L.36

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PRE-LEAVING CERTIFICATE EXAMINATION, 2011

PHYSICS – HIGHER LEVEL

TIME – 3 HOURS

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

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SECTION A (120 marks)

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

1. A student carried out an experiment to verify the laws of equilibrium for a set of co-planar forces acting on a metre stick. The metre stick was weighed and its centre of gravity was found to be at the 50 cm mark. The student attached weights and spring balances to the metre stick. The positions of the weights and the spring balances were adjusted until the metre stick was horizontal and in equilibrium, as shown in the diagram.

Explain how the centre of gravity of the metre stick was found.

How did the student measure the weight of the metre stick? (9)

Use the first law of equilibrium to find the weight of the metre stick. (8)

Calculate the sum of the clockwise moments and the sum of the anticlockwise moments about an axis through the 0 cm mark on the metre stick.

Explain how these experimental values verify the second law of equilibrium for a set of co-planar forces. (15)

Why it is important that (i) the metre stick is in a horizontal position; (ii) the spring balances hang vertically? (8) 2. The specific heat capacity of water was found by passing an electrical current through a

coil placed in water in a copper calorimeter. The following data were recorded.

Mass of calorimeter = 52.4 g Mass of water = 72.8 g Initial temperature of water = 14.2 °C Final temperature of water = 25.6 °C Electrical energy supplied = 3700 J

Describe how the mass of the water and amount of electrical energy supplied were found. (9)

Why is it beneficial to set the initial temperature of the water below room temperature (20 °C)? (9)

Use the data to calculate the specific heat capacity of water. (15)

What effect would increasing the current flowing through the coil for the same temperature rise have on the accuracy of your final result? (7)

(specific heat capacity of copper = 390 J kg–1 K–1)

9 cm

3.6 N

17 6 6

2 N

74

4.2 N

8 6

2 N3 N

springbalance

fixed support fixed support

springbalance

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3. In an experiment to measure the wavelength of a monochromatic light, a narrow beam of the light was passed through a diffraction grating with 400 lines per mm. A number of bright images were observed. The angle between the central bright fringe and the first, second and third order images to the left and right of the central image were measured. The following data were recorded.

n 3 2 1 0 1 2 3

θ / degrees 45.0 28.2 13.5 0 13.4 28.0 44.9

Describe, with the aid of a labelled diagram, how the above data were obtained. (12) Use the above data to calculate the wavelength of the monochromatic light. (18) How many extra fringes could have been observed? (10) 4. In an experiment to investigate the variation of current I with potential difference V for a

semiconductor diode connected in forward bias, a student recorded the following data.

V / V 0 0.2 0.4 0.6 0.65 0.7 0.75 0.8

I / mA 0 0.4 0.6 1.6 5.3 12.2 31.4 90.1

Draw a circuit diagram used by the student to collect these data. Explain how the student varied the potential difference. (12) Draw a graph to show how the current varies with the potential difference. Does your

graph indicate that a semiconductor diode obeys Ohm’s law? Explain your answer. (15) Explain why the current varies with potential difference as indicated by your graph. (9) What can be done to ensure that the diode is not damaged during this experiment? (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 Archimedes’ principle. (7) (b) What is the angular velocity of an object on the surface of the earth, due to the

rotation of the earth about its axis? (7) (c) Why can you not observe total internal reflection when travelling from a less dense

medium to a more dense medium? (7) (d) Which wave phenomenon distinguishes transverse waves from longitudinal waves? (7) (e) Name the thermometric property associated with a mercury-in-glass thermometer

and state one other thermometric property. (7) (f) Explain how point discharge occurs. (7) (g) How much heat energy is gained by water in a kettle if a current of 12 A flows for

1 minute in the element of a kettle that has a resistance of 21 Ω? (Assume no energy loss to surroundings.) (7)

(h) What is the length of a wire carrying a current of 4 A that experiences a force of

20 N when placed at an angle of 30° to a magnetic field of flux density = 5 T? (7) (i) What is the role of (i) the moderator and (ii) the control rods in a fission reactor? (7) (j) Why is the mass of a baryon greater than that of a meson? (7)

or

Name the parts labelled A, B and C of the induction coil shown in the diagram. (7)

B

C

A

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6. What is meant by simple harmonic motion? (6) State Hooke’s law. (6) Use Hooke’s law to show that the period T of a mass m suspended from a spring of

spring constant k is k

mT π2= when it is displaced from its equilibrium position. (12)

Tidal movements result in a change in the depth of water

in a harbour throughout the day. This change in depth of the surface of the water with time can be described by simple harmonic motion. The depth of the surface of the water on a particular day is 25 m at high tide (10.20 a.m.) and 12 m at low tide (4.40 p.m.). A boat of mass 20000 kg is anchored in the harbour so that it can only move vertically.

(i) What is the period and amplitude of the motion of the boat? (9)

(ii) What is the next time after low tide that the boat will be moving at its fastest? (6)

(iii) Calculate the force the boat experiences at high tide. (6)

(iv) Find the two depths of the water when the force on the boat is 1 mN. (8) Give one other example of a body executing simple harmonic motion. (3) 7. State the laws of refraction of light. (12) The magnification of an image produced by an optical microscope

depends on the focal length of the objective and eyepiece lenses and the distance between the lenses. Both lenses magnify the object so the total magnification of the image observed is equal to the product of the magnification of each lens, i.e. M = ME × MO, where ME and MO are the magnifications of the eyepiece and objective lenses, respectively. The image produced by the objective lens is a real image while the image produced by the eyepiece lens is a virtual image.

Why must the image produced by the objective lens be real?

Draw a ray diagram showing how a magnified real image is produced. (15) In a particular microscope the focal length of both lenses is 7.5 mm. If the magnification

of the objective lens is 8, how far from the objective lens must the specimen be placed? (9) At what distance from the lens will the image observed by the eyepiece lens appear, if the

magnification of the eyepiece lens is also 8? (9) How many times smaller would the image appear if the specimen was placed 6.5 mm from

a magnifying glass of focal length 7.5 mm instead of the micorscope? (8) Will the image of the specimen observed under the magnifying glass be inverted or erect? (3)

Objectivelens

Eyepiecelens

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8. What is magnetic flux? (6) State Faraday’s law of electromagnetic induction. (6) Describe an experiment that demonstrates Faraday’s law. (12) A coil of wire of sides 5 cm × 3 cm is rotating at 5 revolutions per second in an area where

there is no magnetic field. The axis about which the coil is rotating is also moving towards an area of uniform magnetic flux density of 10 T at 0.5 m s–1, shown in the diagram. If the coil is in position A as it enters the magnetic field:

(i) How long does it take for the centre of the coil to enter the magnetic field?

(ii) How long does it take for the coil to rotate to position B?

(iii) Find the average induced emf in the coil when it is in position B.

(iv) Calculate the magnetic flux cutting the coil when the coil has rotated through a further 45° and hence find the average induced emf between when it is in the vertical position and this point. (26)

Why would there be no induced emf if the coil was not rotating and remained in

position A while entering the magnetic field? (6)

3 cm

5 cm

v = 0.5 m s-1

B

B

A

A

B = 10 T

B = 10 Tperpendicularlyinto the page

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9. At the end of the 19th century and the beginning of the 20th century, the understanding of the structure of the atom developed from the belief that atoms were indivisible particles to discovering that atoms were made up of three subatomic particles; electrons, protons and neutrons. In 1891, the term ‘electron’ was proposed to describe the fundamental amount of charge found in electrolysis. In 1911, the value of the charge on the electron was first measured. In the same year, it was discovered that the positive charge in an atom was concentrated in a small volume in the centre of an atom (called the nucleus). This positive charge was later found to be made up of particles called protons. In 1932, the neutron was discovered.

Name the scientist who: (i) introduced the term ‘electron’ in 1891 (ii) determined the value of the charge on the electron in 1911 (iii) discovered that the positive charge in an atom was concentrated in the nucleus. (9) Describe the experiment that the scientist performed in 1911 to show that the positive

charge was concentrated in the nucleus. (12) Why did it take much longer to discover the neutron than the other particles? (6) In 1913, Danish scientist Niels Bohr proposed a model for how electrons are arranged

in orbits around an atom. He proposed that electrons could only exist at certain energy levels in atoms.

Explain, using Bohr’s model, how light is emitted in a discharge tube when the atoms

in a gas are excited by an electrical discharge. Calculate the wavelength of light produced when an electron moves between orbits

of energy levels 1.56 eV and 3.43 eV. (18) During the same period radioactivity was discovered and this also contributed greatly to

the understanding of the structure of atoms. Alpha particles, which were emitted from radioactive materials, led to the discovery of the proton in 1918 when scientists bombarded nitrogen gas with alpha particles.

Radium was used as a source of alpha particles in these experiments. If radium-226 has a

half-life of 1602 years and a mass of 200 g, what is the number of alpha particles emitted each second? (11)

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10. Answer either part (a) or part (b). (a) What are the four fundamental forces of nature? (8) List the forces in order of increasing strength. Give an example of where each of

these forces is observed. (7) In 1932, Einstein’s E=mc2 formula was experimentally verified by two scientists

at Cambridge University. Name the two scientists who verified Einstein’s formula and, with the aid of a labelled diagram, describe their experiment. (15)

Write a nuclear equation to represent this reaction. Using the values below, find the value of E (the disintegration energy) in E=mc2

that they would have calculated. (18) Name and give the quark structure of the baryon present in this experiment. (8)

(mass of a lithium nucleus = 1.1646 × 10–26 kg) (b) Boolean algebra invented by George Boole, the first professor of mathematics at

University College Cork (then Queen’s College), is the basics for the logic used in modern electronic devices such as computers. Logic gates are devices that make decisions for controlling electronic equipment. Common logic gates are AND, OR and NOT gates.

Construct a truth table for AND, OR and NOT gates. (12) Describe an experiment that establishes the truth table for one of these logic gates. (12) Copy and complete the truth table for the following arrangement of logic gates, by

working out the output values at F. (8)

A B C F 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

A NOT gate can be constructed using a voltage inverter containing a bipolar transistor.

Draw the circuit diagram for this type of voltage inverter. Label where the input voltage is connected and where the output voltage is measured. (15)

Explain how this circuit operates as a NOT gate. (9)

FAB

C

D

E

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11. Read the following passage and answer the accompanying questions. Lord Kelvin was one of the most extraordinary figures of the 19th

century – indeed of any century. The German scientist, Hermann van Helmholtz, no intellectual slouch himself, wrote that Kelvin had by far the "greatest intelligence and lucidity, and mobility of thought" of any man he ever met. The sentiment was understandable, for Kelvin was a kind of Victorian superman. In the course of a long career (he lived until 1907 and to the age of 83), he wrote 661 papers, accumulated 69 patents (from which he grew abundantly wealthy) and gained renown in nearly every branch of the physical sciences. Among much else, he suggested the method that led directly to refrigeration, devised the scale of absolute temperature that still bears his name,

invented the boosting devices that allow telegrams to be sent across oceans and made innumerable improvements to shipping and navigation from the invention of a popular marine compass to the creation of the first depth sounder. Kelvin did extensive mathematical analysis of electricity and magnetism including the basic ideas for treating light as an electromagnetic phenomenon as well as developing significant theories in thermodynamics. Thermodynamics is the study of energy flow and transformation. Kelvin saw that the conversion of one form of energy into another is never perfectly efficient; some energy is always lost as heat and is unavailable to do useful work. Consequently every finite system, including the universe, is constantly running down and will eventually stop. This basically is the second law of thermodynamics.

(Adapted from “A Brief History of Nearly Everything” by Bill Bryson, Black Swan Books, 2004.)

(a) In the heat pump in a refrigerator, evaporation of a liquid occurs. How does this

cause a refrigerator to become cold? (7) (b) How is evaporation in the heat pump of a refrigerator achieved? (7) (c) What properties would make a liquid suitable for circulating in a heat pump? (7) (d) If 30 g of water at 293.15 K is added to an ice tray, what is the minimum amount of

energy that must be taken from the freezer to produce ice? (7) (e) Kelvin was one of the first scientists to link light to electromagnetism. State two

other forms of electromagnetic radiation with a higher frequency than light. (7) (f) Why is knowledge of the direction of the Earth’s magnetic field important when

designing marine compasses? (7) (g) Ultrasonic waves are used in depth finders on ships. If the wavelength of the

ultrasonic wave produced from the ship multiplies by 4.4 when it passes from air to water and the time taken for the reflected wave to return to the ship is 0.46 s, find the depth of the water at that point. (7)

(h) A transformer, with 200 turns in the primary coil and 1000 turns in the secondary

coil, is 80% efficient. If the voltage in the primary coil is 230 V and the current is 2 A, what is the current in the secondary coil? (7)

(specific heat capacity of water = 4180 J kg–1 K–1; specific latent heat of fusion of ice = 3.3 × 105 J Kg–1; speed of sound in air = 340 m s–1)

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12. Answer any two of the following parts (a), (b), (c), (d). (a) A hot air balloon of total mass 1000 kg leaves the ground rising with an acceleration of

2 m s–2 for 20 seconds. At this time the person operating the balloon adjusts the heat so that the balloon then rises at a constant velocity. After a further 10 seconds a stone is dropped from the balloon.

How does the hot air cause the balloon to rise? (6) Calculate: (i) the height from which the stone is dropped;

(ii) the length of time it takes the stone to hit the ground after it is let go. (22)

(acceleration due to gravity, g = 9.8 m s–2) (b) What are stationary waves? (9) Explain how a stationary wave is formed in a pipe opened at both ends. (8) Draw diagrams demonstrating the first three harmonics produced on a pipe

open at both ends. Explain from these diagrams how the frequencies are related for the first

three harmonics. (11)

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(c) State two factors on which the capacitance of a parallel plate capacitor depends. (6) Describe an experiment that demonstrates the dependence of one of these factors

on the capacitance of a parallel plate capacitor. (12) When a capacitor and a resistor are connected in series to a 6 V battery as shown,

explain how the potential difference changes with time across both components after the switch has been closed. (10)

(d) What is the photoelectric effect? (6) A 100 W UV light source of wavelength 280 nm has all its light

focused on a zinc plate.

(i) Prove that electrons will be emitted from the zinc plate. (9)

(ii) With what speed will the electrons be emitted and how many electrons will be emitted from the zinc per second? (13)

(threshold frequency of zinc = 1.04 × 1015 Hz)

R C

6 V

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