . [3] …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. c) The frequency of the sound emitted by the source is changed to 4000 Hz while Albert remains at the same location as he was in (a), and the power output is maintained at the same level as in (a). Use the graph to state and explain the changes, if any, of the loudness of the sound heard by Albert. [2] …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. Turn over 2207-6512 1533 – 16 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ D2.This question is about scaling. The bodies of a lion and a domestic cat are similar in shape and density. The linear dimensions of the body of a particular lion are 4. 0 times larger than those of a particular domestic cat. (a) Estimate the ratio mass of body of the lion . mass of body of the domestic cat [2] …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. b) The breaking stress of the leg bones is defined as the force per unit area that just breaks the bone. The minimum diameter of the leg bone is the diameter that will just support the weight of the body without breaking. Assume that the animals have similar bone material. (i) Use your answer to (a) to determine the ratio minimum diameter of the leg bone of the lion . minimum diameter of the leg bone of the domestic cat [2] ………………………………………………………… ………………………………………………………… ……………………………………………………….. ………………………………………………………… (ii) Use your answers to (a) and (b)(i) to explain why the lion has legs that are not 4. 0 times the diameter of those of the domestic cat. ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… 2207-6512 1633 [2] – 17 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ D3.This question is about medical imaging. (a) Outline the basis of computerized tomography (CT scanning). [4] …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. (b) State and explain one disadvantage of the use of computerized tomography. [2] ……………………………………………………………. …………………………………………………………….. …………………………………………………………….. Turn over 2207-6512 1733 – 1 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ Option e — The history and Development of physics e1. This question is about models of the Universe. (a) Explain the model proposed by Aristarchus to account for the observed motion of the stars. [2] …………………………………………………………….. …………………………………………………………….. ……………………………………………………………. …………………………………………………………….. (b) State two ways in which Ptolemy’s model differs from the Aristarchus model of the Universe. 1. [2] ………………………………………………………… ………………………………………………………… 2. ………………………………………………………… ………………………………………………………… (This question continues on the following page) 2207-6512 1833 – 1 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ Question E1 continued) (c) The diagram below shows the positions of some of the stars in the constellation Ursa Minor. The star Polaris may be taken to be at the northern celestial pole. Ursa Minor Polaris On the diagram above, draw a sketch showing the positions of the stars as they would be seen six hours later. (d) [3] State how the Aristarchus model explains your sketch in (c). [1] …………………………………………………………….. …………………………………………………………….. ……………………………………………………………..Turn over 2207-6512 1933 – 20 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ e2. This question is about caloric theory. In 17, Rumford published a paper in support of an alternate view to the caloric theory, based on observations involving the boring of cannons. (a) Outline Rumford’s observations. [1] …………………………………………………………….. …………………………………………………………….. (b) Explain how Rumford’s observations are inconsistent with the caloric theory. [2] …………………………………………………………….. ……………………………………………………………. …………………………………………………………….. …………………………………………………………….. e3. This question is about electric charge. Priestley and Franklin attempted to establish an inverse-square law for electrostatic force, as did Coulomb. Compare the two approaches. ………………………………………………………………… ………………………………………………………………… ………………………………………………………………… ……………………………………………………………….. ………………………………………………………………… ………………………………………………………………… 2207-6512 2033 [3] – 21 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ e4. This question is about investigations of electrons and neutrons. (a) State and explain why the properties of electrons can be determined more easily than those of neutrons. [2] …………………………………………………………….. …………………………………………………………….. ……………………………………………………………. …………………………………………………………….. (b) Experimentation in the 130s showed that the radiation produced by the ? -bombardment of beryllium could penetrate several centimetres of lead. This radiation ejects high-energy protonsfromparaffinwax. DiscusshowtheseobservationsledChadwicktoconclude that this radiation is neutrons. [4] …………………………………………………………….. …………………………………………………………….. ……………………………………………………………. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. Turn over 2207-6512 2133 – 22 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ Option F — Astrophysics F1. This question is about luminosity. (a) Defineluminosity. [1] ……………………………………………………………. …………………………………………………………….. (b) The sketch-graph below shows the intensity spectrum for a black-body at a temperature of 6000 K. intensity 0 0 wavelength On the axes above, draw a sketch-graph showing the intensity spectrum for a black-body at 000 K. [2] (This question continues on the following page) 2207-6512 2233 – 23 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ (Question F1 continued) (c) A sketch of a Hertzsprung-Russell diagram is shown below. luminosity temperature On the diagram above, identify the i) main sequence (label this M), (ii) red giant region (label this R), (iii) white dwarf region (label this W). (d) [2] In a Hertzsprung-Russell diagram, luminosity is plotted against temperature. Explain why the diagram alone does not enable the luminosity of a particular star to be determined from its temperature. [3] …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. ……………………………………………………………. …………………………………………………………….. Turn over 2207-6512 2333 – 24 – F2. This question is about stellar magnitudes and stellar distances. (a) M07/4/PHYSI/SP3/ENG/TZ1/XX+ Define (i) apparent magnitude. [1] ………………………………………………………… ………………………………………………………… (ii) absolute magnitude. [1] ………………………………………………………… ………………………………………………………… (b)Star A has an apparent magnitude of 5. 0 and is 100 pc from Earth. The luminosity of star A is 4. 0 times the luminosity of star B. The apparent brightness of star A is 100 times greater than the apparent brightness of star B. Deduce that (i) star B is 500 pc from Earth. [3] ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… ……………………………………………………….. ………………………………………………………… ………………………………………………………… (ii) the absolute magnitude of star A is 0. ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… 2207-6512 2433 [2] – 25 – F3. M07/4/PHYSI/SP3/ENG/TZ1/XX+ This question is about cosmology. (a)State one piece of evidence that indicates that the Universe is expanding. [1] …………………………………………………………….. …………………………………………………………….. (b) The rate at which the Universe is expanding depends on the density of the Universe. (i) Definecritical density. [1] ………………………………………………………… ………………………………………………………… (ii) Explain the importance of comparing the density of the Universe to the critical density in predicting the future of the Universe. [3] ……………………………………………………….. ………………………………………………………… ………………………………………………………… ………………………………………………………… Turn over 2207-6512 2533 – 26 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ Option G — Relativity G1. This question is about the measurement of time. Mavis is stationary with respect to a source that produces a light pulse. The light pulse is reflectedatasurface,andreturnstoadetectorlocatedveryclosetothesource. Thedistance between the source and the surface is d. urface d Mavis detector source Ronald v Ronald is moving with constant speed v relative to the source in a direction parallel to the surface. (a) On the diagram above, draw the path of the pulse as seen by Ronald. [2] (This question continues on the following page) 2207-6512 2633 – 27 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ (Question G1 continued) (b) The time taken for the light to travel from the source to the detector, as measured by Ronald, is t. Use your diagram in (a) to deduce that the distance L travelled by the pulse, as measured by Ronald, is given by the expression 2 ? vt ? L = 2 d +? ? . ?2? 2 [3] ……………………………………………………………. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. (c) The time taken for the pulse to travel from the source to the detector, as measured by Mavis, is t0. (i) State the relation between t0, d and c where c is the speed of light. [1] ……………………………………………………….. ………………………………………………………… (ii) Use your answer in (b) and (c) (i) to deduce that t = t0 v2 1? 2 c . [3] ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… …………………………………………………………Turn over 2207-6512 2733 – 2 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ G2. This question is about the observation of clocks. Albert is standing equal distances from two clocks A and B. Frank is moving with constant speed v from clock A towards clock B. clock A clock B Albert Frank v At the instant that Frank is opposite Albert, Albert observes the second-hand of both clocks to be at 0. At some time later, Albert observes the second-hand of both clocks change position to be at 1, as shown in the diagram below. At this instant, Frank is in the position shown in the diagram below. clock A 1 clock B 1 Albert Frank vDiscuss whether, at this instant, Frank observes the second-hand of each clock to be at 1. ………………………………………………………………… ………………………………………………………………… ………………………………………………………………… ………………………………………………………………… ………………………………………………………………… ………………………………………………………………… 2207-6512 2833 [4] – 2 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ G3. This question is about muons. a) A muon is formed 4500 m above the surface of the Earth, as measured by an observer on Earth. This muon takes 2. 2 µ s, as measured in its frame of reference, to reach the Earth’s surface. Describe how these observations support the concept of length contraction. [4] …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. ……………………………………………………………. …………………………………………………………….. (b) A muon created in the laboratory is accelerated from rest through a potential difference of 2. 1 ? 10 V. The rest mass of the muon is 105 MeV c–2. Calculate the mass of the accelerated muon, as measured in the laboratory frame of reference. The charge on a muon is the elementary charge e. [3] …………………………………………………………….. …………………………………………………………….. ……………………………………………………………. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. Turn over 2207-6512 2933 – 30 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ Option h — Optics h1. This question is about refraction and dispersion. (a) State what is meant by dispersion. [1] …………………………………………………………….. …………………………………………………………….. ……………………………………………………………. …………………………………………………………….. (b) A thin beam of white light is incident on one surface of a glass prism as shown below. On the diagram above, draw lines to show the approximate paths of the red and of the blue light as it passes through the prism and back into the air. (c) [3] State and explain, with reference to your diagram, whether the refractive index of glass for blue light is greater or less than that for red light. [3] …………………………………………………………….. ……………………………………………………………. …………………………………………………………….. …………………………………………………………….. (This question continues on the following page) 2207-6512 3033 – 31 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ (Question H1 continued) (d) Asecondsimilarprismisplacedclosetothefirstprismin(b)asshownbelow. Suggest the appearance and the direction of the light that emerges from the second prism. [2] …………………………………………………………….. …………………………………………………………….. ……………………………………………………………. …………………………………………………………….. Turn over 2207-6512 3133 – 32 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ h2. This question is about lenses. The diagram below shows a thin converging lens and an object, O. O F F The principal foci of the lens are at F. (a) Construct rays to locate the position of the image of the object. [3] (b) Describe fully the nature of the image formed. [2] …………………………………………………………….. …………………………………………………………….. ……………………………………………………………. …………………………………………………………….. (This question continues on the following page) 2207-6512 3233 – 33 – M07/4/PHYSI/SP3/ENG/TZ1/XX+ (Question H2 continued) (c) The diagram below shows the relative positions of the objective lens and eyepiece lens used in a compound microscope in normal adjustment. objective lens eyepiece lens O An object O is placed in front of the objective lens. On the diagram above, draw the approximate positions of (i) the principal foci of the objective lens (label these with the letter A), ii) the image formed by the objective lens (label this with the letter B), (iii) the principal foci of the eyepiece lens (label these with the letter C), (iv) thepositionofthefinalimage(labelthiswiththeletterD). (d) Suggest why, for large magnifications, a compound microscope is used, rather than a single lens. [2] …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. …………………………………………………………….. 2207-6512 3333 [4]