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L.36

PRE-LEAVING CERTIFICATE EXAMINATION, 2013

PHYSICS – HIGHER LEVEL

TIME – 3 HOURS

Answer three questions from Section A and five questions from Section B.

N.B. Relevant data are listed in the Formulae and Tables booklet,

which is available from the Superintendent.

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SECTION A (120 marks)

Answer three questions from this section. Each question carries 40 marks.

1. In an experiment to measure the acceleration due to gravity, a student measured the time t for an object to fall from rest through a distance s. The procedure was repeated for a series of values of the distance s.

The table shows the data recorded by the student.

s/cm 20 30 40 50 60 70 80 90

t/ms 219 245 287 321 348 379 407 428

Draw a labelled diagram of the apparatus used by the student in the experiment. Explain how the distance s and the time interval t were measured. (12) Using the data, draw a suitable graph on graph paper to show the relationship between the distance

travelled by an object falling under gravity and the time taken for it to fall through that distance. (12) Use your graph to calculate a value for acceleration due to gravity g. (9) Explain why one of the points on your graph deviates from the demonstrated relationship. (7) 2. In an experiment to measure the specific latent heat of vaporisation of water, a student added steam

to water in an insulated copper calorimeter. The following data were recorded. mass of copper calorimeter ............................... = 42.8 g mass of water (before steam added) ................. = 53.6 g initial temperature of water .............................. = 11.6 C temperature of steam ........................................ = 100 C

mass of steam added ......................................... = 1.5 g final temperature of water ................................ = 27.8 C How was the mass of the water and the mass of the steam determined? (9) If the calorimeter used in the experiment was not perfectly insulated, what would have been a

desirable value for room temperature during the experiment in order to improve the accuracy of the result? Explain your answer. (9)

Give one other precaution that the student could take to ensure a more accurate result. (4) Using the data, calculate a value for the specific latent heat of vaporisation of water. (18) (specific heat capacity of water = 4180 J kg–1 K–1; specific heat capacity of copper = 390 J kg–1 K–1)

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3. A student performed an experiment to measure the speed of sound in air by measuring the length of a column of air, l when it resonated with a tuning fork of known frequency f.

The student plotted the following points, based on the recorded data.

0.10

0.20

0.30

l/m

0.001 0.002 0.003 0.004 1/f/Hz-10.00

Describe, with the aid of a labelled diagram, how the student obtained the data. (14) Use the graph to find the highest frequency tuning fork used by the student in this experiment. (6) Use the graph to calculate the speed of sound in air. (10) The line in the graph does not pass through the origin. Explain why. From the graph, find the approximate diameter of the column of air used in the experiment. (10)

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4. The following diagram was drawn as part of a student’s report of an experiment to measure the resistivity of nichrome wire. The scale of the diagram is 1 cm to 6 cm. On this diagram, the student displayed the results of two of the measurements. One of these measurements is given below.

24.5 Ω

Clamp Clamp

Crocodileclip

Crocodileclip

Calculate the value of the other measurement that can be read from the diagram. (6) Name the instruments used to take the measurements in this experiment. (9) A third measurement taken could not be read accurately from the student’s diagram and was

recorded separately. Given that the student calculated the value for the resistivity of nichrome to be 1.1 × 10-6 m,

calculate the value for the third measurement that the student would have recorded. (15) While measuring this third value, give two precautions that should be taken to improve the

accuracy of the reading recorded. (6) Give a reason, other than experimental error, why the student may get a different value for

resistivity if the same measurements were taken on a different day. (4)

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SECTION B (280 marks) Answer five questions from this section. Each question carries 56 marks.

5. Answer any eight of the following parts (a), (b), (c), etc. (a) State Newton’s second law of motion. (b) A barge is towed by two other boats, one

with a force of 3000 N north and the other with a force of 4000 N east, as shown.

What is the resultant force acting on the barge? (c) State the principle of a hydrometer. (d) The sound intensity increases from 2 × 10–6 W m–2 to 3.2 × 10–5 W m–2 as a person

approaches a loudspeaker. What is the increase in sound intensity level? (e) Why is red light bent through the smallest angle when white light is passed through a prism

and dispersed? (f) A charged object A is moved so that its distance from another charged object B is 3 times its

original distance. By what factor does the electric field strength at the position of object B change?

(g) Explain why bringing a negatively-charged conductor near a positively-charged conductor

increases the capacitance of the positively-charged conductor. (h) Give three factors that determine the size of the force exerted on the rotating coil

in a d.c. motor. (i) What is the function of (i) the moderator, (ii) the control rods in a nuclear reactor? (j) Write an equation that represents pair annihilation.

or

How can a galvanometer be converted to an ammeter?

(8 × 7)

4000 N

3000 N

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6. (a) Define simple harmonic motion. (6) (b) A man of mass 64 kg does a bungee jump using an elastic

bungee cord that obeys Hooke’s law. The natural length of the bungee cord is 75 m and when the man eventually comes to rest, the length of the cord is 83 m. The maximum length of the bungee cord during the first oscillation is 93 m. The motion of the person is in the vertical direction and friction can be ignored during the first oscillation.

(i) Calculate the spring constant of the bungee cord. (11) (ii) Derive an expression for the acceleration of the man with respect to displacement from

the equilibrium position when he is below the equilibrium point. (12) (iii) Calculate the length of time it takes the man to travel from when the cord is 93 m long

to the next time it is 83 m long. (15) (iv) What is the magnitude of the maximum force exerted on the man during the first

oscillation? (6) (v) Why is the man not executing simple harmonic motion for the full oscillation? (6) 7. (a) State the laws of reflection of light. (9) Draw a ray diagram showing how an image is formed in a plane mirror. (12) The manager of a department store wants to

purchase mirrors for the dressing rooms. To reduce costs, she wants to purchase mirrors that are as short as possible but will still allow a person of height 2 m to see themselves standing full length in the mirror.

What is the shortest mirror she should purchase? Explain your answer. (9) (b) Plane mirrors can be used to construct periscopes, but prisms are more widely used. (i) Give one advantage of using prisms instead of mirrors in periscopes. (4) (ii) If prisms are used in periscopes, calculate the minimum refractive index of the glass

that should be used to make the prisms. (9) (iii) Calculate the percentage reduction in the speed of the light after entering the prism if

glass of the minimum refractive index is used in the periscope. (7)

(iv) If glass of refractive index 1.38 was used to make the prisms in the periscope, how

would this change what the periscope operator views? Explain your answer. (6)

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8. In 1897, J.J. Thomson discovered the electron and concluded that these particles were subatomic. The name ‘electron’ came from the unit of charge used in electrolysis for a number of years. Though he could not measure the mass and the size of the charge on the electron separately, he did calculate the charge-to-mass ratio (e/m). In a series of experiments began in 1909 by an American scientist, the charge on the electron was determined and therefore its mass could also be calculated.

(i) What was the value for e/m determined by Thomson? (6) (ii) Name the scientist who (i) introduced the name ‘electron’, (ii) determined the value of the

charge on an electron in 1911. (8) The electron was discovered by Thomson from studying the rays produced in cathode ray tubes. (iii) What speed is reached by an electron in a cathode ray tube where the voltage between the

cathode and anode is 2000 V? (12) (iv) Derive an expression for the force on an electron travelling at velocity v in magnetic field

of flux density B. (15) (v) An electron gun produces electrons of the same speed as those in the cathode ray tube in

part (iii). These electrons were fired at right angles into a magnetic field of flux density 2 T. Explain why the beam of electrons travels in a circular path.

Calculate the radius of this circular path. (15) 9. In a gas boiler, a semiconductor device called a thermistor, whose

resistance varies with temperature, is often used to regulate the flow of gas. It controls the amount of gas that is needed to keep the water being heated at a particular temperature.

(i) Sketch a graph showing how the resistance of a thermistor

varies with temperature. Use the shape of the graph to explain the principle on

which a thermistor works. (14) (ii) State two other ways in which the resistivity of a semiconductor can be changed. (6) (iii) Describe how p-type and n-type silicon semiconductors are produced. Explain how these semiconductors have greater conductivity than intrinsic

silicon semiconductors. (15) A semiconductor diode is produced when one side of a semiconductor is made n-type and

the other side is made p-type. (iv) Describe how (i) a junction voltage, (ii) a depletion layer is produced at the junction

between both layers. (12) (v) How does a diode act as a rectifier? (9)

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10. The Nobel Prize in Physics 1903 was divided; one half awarded to Antoine Henri Becquerel “in recognition of the extraordinary services he has rendered by his discovery of spontaneous radioactivity”; the other half jointly to Pierre Curie and Marie Curie, née Sklodowska, “in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel”.

(Adapted from: http://www.nobelprize.org/nobel_prizes/physics/laureates/1903.) (i) What is radioactivity? (6) (ii) Describe an experiment to compare the penetrating power of the three types

of nuclear radiation. (12) Becquerel discovered radioactivity from exposure of photographic plates to uranium salts. The

following partially-filled table describes the decay series of the uranium isotope U-238 (i.e. the decay product in one decay process becomes the parent nucleus in the next decay process).

Parent Nucleus Radiation Half-Life Decay Product

U-238 Alpha 4,460,000,000 years (a)

(a) (b) 24.1 days (c)

(c) (d) 1.17 minutes U-234

U-234 Alpha 247,000 years Th-230

Th-230 Alpha 80,000 years Ra-226

Ra-226 Alpha 1,602 years Rn-222

Rn-222 Alpha 3.82 days Po-218

Po-218 Alpha 3.05 minutes Pb-214

Pb-214 Beta 27 minutes

19.7 minutes

1 microsecond

22.3 years

5.01 days

138.4 days Pb-206

Pb-206 None Stable None (iii) Identify the missing information from the spaces labelled (a), (b), (c) and (d) in the table. (Refer to Formulae and Tables booklet, p. 82.) (10) (iv) Write out the decay series (using nuclear formulae) from Pb-214 to Pb-206, given that lead,

bismuth and polonium are the only elements present in that part of the decay series. Indicate the form of radiation for each decay. (15) (v) At midday, 2 × 106 Pb-214 nuclei in the sample are decaying per second. Including only those nuclei that were Pb-214 at midday, at what time will there be 5.84 × 108

Pb-214 nuclei present in the sample? (13)

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11. Answer either part (a) or part (b). (a) Read the following passage and answer the accompanying questions. It appears that the faster-than-light neutrino results, announced last September by the

OPERA collaboration in Italy, was due to a mistake after all. A bad connection between a GPS unit and a computer may be to blame.

Physicists had detected neutrinos travelling from the CERN laboratory in Geneva to the Gran Sasso laboratory near L’Aquila that appeared to make the trip in about 60 nanoseconds less than light speed. Many other physicists suspected that the result was due to some kind of error, given that it seems at odds with Einstein’s special theory of relativity, which says nothing can travel faster than the speed of light. That theory has been vindicated by many experiments over the decades.

According to sources familiar with the experiment, the 60 nanoseconds discrepancy appears to come from a bad connection between a fibre optic cable that connects to the GPS receiver used to correct the timing of the neutrinos’ flight and an electronic card in a computer. After tightening the connection and then measuring the time it takes data to travel the length of the fibre, researchers found that the data arrive 60 nanoseconds earlier than assumed. Since this time is subtracted from the overall time of flight, it appears to explain the early arrival of the neutrinos. New data, however, will be needed to confirm this hypothesis.

(Adapted from http://news.sciencemag.org/scienceinsider/2012/02.) (i) What observation led to the existence of the neutrino being proposed by

Wolfgang Pauli in 1931? (ii) Complete the formula below which required the presence of the neutrino

to be proposed.

_____________ _____________ + _____________ + (iii) It took 25 years after the existence of neutrinos was proposed for them to be detected

experimentally. Why did it take so long to discover neutrinos? (iv) The experiment that first vindicated Einstein’s formula E = mc2 was performed in 1932

by John Cockroft and Ernest Walton. Write down the nuclear equation for the reaction that took place in this experiment. (v) If the mass of a lithium nucleus is 1.165007 × 10–26 kg, calculate the loss in mass that

would have occurred in Cockroft and Walton’s experiment. (vi) How would they have used this value to experimentally verify E=mc2? (vii) There are large circular particle accelerators in the CERN laboratory in Geneva. After

the verification of E = mc2 by Cockroft and Walton, why was there increased interest in the building of particle accelerators?

(viii) The particles discovered in accelerators have been classified into a number of families:

leptons, baryons and mesons. Give the quark structure of any two particles from these families.

(8 × 7)

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11. (b) Read the following passage and answer the accompanying questions. In November and December of 1887, Tesla filed for seven U.S.

patents in the field of polyphase a.c. motors and power transmission. These comprised a complete system of generators, transformers, transmission lines, motors and lighting. So original were the ideas that they were issued without a successful challenge, and would turn out to be the most valuable patents since the telephone.

An adventurous Pittsburgh industrialist named George Westinghouse, inventor of railroad air brakes, heard about Tesla’s invention and thought it could be the missing link in long-distance power transmission. With the breakthrough provided by Tesla’s patents, a full-scale industrial war erupted. At stake, in effect, was the future of industrial development in the United States, and whether Westinghouse’s alternating current or Edison’s direct current would be the chosen technology.

It was at this time that Edison launched a propaganda war against alternating current. Westinghouse recalled: ‘I remember Tom [Edison] telling them that direct current was like a river flowing peacefully to the sea, while alternating current was like a torrent rushing violently over a precipice. Imagine that! Why they even had a professor named Harold Brown who went around talking to audiences... and electrocuting dogs and old horses right on stage, to show how dangerous alternating current was.’

In spite of the bad press, good things were happening for Westinghouse and Tesla. The Westinghouse Corporation won the bid for illuminating The Chicago World’s Fair, the first all-electric fair in history. The fair was also called the Columbian Exposition — in celebration of the 400th Anniversary of Columbus discovering America. Up against the newly-formed General Electric Company (the company that had taken over the Edison Company), Westinghouse undercut GE’s million-dollar bid by half. Much of GE’s proposed expenses were tied to the amount copper wire necessary to utilize d.c. power. Westinghouse’s winning bid proposed a more efficient, cost-effective a.c. system.

(Adapted from: www.pbs.org/tesla/ll/ll_warcur.html) (i) Sketch graphs showing the difference between alternating current and direct current. (ii) Why was alternating current chosen as the more suitable method for transmitting

electricity? (iii) What energy conversion takes place in a generator? (iv) Draw a diagram showing how the coil in a generator is connected to an external circuit. (v) At what point in the rotation of the coil in a generator is the a.c. voltage at

(i) its maximum value and (ii) zero? (vi) a.c. induction motors are widely used in industry instead of d.c. motors. Give two advantages of using an a.c. induction motor over a d.c. motor. (vii) Explain how the principle of the induction motor depends on Lenz’s law. (viii) Give two factors that affect the efficiency of a transformer.

(8 × 7)

George Westinghouse

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12. Answer any two of the following parts (a), (b), (c), (d). (a) (i) What is meant by a couple? (6) Three tubes, each 2 m long, have different diameters. They are connected end on end in order

of increasing diameter as shown below. When lifted by two people, the person on the narrow end exerts a force upwards of

160 N and the person on the wide end exerts a force upwards of 240 N. If lifted by one person only calculate (ii) the force upwards the one person needs to exert (3) (iii) how far from the narrow end of the three poles this force should be applied. (9) (iv) An extra weight of mass 20 kg and negligible length was placed at the wide end

of the connected tubes. How far should the person move along the tube to carry the tubes with the least

required force? (10) (b) A ray from a laser of wavelength 532 nm (green light) is passed through a diffraction grating

with 300 lines per mm at right angles. The diffraction grating is parallel to and a distance of 3 m from a wall at the opposite side from the laser.

(i) What is the distance between the first order fringes formed on the wall? (13) (ii) What is the maximum number of fringes that could be observed on the wall? (9) (iii) How would the pattern on the wall change if (i) a red laser was used, (ii) the laser

beam was not at right angles to the grating? (6)

Laser

Diffractiongrating

Wall

2m

3m

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(c) (i) Explain the term thermometric property. (6) Refrigeration is used in a lot of industrial processes. It is important to know both the pressure

and the temperature of refrigeration gases. (ii) Describe how a pressure gauge could be converted to a temperature gauge, for

measuring the temperature of gases in a chamber of fixed volume, by producing a calibration curve. (12)

(iii) Give a reason why a pressure gauge would be

used as a thermometer rather than other types of thermometer for this application. (4)

(iv) Why can a pressure gauge be used as method

for measuring altitude in a plane? (6) (d) (i) State Faraday’s law of electromagnetic induction. (6) (ii) In a 100% efficient step up transformer, the voltage increases from 230 V to 2000 V. If the current in the primary coil is 4 A, what is the current in the secondary coil? (6) (iii) A length of wire 37.7 m long is made into a square coil with 200 turns. It is placed in a

constant magnetic field and when pulled out of that field with a speed of 2 m s–1, it induces an emf of 2.2 V.

Calculate the magnetic flux density of the field. (16)