FIRST YEAR

END-OF-YEAR TEST

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

Directions to Candidates

Show ALL working.

Write units where appropriate.

Answer ALL questions in Section A

Answer any FOUR questions from Section B

You have been provided with two booklets. Use one booklet for Section A, the other for Section B.

UNIVERSITY OF MALTA

G.F. ABELA JUNIOR COLLEGE

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Formulae Pages

The following equations and formulae 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

Ray optics:

Refractive index: 2211 sinsin nn

2

1

2

121

sin

sin

v

vn

1 3 1 2 2 3.n n n

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)

Mechanics:

Newton’s second law: dt

mvdF

)(

Power:P = Fv

Momentum: p = mv

Materials:

Hooke's law: F = kx

Stress: A

F

Strain: l

l

Young's modulus:

Y

Energy stored in a stretched wire:

21

2 E k l

Circular motion and rotational dynamics:

Angular speed: r

v

dt

d

Angular acceleration: r

a

dt

d

Centripetal force: r

mvF

2

Torque: I

Work done in rotation: 212

τ θ Iω

Simple harmonic motion:

Displacement: x = xo sin(t + )

Velocity: v = xo cos(t + )

2 2

ov ω x x

Acceleration: a = –2 x

Period:

21

fT

Mass on a light spring: k

mT 2

Stationary waves:

Speed of waves on strings: Tvμ

Wave motion:

Two slit interference: d

Ds

Diffraction grating: d sin = n

Single slit diffraction: a

Diffraction of circular aperture:

sin 1.22λ

θ θa

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Fields:

Electric field strength:

F dVE

q dr

Uniform field: d

V

q

FE

Force between point charges: 2

0

21

4 r

QQF

Electric field strength of a point charge:

2

04 r

QE

Force between point masses: 2

21

r

MMGF

Electric potential: r

QV

04

Gravitational potential: r

GMVG

Work: W QV

Capacitance:

Capacitance of parallel plates: d

AC r 0

Capacitors in parallel: C = C1 + C2 +…

Capacitors in series: ...111

21

CCC

Energy stored: 2

2

1CVW

Charging: tRCQ Q e

0 1

Discharging: tRCQ Q e

0

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

Boltzmann constant k = 1.38 × 10−23

J K−1

Molar gas constant R = 8.31 J K−1

mol−1

Avogadro’s constant NA = 6.02 × 1023

mol−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

Permeability of free space o = 4 × 10−7

H 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 Answer all questions in this section. Please make sure to write the question number in the margin. Each question carries 10 marks 1. The conductivity of silicon may be enhanced by a process known as doping. What does the term in italics mean? [1] (a) Two distinct types of dopants may be used. State the valency of such dopants and explain how they change the silicon into (i) an n-type seminconductor and (ii) a p-type semiconductor respectively. [1,1,2,2] (b) A semiconductor diode may be biased in two different ways. What name is given to that type of bias that will put the semiconductor in conducting mode? [1] (c) When a silicon diode is biased as described in (b) above, it may still not conduct if the applied voltage is, say, about 0.2 V. Explain this observation. [2] 2. A buoy is seen to oscillate up and down in the sea with a frequency of 2 Hz. The distance between its lowest position in the water and its highest position is estimated to be 1.20 m.

(a) Write an equation that gives the displacement x of the buoy at any time t given that at time = 0 s the buoy was at its highest position in the water. [2] (b) Sketch a graph to show how the displacement varies with time. Include any known values on your graph. [2]

buoy

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(c) Sketch another graph to show how the acceleration of the buoy varies with time. [2] (d) In what way are your graphs in (b) and (c) consistent with the definition of simple harmonic motion? [2] (e) With what speed does the buoy pass through its mean (equilibrium) position? [2] 3. A ball is thrown vertically up in the air, reaches maximum height and returns to its original point of throw. The air resistance on the ball is negligible throughout its motion. (a) Sketch graphs to show the variation with time of the (i) velocity of the ball [2] (ii) acceleration of the ball. [2] State the sign convention used. (b) Sketch a free body diagram of the ball, showing and labelling any forces that act on it (i) on its way up [2] (ii) on its way down [2] (c) The original ball took 4.0s to return to its original point of throw. Comment on the time that would have been taken by a new ball having (i) twice the mass as the first [1] (ii) half the mass as the first. [1] You are to assume that the velocity of projection did not change and that air resistance was still a negligible factor in the motion of the new ball. 4. This question is about electric and gravitational fields. (a) What property of a body allows it to experience a force in (i) an electric field? [1] (ii) a gravitational field? [1] (b) State one way in which electrostatic forces and gravitational forces may be considered (i) similar [1] (ii) different. [1]

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(c) By looking at a field diagram, how would the field lines show that a particular field is uniform? [1]

(d) Two protons each of mass 1.6×10-27 kg and charge +1.6 10−19C are a

distance of 3 10−15 m apart. Work out a value for the (i) electrostatic force (ii) gravitational force they exert on each other. [2,2] (e) In view of your answer to (d) above explain why gravitational forces tend to be ignored for bodies on the atomic/subatomic scale. [1] 5. Microwaves from a single source (not shown) fall on two slits. The microwaves emerging from the slits diffract and interfere into each other. A detector, placed in the region of interference, is moved parallel to the plane containing the slits and detects alternate points of high microwave intensity and zero microwave intensity. The diagram shows the detector at one specific point and shows the actual number of waves that occupy the space between each slit and the detector.

= 13 cm

S1 S 2

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(a) Microwaves used in this experiment were of frequency 1 1010 Hz. Use this information to work out an appropriate value for the width of each of the two slits. Explain your reasoning. [3] (b) Use the diagram to work out a value for the path difference (in metres) between the two trains of waves as they reach the detector. [2] (c) Does the detector detect maximum intensity or zero intensity at the point shown? Explain. [1,1] (d) The slits were 10 cm apart. Determine the distance between two adjacent maxima that were read by the detector given that the perpendicular distance between slits and detector was 13cm. [3] 6. Newton’s third law states that for every action there is an equal and opposite reaction. (a) Explain why it is incorrect to conclude that these two forces cancel each other out and give a resultant of zero. [2] (b) A truck and a pick-up van, travelling at the same speed, collide head-on as shown. The truck has a bigger mass than the van. Assuming that drivers do NOT press the brake pedal upon impact:

(i) Label each statement from A to F below as being either TRUE or FALSE (No need to write full statement on your answer booklet, just write A, B, C etc.) Right after impact A. the truck and van move off with equal speeds [1] B. the impulse experienced by truck and van respectively is of the same magnitude [1] C. the van experiences a greater force than the truck [1]

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D. the change in momentum for both truck and van is of the same magnitude [1] E. both truck and van experience the same acceleration [1] F. the combined kinetic energy of truck and car increases [1] (ii) Crash test analyses seem to indicate that occupant injury and fatality risk can be reduced by designing vehicles with softer front end structures. Explain how this is consistent with Newton’s second law of motion. [2] 7. Sound waves are said to be mechanical waves and longitudinal. (a) Explain this description of sound waves. [2] (b) A loudspeaker is fitted at one end of a narrow tube which is open at the other end. narrow tube Loudspeaker

(i) Sketch a graph to show how the displacement of the particles along the axis (dotted line) of the tube varies with distance from the loudspeaker at one specific moment in time. [2] (ii) Sketch a corresponding graph to show the pressure variation with distance inside the tube at that same instant. [3] (c) If the other end of the tube were closed, explain why it could be possible for stationary waves to be formed inside the tube. You should specify the conditions needed for stationary waves to be formed and how these would be satisfied in the new arrangement. [3]

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8.

(a) Assuming that the upper half of the body is maintained in equilibrium by

these forces, write down (i) an equation for the vertical components of the forces [2] (ii) an equation for the horizontal components of the forces. [2] (b) Using the equations in (a) work out a value for the force F acting at the base

of the spine if = 40o and θ = 30o. The mass of the painter in the diagram is 77 kg. [3]

(c) Hence calculate the tension T in the back muscle. [3]

F The diagram shows the principal forces acting on the upper half of a human body whilst bending forward. W is the weight F is the force acting at the base of the spine T is the tension in the back muscle

θ

T W

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Section B. Answer any FOUR questions from this section. USE THE OTHER BOOKLET FOR THIS SECTION. DO NOT forget to write the question number in the margin. Each question carries 25 marks 9. The graph shows the stress–strain curve for two types of human bone under compression. The graphs extend to almost breaking point for each type of bone.

(a) Define stress and strain. [2,2] (b) Use the graph to identify and describe one property of cortical bone. [2] (c) The table gives the following information for the two types of bone.

Material Young Modulus/109 Pa Maximum Compressive Stress/ 106 Pa

Maximum Tensile Stress / 106 Pa

Cortical Bone

17.9 170 120

Trabecular Bone

0.076 2.2

(i) Which of the two types of bone is the more flexible? Explain. [2] (ii) State the difference between compressive stress and tensile stress. [2]

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(iii) State how a stress-strain graph could be used to confirm the value of the Young modulus of a material. [1] (iv) A person of mass 90 kg stands on one foot. Show that the maximum weight which can be supported is about 70 times this person’s weight. Assume all the weight is supported by the femur (thigh bone) and that it is made of cortical bone. The cross-sectional area of the femur is 3.7 × 10

−4 m2. [4] (v) With the help of the graph, determine the maximum decrease in length a 2cm-length of trabecular bone can withstand before breaking. [3] (c) Two specimens of cortical bone and trabecular bone are compressed such that the compressive strain for each specimen is 2%. (i) Which of the two would store the greater amount of energy per unit volume? Explain. [2] (ii) Determine the energy stored in a 5cm-long cylinder made from a material that has exactly the same elastic properties as cortical bone when compressed by 1mm. The diameter of the cylinder is 1.2cm. [5] 10. For a rigid body rotating around an axis of symmetry, the angular momentum can be expressed as the product of the body's moment of inertia and its angular velocity. (a) Define the two terms in italics. [2,2] (b) State the law of conservation of angular momentum. Outline any assumption associated with this law. [2,1]

(i) A star has a mass of 4.75 1030 kg and radius of 1.2 105 km and spins at

about 8.3 10−5 rad s−1. Given that the moment of inertia I of a sphere of mass m and radius r, spinning about its central axis, is given by I = 2/5 m r 2 , determine the angular momentum of the star. [3] (ii) If the star were to collapse and shrink under its own gravity (no mass is lost) to reach a final radius of 12km, determine the new spinning rate of the star. [3] (c) A hollow cylinder and a solid cylinder are placed at the top of an incline. The cylinders are made from different materials such that they both have the same mass m and the same radius r.

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The two cylinders are allowed to roll down the incline. The diagram shows one of the cylinders and the two principal forces acting on it along the plane: P (the component of the weight acting down the plane) and f (the frictional force).

(i) Express the force P in terms of m and θ. [1] (ii) Hence show that the linear acceleration a of each cylinder is given by: a = g sin θ − f/m [2]

(iii) The frictional force exerts a torque about the centre of the cylinder. Show that the angular acceleration α of the cylinder, caused by this torque, is given by: α = f r / I where I is the moment of inertia of the cylinder. [3] (iv) Given that a = α r show that for each cylinder, the linear acceleration a is given by:

a =

+

s in

2r

Im

mg [4]

(v) Explain which cylinder you would expect to reach the bottom first. [2] 11. A very narrow beam of monochromatic light is directed onto a slit at normal incidence. The light beam is diffracted on passing through the slit and a diffraction pattern is formed on a screen directly behind the slit. (a) The light had wavelength 625 nm, the slit width was 0.05 mm and the screen was 1.000 m behind the slit.

f P θ

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(i) Draw a graph to show the intensity variation of the diffraction pattern obtained on the screen. [3] (ii) Work out a value for the width of the central maximum. [5] (b) The photos below show two stars as they are seen by two different telescopes. The telescope (A) on the left gathers light through a lens of diameter 0.1524m while the telescope (B) on the right gathers light through a lens of diameter 0.508 m.

(i) Which telescope has the better resolving power? [1] (ii) State one other factor apart from size of aperture which affects the resolving ability of an optical instrument. [1] (iii) Calculate the theoretical minimum angular separation of two stars (in radians) if they are to be resolved by telescope A. You may assume that the telescope uses filtered light of wavelength 420 nm for this purpose. [3] (iv) Hence determine the closest distance (in km) the stars must be from each other, if they are to be resolved, given that these stars are 30 light years away. (1 light year = 9.46 × 1012 km) [4] (c) In a spectrometer, a beam of white light may be dispersed by passing it either through a prism or through a diffraction grating. (i) What is the meaning of “dispersed” in the statement above? [1] (ii) State TWO important differences between the dispersion carried out by a diffraction grating and that produced by a prism. [4]

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(d) For a diffraction grating, calculate the wavelength of monochromatic light where the second order image is diffracted through an angle of 20o. The grating has 300 lines per millimetre. [3] 12. A small body tied to a string is whirled around in a vertical circle as shown. (a) The body is rotated with constant speed.

(i) Explain how Newton’s first law of motion leads us to conclude that the body must be acted upon by a resultant force. [3] (ii) Derive an equation for this acceleration a in terms of the speed v of the rotating body and the radius r of the circular path. [8] (iii) The rotating body had a mass of 30 g and was being whirled in a circle of radius 30cm. If the tension in the string was 5 N when the body passed through its topmost of its circular path, determine the speed (in m s−1) with which it was being rotated. [4] (iv) Hence determine the angular speed with which the body moved. [1] (v) Explain, with reasons, the point along the circular path, at which the string would be most likely to break. [4]

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(b) Horses were once used to power machinery in factories, mines and mills. The figure shows two horses attached to a beam which turns a wheel. This wheel drives machinery.

(i) Calculate the torque produced by the couple exerted by the two horses. [2]

(ii) The two horses move at a constant pace of 1.30 m s−1. Calculate the combined power output of the two horses. [3] 13. The astronauts of Apollo 14 played golf on the Moon. They struck a number of shots such as the one shown below. The acceleration due to gravity on the Moon is 1.6 m s-2.

(a) (i) Calculate the horizontal and vertical components of velocity of the golf ball at the instant it was struck. [1,1]

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(ii) Describe the essential difference between the horizontal and vertical components of velocity during the flight of the ball. [2] Assuming the shot is played on horizontal ground, calculate (iii) the total time of flight, [3] (iv) the horizontal distance the ball travels, [2] (v) the maximum height reached. [2] (vi) A similar golf shot is played on Earth. Give two reasons why your answer to (b)(iii) would be different. [2] (b) The golf ball in question (a) had a mass of 46 g. (i) Determine the initial momentum that was imparted to it when it was struck. [2] (ii) Given that the time of contact between the bat and the golf ball was 1.2 ms, determine the force which was exerted on the ball. [2] (c) Sketch graphs to show how each one of these quantities varies with time for the projected golf ball. No need to include values. (i) horizontal momentum [2] (ii) vertical momentum [2] (iii) horizontal acceleration [2] (iv) vertical acceleration [2] 14. When light passes from one medium to another, it is refracted. (a) What do you understand by the term in italics? [1] (b) A beam of monochromatic light is incident several times on an air-glass interface. The angle of incidence i is changed at each successive incidence and the corresponding angle of refraction r is measured. (i) For any specific refraction of the light, state one property of light that changes and one property that remains the same. [2] (ii) How would you use the values of i and r to determine (graphically) a value for the refractive index of glass for the particular wavelength of light used? [2]

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(iii) The glass used had a refractive index of 1.54 for the type of light used. With what speed did this light travel in the glass? [2] (b) The diagram below shows the set-up for an experiment to determine the focal length of a converging lens. The focal length is the distance between the centre of the lens and its principal focus.

(i) Define the term principal focus as applied to a converging lens. [2] (ii) Explain how you would use the set-up shown, to determine the focal length of the lens. Your account should include a description of

the method used,

the readings taken,

the table of results

the graph plotted

how f is calculated [10] (c) The image obtained with a converging lens is upright and three times the height

of the object. The focal length of the lens is 20cm. (i) State whether the image produced is real or virtual. [1] (ii) Calculate the object distance from the lens. [3] (iii) Calculate the image distance from the lens. [2]