FIRST YEAR

END-OF-YEAR test

SUBJECT: PHYSICS DATE: 18th June 2013

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

Page 2 of 16

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: vrT π2=

Materials:

Hooke's law: F = k∆x

Stress: A

F=σ

Strain: l

l∆=ε

Young's modulus: εσ=Y

Energy stored in a stretched wire:

( )212E 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 = F∆d

Fields due to point sources:

Force between point charges: 2

0

21

4 r

QQF

πε=

Force between point masses:

2

21

r

MMGF =

Vibrations and waves:

Acceleration in s.h.m.: a = –k x

Period: k

T π2=

Velocity of a wave: λfv =

Current electricity:

Current: I = nAve

Ohm’s law: IRV =

Resistors in series: RTOTAL = R1 + R2 + …

Resistors in parallel: ...111

21

++=RRRTOTAL

Power: RVRIIVP

22 ===

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−= =Φ

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Capacitance: Charge on capacitor: CVQ =

Parallel-plate capacitor: 0 r AC

d

ε ε=

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 Nλ=

Half-life T1/2 = 0.693/λ

Mass-energy relation: 2mcE =

Line spectra: λhchfE ==∆

Mathematical Formulae:

Surface area of a sphere: 24S rπ=

Volume of a sphere: 34

3V rπ=

Surface area of a cylinder: 22 2S rh rπ π= +

Volume of a cylinder: 2V r hπ=

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. The speed of a transverse wave on a string is given by the expression

µT

c =

where T is the tension and µ is the mass per unit length of the string.

(a) Write down the base units of µ. [2]

(b) Show that the equation is homogeneous with respect to base units. [4]

(c) Explain why an equation which is homogenous with respect to base units is not

necessarily a correct physical equation. [1]

2. A relief airplane is delivering a food package to a group of people stranded on a very

small island. The island is too small for the plane to land on, and the only way to

deliver the package is by dropping it. The airplane flies horizontally with constant

velocity of 414 km h−1

at an altitude of 550m .

(a) How long, after dropping, will it take the package to reach the stranded people?

[2]

(b) How far away, horizontally, from the island must the plane be at the moment the

package is dropped?

[2]

(c) Ignoring air resistance and assuming the plane maintains its velocity of 414 km h−1

,

explain why the plane would be flying overhead (i.e. vertically above) the island,

when the package is received? [2]

(d)

Name the main force that acts on the package after it is dropped from the plane.

[1]

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3. (a) What is meant by the term gravitational field strength?

[2]

(b) Treating the earth as a perfect sphere, show that the field strength at its surface is

about 9.8 N kg−1

.

Mass of Earth = 5.97 × 1024

kg

Mean radius of Earth = 6371 km [2]

(c)

If a man of mass 80kg were to be in a spacecraft at an exact distance of 6371 km

above the earth’s surface, what would his weight at that particular height be? [3]

4.

(a)

Explain what you understand by the term radioactivity?

[1]

(b) The nucleus of a particular isotope of thorium (Th) is made up 144 neutrons and 90

protons. It decays by the emission of a beta particle. If the daughter nucleus of this

decay is a protactinium (Pa) nuclide, express this decay as a nuclear equation.

[2]

(c) If the particular isotope of protactinium, described in (b), has a half-life of 6.7 hours,

work out a value for the number of protactinium nuclides present in a source that

has an activity of 2×1015

Bq.

[3]

(d) State one use of radioactive sources. [1]

5. (a) The figure shows a ship fitted with a sail attached to a cable. The force of the wind

on the sail assists the driving force of the ship’s propellers.

(i)

The cable exerts a steady force of 170 kN on the ship at an angle of 35° as shown.

Calculate the horizontal component of this force.

[1]

(ii)

(iii)

What is the work done by this force to move the ship 1km?

The ship is moving at a constant velocity of 7 m s −1

and the horizontal component of

the force of the cable on the ship acts in the direction in which the ship is moving.

Calculate the power provided by the wind to this ship.

[2]

[2]

(b) At one point, the sail is removed while the forward thrust derived from the ship’s

direction of motion of ship

170kN

Page 6 of 16

propeller engines remains unchanged. State what happens to the ship with regard

to its motion.

[2]

6.

The figure shows a layer of oil that is floating on water in a glass container. A ray of

light in the oil is incident at an angle of 44ο on the water surface and refracts.

The refractive indices of the materials are as follows.

refractive index of oil = 1.47

refractive index of water = 1.33

refractive index of the glass = 1.47

(a)

Show that the angle of refraction θ is about 50°.

[2]

(b) Without calculation, state the angle of refraction in glass at the water-glass

boundary. Explain how you reached your answer. [2]

(c)

Calculate the critical angle for light passing from oil into water.

[3]

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7. A cyclist pedals downhill on a road, as shown, from rest at the top of the hill and

reaches a horizontal section of the road at a speed of 16 m s−1

.

The total mass of the cyclist and her bike is 68 kg.

(a)

Calculate the total kinetic energy of the cyclist and her bike on reaching the

horizontal section of the road. [2]

(b)

The height difference between the top of the hill and the horizontal section of

road is 12 m.

Calculate the loss of gravitational potential energy of the cyclist and the cycle. [2]

(c)

(d)

The work done by the cyclist when pedalling downhill is 2400 J. Calculate the energy

lost to friction and air resistance during the descent.

The cyclist stops pedalling on reaching the horizontal section of the road and slows

to a standstill 160 m further along this section of the road. Assume the deceleration

is uniform, calculate the time taken by the cyclist to travel this distance.

[1]

[2]

8.

The figure shows a continuous progressive wave on a rope. There is a knot in the

rope.

(a)

The wave is said to be transverse. Explain what this means by referring to the

motion of the knot over the next complete cycle.

[2]

(b) Another continuous wave of the same amplitude and frequency moves along the

rope in the opposite direction and passes through the first wave. The knot becomes

motionless. Explain how this could happen.

[3]

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(c) With reference to (b), sketch a diagram of the resultant wave on the rope and mark

a position where the knot might be found. [2]

9. A converging lens is to be used as a magnifying glass. It has a focal length of 10cm.

(a) Draw a ray diagram to explain why the image seen through a magnifying glass is said

to be virtual.

[2]

(b) The lens is held 6cm above a sheet of paper that has the words “MAGNIFYING

GLASS” printed on it. How much magnified do these words appear when seen

through the magnifying glass?

[4]

(c) Explain why no magnified image of the words is obtained when the magnifying glass

is held 12cm above the paper. [1]

10. In an experiment, a hacksaw blade was connected to an oscillator such that it was

forced to vibrate. A student noted how the amplitude of the vibrating blade varied

with the frequency of the oscillator (the driving frequency). The results yielded the

graph shown overleaf.

Page 9 of 16

(a) What do you understand by the terms frequency and amplitude as used in this

context?

[2]

(b) What maximum displacement did the blade ever reach during the experiment?

[1]

(c) If the blade were not connected to the oscillator but was set to vibrate freely on its

own, state the approximate frequency with which it would be expected to oscillate.

Explain how you reached your conclusion.

[4]

Page 10 of 16

Section B.

Attempt the question in this section. PLEASE START A NEW BOOKLET.

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

test.

11. The resistance R of a metal wire is found to vary with temperature

θ according to the following equation:

R = A + B θ

where A and B are constants.

In a particular experiment the current, I , through a metal wire

and the corresponding voltage, V, were measured at five different

temperatures and the results were tabulated as shown.

θ /oC V / V I /A R /Ω

10 5.03 0.97

20 5.06 0.94

30 5.09 0.91

40 5.12 0.88

50 5.14 0.85

(a) Given that the resistance R of the metal wire is equal to V/I, copy

and complete the table by working out the values of R. [5]

(b) Show that the equation R = A + B θ is of the form y = mx + c.

[4]

(c) By plotting a suitable graph, determine the value of B. [5,6]

Page 11 of 16

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.

12. (a) The diagram shows a simple school-lab experiment in which the extension of a

spring, under various loads, is investigated

The spring is found to obey Hooke’s Law.

(i) State Hooke’s law as it would be applied to this particular spring.

[2]

(ii) What does it mean to say that the spring is elastic?

[2]

(iii) Why is it important that the support does not sag (bend down) in this

investigation?

[2]

(iv) The spring used had a spring constant of 2 N mm−1

. Explain exactly what this

value signifies.

[2]

(v) In view of your answer to (iv) above, what difference in behaviour would you

notice in a spring that has a much larger spring constant? [2]

(b)

A rubber cord of a catapult has a cross-sectional area of 2mm2 and an initial

length of 0.20m. It is stretched to 0.24 m so as to project a small stone of

mass 0.01kg

Page 12 of 16

(i) Assuming that the Young’s modulus for this type of rubber was 6 × 10

8 Pa

and that Hooke’s law was obeyed, determine the force that was needed to

extend the cord to 0.24m.

[3]

(ii) How much energy was stored in the stretched cord?

[2]

(iii) With what initial velocity was the stone projected?

[3]

(iv) Why does the assumption that Hooke’s law was obeyed by this particular cord

strike you as odd?

[2]

(v) After using the catapult to project several stones in succession, the rubber

cord was noticed to have become warm. Explain this particular observation,

with reference to one particular property of rubbers.

[3]

(vi) Why are materials with very high Young moduli unsuitable for use in such type

of catapults? [2]

13 (a) One particular principle in the study of Waves states that when two waves

overlap, the total wave displacement is just the sum of the corresponding

displacements of the individual waves.

(i) What name is given to this particular principle?

[2]

(ii) This principle is the basis of a classical experiment in Physics, known as

Young’s Double Slit Experiment. Give a detailed account of this particular

experiment making sure to include:

1. a diagram of the set-up

2. an explanation of the role played by the slits

3. an explanation of how the principle in (i) is applied

4. a description of what is observed [12]

(b) A similar experiment may be carried out using sound emitted from two

Page 13 of 16

loudspeakers.

(i)

(ii)

The speakers emit sound waves in phase and with a frequency of 400 Hz.

Taking the speed of sounds as 320 ms−1

, determine the wavelength of the

sound waves generated.

State two conditions needed for two sets of sound waves to cancel each other

out completely upon interference.

[2]

[2]

(iii)

Determine the kind of interference that will happen at point Q, which is 4.0 m

away from speaker X and 5.2m away from speaker Y as shown. (Show all

necessary calculations).

[4]

(iv)

(v)

Explain whether the interference at Q would have been different had the two

speakers been in anti-phase with one another.

With the speakers still in anti-phase with one another, identify a point where

the interfering sound waves from X and Y respectively would surely cancel

each other out.

[2]

[1]

14.

(a)

(b)

State the law of conservation of momentum.

During an American football match, two players collide head-on with each

other.

Kevin Fletcher, sporting shirt number 34, collides into Russell Agger (shirt

number 26). Fletcher has a mass of 85 kg, 5 kg less than Agger. Fletcher’s

[2]

Page 14 of 16

speed just before impact was 6 m s

−1; Agger’s was 4 m s

−1. .

(i) Who, if any, experiences the greater force upon impact? Explain. [2]

(ii) What was the total momentum of the two players just before impact? [3]

(iii)

State, without calculation, whether the total momentum would have been

less, more or the same, if Agger had been at rest at the moment of impact.

[2]

(iv) With what common velocity do the two entangled footballers move off

immediately after impact?

[3]

(v) Hence work out their total kinetic energy right after impact. [2]

(vi)

If, right after impact, the two footballers slide a total distance of 2.5m on the

grass before being brought to rest, determine the frictional force that

decelerates them to rest over this distance. [3]

(vii)

For how long do they slide on the grass before coming to rest? [4]

(c)

In question (b) above, state two quantities which you were asked to find that

were (i) vectors. [2]

and (ii) two that were scalars. [2]

15

(a)

(b)

(i)

Explain why a body performing circular motion must necessarily be acted

upon by a force, even if the speed remains unchanged. Why is it said to be

“centripetal”?

In the ladies’ hammer throw, in the Olympic Games, the hammer is of mass

4.0kg and is affixed to a cable that is 1.2m long.

At a moment when the hammer is being whirled around horizontally at a

speed of 20 m s−1

, determine the tension in the cable.

[3]

[1]

[3]

Page 15 of 16

(ii)

(iii)

(c)

(i)

(ii)

(iii)

(d)

Suppose this tension extends the cable by 5 mm, determine the elastic

potential energy stored in the cable.

What would be the initial path taken by the hammer if the cable were to

break at some instance during rotation?

The figure shows a parcel on the floor of a delivery van that is passing over a

hump-backed bridge on a straight section of road. The radius of curvature of

the path of the parcel is r and the van is travelling at a constant speed v. The

mass of the parcel is m.

On a diagram similar to the one shown below, draw the forces that act on the

parcel as it passes over the highest point of the bridge. Label these forces.

What force does the floor of the van exert on the parcel, as the van passes

over the highest point of the bridge, if v is 11 m s-1

, r is 23 m and m is 12 kg?

What is the centripetal acceleration of the parcel?

The parcel contains fragile figurines each packed in bubble plastic wraps.

[2]

[2]

[2]

[5]

[2]

parcel

floor of van

Page 16 of 16

bubble plastic

[2]

[3]

(i) How does the use of bubble

plastic reduce the risk of fracture of

the figurines?

(ii) If the van brakes suddenly to rest

from an initial speed of 11 m s−1

,

determine the force exerted on a 50g

figurine if the bubble plastic wrap

decelerates it to rest in 1.5 s?