FIRST YEAR

END-OF-YEAR TEST

SUBJECT: PHYSICS DATE: 13th June 2014 LEVEL: INTERMEDIATE TIME: 09.00h to 12.00h

Directions to Candidates

Show ALL working Write units where appropriate Answer ALL questions in Section A Answer the single question in Section B Answer any TWO questions from Section C You have been provided with two booklets. Use one booklet for Section A, the other for Sections B and C.

UNIVERSITY OF MALTA G.F. ABELA JUNIOR COLLEGE

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Data and Formulae Booklet The following equations may be useful in answering some of the questions in the examination.

Uniformly accelerated motion:

Useful formulae: atuv

2

2

1atuts

as u v 222

tvu

s

2

Circular motion:

Centripetal acceleration: r

va

2

Period: v

rT 2

Materials:

Hooke's law: F = kx

Stress: A

F

Strain: l

l

Young's modulus:

Y

Energy stored in a stretched wire:

2

12E k l

Mechanics:

Momentum: p = m v Newton’s second law: maF

Kinetic energy: 212KE mv

Gravitational potential energy: PE mgh

Mechanical work done: W = Fd

Fields due to point sources:

Force between point charges: 2

0

21

4 r

QQF

Force between point masses:

2

21

r

MMGF

Vibrations and waves:

Acceleration in s.h.m.: a = –k x

Period: k

T 2

Velocity of a wave: fv

Current electricity:

Current: I = nAve

Ohm’s law: IRV

Resistors in series: RTOTAL = R1 + R2 + …

Resistors in parallel: ...111

21

RRRTOTAL

Power: R

VRIIVP22

Electromagnetism:

Electric field strength: q

FE

Electric potential (uniform field): dEV

Energy of a particle accelerated by an electric field:

212QV mv

Force on a moving charge: BQvF

Force on current: BIlF

Electromagnetic induction: dE Blvdt

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Capacitance: Charge on capacitor: CVQ

Parallel-plate capacitor: 0 r AC

d

Alternating current:

Root mean square for sinusoidal alternating current

and voltage: 2

0II rms ;

2

0VVrms

Ray optics:

Thin lenses: vuf

111 (real is positive)

uvf

111 (Cartesian)

Magnification: o

i

h

h

u

vm (real is positive)

o

i

h

h

u

vm (Cartesian)

Physics of nuclei and atoms:

Radioactivity: A N

Half-life T1/2 = 0.693/λ

Mass-energy relation: 2mcE

Line spectra:

hchfE

Mathematical Formulae:

Surface area of a sphere: 24S r

Volume of a sphere: 34

3V r

Surface area of a cylinder: 22 2S rh r

Volume of a cylinder: 2V r h

The following constants may be useful in answering some of the questions in the examination.

Acceleration of free fall on and near the Earth’s surface g = 9.81 m s−2

Gravitational field strength on and near the Earth’s surface g = 9.81 N kg−1

Coulomb’s law constant k = 1/(4πεo) = 8.99 × 109 N m2 C−2

Charge of an electron e = −1.60 × 10−19 C

Mass of an electron me = 9.11 × 10−31 kg

Electronvolt 1 eV = 1.60 × 10−19 J

Gravitational constant G = 6.67 × 10−11 N m2 kg−2

Permittivity of free space εo = 8.85 × 10−12 F m−1

Planck constant h = 6.63 × 10−34 J s

Speed of light in a vacuum c = 3.00 × 108 m s−1

Unified atomic mass unit u = 1.66 ×10−27 kg

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.

Section A

Attempt ALL questions in this section. Please do not forget to write the question number in the margin. Each question carries 7 marks. This section carries 50% of the total marks of the test. 1. In the equation d = p t2 + q t d represents displacement while t represents time. The equation is homogeneous with respect to base units. (a) What do you understand by the statement in italics? [1] (b) State the base units of each of the terms: (i) p t2 (ii) q t (iii) p (iv) q [4] (c) State the two quantities that are represented by p and q respectively. [2] 2. A small ring is held in equilibrium by two ropes and a 4kg-mass hanging down from it, as shown in the diagram. One rope pulls the ring with a force T1 while the other rope pulls the ring with a force T2.

(a) What is the downward pull exerted by the 4kg-mass on the ring? [1]

40o

T1 50

o

ring T2

4 kg

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(b) Write down two different equations, in terms of T1 and T2, which must be satisfied if the ring is to be in equilibrium. [2,2] (c) Hence work out the values of T1 and T2 respectively. [2] 3. A man slides down a water chute that is 6 m high and 30 m long.

(a) What is the loss in gravitational potential energy of the man by the time he reaches the bottom of the chute? The man’s mass was 79kg. [1] (b) Assuming no retarding forces act on the man as he slides down, determine the maximum velocity he would attain at the bottom of the chute? [2] (c) The man actually attained a final velocity of 7 m s−1 by the time he reached the bottom of the chute. What was the average retarding force acting on him during the entire slide? [4] 4. A beam of monochromatic light travels at 65% of its speed in free space when it travels inside a particular type of glass. (a) Determine the refractive index of this glass for this particular type of light. [2]

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(b) A fibre optic cable consists of a core of refractive index 1.5 and an outer cladding of refractive index 1.47

(i) Light from the core hits the core-cladding boundary and is just totally internally reflected as shown. The angle θc may be assumed to be equal to the critical angle for light incident at this particular boundary. Using the values of the refractive indices given for the core and cladding respectively, determine the value of θc . [3] (ii) Calculate the corresponding angle of incidence θA at the air-core boundary.

[2] 5 (a) State Newton’s second law of motion. [1] (b) A goalkeeper catches a ball that was travelling at 25 m s−1. The ball, of mass 440 g, was brought to rest in 0.1 s.

(i) Determine the initial momentum of the ball. [1] (ii) What average force was used on the ball to bring it to rest in 0.1 s? [2]

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(iii) What was the average deceleration of the ball during this time? [1] (iv) Determine the work that was needed to reduce the initial kinetic energy of the ball to zero. [2]

6. The diagram shows a demonstration of stationary waves on a string.

(a) What is the wavelength of these stationary waves? [2]

(b) Comment on the phase relationship between the three points, A, B and C, shown in the diagram. [2]

(c) Given that the pattern shown was obtained when the frequency of the vibrating pin was set to 360Hz, determine the fundamental (first harmonic) frequency of the vibrating string. [2]

(d) State one way in which a stationary wave differs from a travelling (progressive) wave. [1] 7. A girl rides on a chair along a horizontal circular path as shown in the diagram. The chair is supported by a bar of length 5.00m inclined at 30o to the vertical as shown.

(a) What is the radius of the horizontal circular path? [1]

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(b) What is the period of revolution of the girl if her linear speed is 3.76 m s−1? [2] (c) Given that the tension in the bar is approximately 655N during rotation, determine the combined mass of the girl and chair to the nearest kg. [4] 8. A laser beam is aimed at two very narrow and very close slits. The beam falls on both slits such that the cone of light emerging from one slit interferes with the cone of light emerging from the other slit. A pattern of light and darks bands appears on a screen beyond.

(a) The beam opens up into a cone of light as it emerges from a slit. What name is given to this effect and what would have been the effect of having much wider slits than the ones used? [1,1] (b) Light waves emerging from both slits are in phase with one another and have the same frequency. Give one word that describes this particular condition. [1] (c) Explain fully why the central band, equidistant from both slits, is a bright band rather than a dark one. [2] (d) How must the trains of light from both slits interfere in order to cancel each other out completely and produce a dark band? [1] (e) How would the pattern on the screen change if the screen were to be moved further away from the two slits? [1]

slits

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9. A body is to oscillate with simple harmonic motion. (a) State two conditions concerning the acceleration of this body that must be satisfied during the oscillations. [2] (b) Sketch graphs to show how (i) the displacement of the oscillating body and (ii) its acceleration, vary with time. [2,2] (c) Re-draw the graph in (b)(i) for a situation where the oscillating body is subjected to light damping during its oscillations. [1] 10. In a castle, overlooking a river, a cannon was once employed to fire at enemy ships. One ship was hit by a cannonball at a horizontal distance of 150 m from the cannon as shown. The height of the cannon above the river was 67 m and the cannonball was fired horizontally.

(a) Show that the time taken for the cannonball to reach the water surface after being fired from the cannon was 3.7 s. Assume the air resistance was negligible. [1] (b) Calculate the velocity with which the cannonball was fired. [2] (c) Calculate the vertical component of velocity just before the cannonball hit the ship. [2] (d) Hence, find the direction of the velocity of the cannonball just before it hit the ship. [2]

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Section B. Attempt the question in this section. PLEASE START A NEW BOOKLET and do not forget to write the question number in the margin.

This question carries 20 marks which is equivalent to 14% of the total mark of the test.

11. The resistance R of a wire is measured in ohms (Ω) and is given by the equation:

R = A

L

The symbol ρ stands for resistivity. This is a property of the material and is constant over a wide range of temperature. Good conductors have a low resistivity.

L is the length of the wire and A is its cross-sectional area.

In one experiment, the resistance of a number of wires, of different cross-

sectional area, was determined and the results were tabulated as shown. All wires were made from the same material and were 8.0 cm long.

R / 10 −5 Ω A/ 10−5 m2

A

1 /104 m−2

2.1 7.01 1.4

5.3 2.64

8.4 1.56

11.0 1.22

13.2 1.00

21.0 0.63

(a) Copy the table and include the calculated values of A

1/104m−2. The first value

has been calculated for you. [5]

(b) Plot a graph of R against A

1 . [6]

(c) Use your graph to determine a value for the resistivity ρ of the material. [7]

(d) How would the graph have changed if the wires were longer than 8.0cm? [2]

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Section C Continue this section on the booklet used for Section B. You are to attempt TWO questions only from this section. Each question carries 25 marks. This section carries 36% of the total mark of the exam. Please do not forget to write the question number in the margin. 12. This question is about elasticity. (a) Define stress and strain. [2,2] (b) State Hooke’s law. [2] (c) The graph shows the stress-strain variation for a particular material.

(i) If a sample of this material is 100 cm long, to what maximum extension can it be stretched for Hooke’s law to remain applicable? [2] (ii) When the stress on the wire is 100000kPa, the corresponding strain is 0.01. If the sample is stretched to this point, determine how much elastic energy would be stored in it? The sample is in the form of a wire of radius 2mm. [4] (iii) With the help of the graph, work out an approximate value for the Young’s modulus of this material? [3] (iv) At stresses around 300,000kPa, the material begins to show plastic behaviour. Name the point that marks the beginning of plastic behaviour and state one important difference between plastic behaviour and elastic behaviour. [1,2]

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(v) Is this material brittle or ductile? [1] (d) When a sample of rubber undergoes a loading-unloading cycle it is said to demonstrate elastic hysteresis. (i) State two notable differences in elastic behaviour between a rubber wire and a metallic wire like copper. [1,1] (ii) Sketch a stress-strain graph for a rubber sample and use it to explain the meaning of elastic hysteresis. The sketch should including both loading and unloading sections. [4] 13. This question is about gravitation. (a) State Newton’s law of gravitation. [3] (b) Two friends, each of mass 60 kg, stand 50cm away from each other. What gravitational force of attraction do they exert on each other? Comment on your result. [2,1] (c) On January 11, 2007, the Chinese destroyed a weather satellite by firing a missile towards it. The satellite was reduced to fragments. The satellite had a mass of 750 kg and was at an altitude of 865 km. You may assume that its original orbit around the earth was circular. Mean earth radius = 6371 km (i) What was the gravitational field strength at that height? [3] (ii) Hence, calculate the weight of the satellite at that height. [1] (iii) One of the fragments stayed at the satellite’s original altitude. With what speed did such a fragment travel after the satellite was destroyed? [4] (iv) What was its period of rotation? [2] For all fragments, orbiting around the earth, their respective period T is related to their distance from the centre of the earth, r , by the equation T 2 = k r 3 where k is a constant (v) Using the value of T determined in (iv) work out a value for k. State an appropriate unit for it. [2,1]

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(vi) Another fragment fell to an altitude of 600 km. What was the speed of rotation of this fragment in this orbit? [4] (vii) Explain why the different fragments are not likely to affect one another even if they orbit quite near to one another? [2] 14. This question is about refraction and lenses. (a) The table below gives a list of refractive indices for five different media, for light of wavelength 589 nm.

(i) In which of these five media does light travel fastest? [2] (ii) With what speed does light travel in fused silica? [3] (iii) The refractive index of a medium varies according to the wavelength of light. Explain, with the help of a diagram, how a flint glass prism is able to disperse white light. In your answer, you should state for which colour of light will flint glass have the largest refractive index and for which colour it has the smallest refractive index. [4] (b) A converging lens and a diverging lens may be used to alter the path of a beam of light. Both lenses have a focal length of 15.0cm. (i) With the aid of two different diagrams, explain why we say that a converging (convex) lens has a real principal focus while a diverging (concave) lens has a virtual one. [2,2] (ii) An object is placed 20.0cm in front of the converging lens. Calculate how far a screen should be placed away from the lens in order to get a real image of this object. [3] (iii) Work out a value for the magnification produced by the lens. [2]

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(iv) Explain why a screen would have been useless if the lens in (b)(ii) were the diverging lens rather than the converging lens. [2] (c) A student performed an experiment, using a converging lens, an illuminated object and a screen, in which he obtained different corresponding sets of image distances (v) and object distances (u). The student then worked out values for the product (uv) of each set of values and the respective sum (u + v). (i) Using the lens equation, show that uv = f (u + v) [3] (ii) Hence explain how the student would use his data to plot a suitable graph from which to obtain a value of f. [2]

15. This question is about nuclear physics. (a) The fact that the positive charge within an atom was confined to a very tiny nucleus at the heart of the atom was first discovered by Rutherford just over one hundred years ago. In his experiment, alpha particles were fired from a radioactive source onto a very thin foil of gold. (i) Explain what happened to the vast majority of the alpha particles as they hit the gold foil and what this implied about the size of the nucleus. [3] (ii) The diagram shows three alpha particles approaching a gold nucleus. Copy the diagram and draw the expected paths taken by each of the three alpha particles as they continue with their motion. [3] alpha particles

(b) The zinc nuclide Zn7130 decays by − emission and has a half-life of 2.4 minutes.

gold nucleus

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(i) State how many protons and neutrons are contained in this particular nucleus. [1,1]

(ii) What is a − particle? [1] (iii) State the number of protons and neutrons that are contained in the daughter

nuclide following the decay of Zn7130 . [2,2]

(iv) A sample of this isotope is estimated to have 5 1023 nuclides at a given time. What is the activity (in Bq) of this sample at this time? [4]

(c) The Thorium nuclide Th22890 decays by alpha emission to form a Radium (Ra)

nuclide. (i) Write down a nuclear equation for the decay. [2] (ii) Which nuclide is the less stable, that of Thorium or that of Radium? [1] (iii) The rest masses of the particles involved in the decay are as follows: Th: 227.9793 u Ra: 223.9719 u α: 4.0015 u Determine the energy released during the decay in joules? [4] (iv) What form does this energy take? [1]