2011 njc prelim h2 physics paper 3 .qp final

1

NATIONAL JUNIOR COLLEGEPRELIMINARY EXAMINATIONSHigher 2

CANDIDATE NAME

SUBJECT CLASS

REGISTRATION NUMBER

PHYSICSPaper 3 Longer Structured QuestionsCandidate answers on the Question Paper.No Additional Materials are required.

9646/0314 Sep 2011

2 hours

Section AREAD THE INSTRUCTION FIRSTWrite your subject class, registration number and name on all the work you hand in.Write in dark blue or black pen on both sides of the paper.You may use a soft pencil for any diagrams, graphs or rough working.Do not use paper clips, highlighters, glue or correction fluid.Answers all questions.You are advised to spend one hour on each section.

The number of marks is given in brackets [ ] at the end of each question or part question.

For Examiner’s Use

1

2

3

4

5

Total

NJC (FOR INTERNAL USE ONLY) 9646/03/2011 [Turn over

2

Data

speed of light in free space, c = 3.00 x 108 ms-1

permeability of free space, 0 = 4 x 10-7 Hm-1

permittivity of free space, 0 = 8.85 x 10-12 Fm-1

elementary charge, e = 1.60 x 10-19 C

the Planck constant, h = 6.63 x 10-34 Js

unified atomic mass constant, u = 1.66 x 10-27 kg

rest mass of electron, me = 9.11 x 10-31 kg

rest mass of proton, mp = 1.67 x 10-27 kg

molar gas constant, R = 8.31 JK-1mol-1

the Avogadro constant, NA = 6.02 x 1023 mol-1

the Boltzmann constant, k = 1.38 x 10-23 JK-1

gravitational constant, G = 6.67 x 10-11 Nm2kg-2

acceleration of free fall, g = 9.81 ms-2

Formulae

uniformly accelerated motion,

work done on/by a gas, W = pV

hydrostatic pressure p gh

gravitational potential,

displacement of particle in s.h.m., x = x0 sin t

velocity of particle in s.h.m., and

resistors in series, R = R1 + R2 + …

resistors in parallel,

electric potential,

alternating current/voltage, x = x0 sin t

Transmission coefficient T = ex p(-2kd) Where

radioactive decay, x = x0 exp (-t)

decay constant,


3

Section AAnswer all the questions in this section.

1 (a) A lighting circuit consists of four lamps connected as shown in the figure below. The resistance of each lamp is 120 Ω.

A fault is discovered in the circuit, so switch 1 is turned off and the fuse is removed for safety. A resistance meter is connected between the point A and B and the following readings are obtained for different switch positions.

Switches Resistance Meter Reading/

1 2 3 4 5off off off off off 14600000off off off off on 120off off off on on 60off off on on on 40off on on on on 0.2

(i) If there were no fault in the circuit, what would the resistance meter read when switches 2, 3, 4 and 5 are on and 1 is off.

Reading =_____________ [1]

(ii) Suggest what the fault in the circuit may be.

[2]


12345

Fuse

A

By

4

1 (b) A potentiometer wire is suspected of having been damaged at some point along its length. To test this, the circuit is set up as shown below.

The table shows readings of the potential difference V, taken using a voltmeter of infinite resistance, for lengths of wire l.

l/ m 0.100 0.250 0.400 0.550 0.700 0.850 1.000V/ V 0.17 0.42 0.67 0.93 1.49 1.75 2.00

Using the graph grid below, plot a suitable graph to determine the region of the wire which the damage has occurred. Explain your answer.

[5]


l

V

5

2 Fig 2.1 shows a coil of copper wire made up of two semicircles joined by two straight sections of wire. The total resistance of the coil is 0.025 . The coil is lying flat on a horizontal surface. Starting from the orientation in Figure 2.1, the smaller semicircle of radius 0.20 m rotates at an angular frequency 1.5 rads-1 about the dashed line. The angle is the angle of rotation measured from the horizontal position as shown in Fig 2.2. A uniform magnetic field of magnitude 0.35 T is directed upwards, perpendicular to the horizontal surface.

(a) Define the weber.

[1]

(b) (i) Show that the maximum magnetic flux through the coil is 0.110 Wb.

[1]

(ii) On the axes below, sketch the variation of the magnetic flux, through the coil with , for one full cycle. Indicate all the important values.

[2]


0.20 m0.40 m

Fig 2.1: Top View

Fig 2.2: 3-dimensional view

/ Wb

/

6

2 (b) (iii) Using the laws of electromagnetic induction, sketch on the axes below, the variation of the induced emf (E) in the coil with time (t) for one complete cycle.

[2]

(iv) Determine the maximum induced emf in the coil.

Maximum induced emf = ____________ V [2]

(v) Hence or otherwise, determine the peak power dissipated in the coil.

Peak power = ____________ W [1]

(vi) Determine the average rate of rise of temperature in the coil given that the total mass of copper wire in the coil is 0.256 kg and the specific heat capacity of copper is 385 Jkg-1K-1.

Average rate of rise of temperature = _______ Ks-1 [2]


E / V

t / s

7

3 Fig 3 shows the variation of the amplitude, xo, of the oscillation of a mass with the frequency of the external driver, fd.

(a) Explain the shape of the graph shown in Fig 3.

[2]

(b) Calculate the angular frequency when the mass is oscillating at maximum amplitude.

Angular frequency = ________ rads-1 [2]

(c) Draw, on Fig 3, a new graph to show the variation of amplitude with driver frequency if the mass of the oscillator is increased. [1]


fd / Hz

xo / m

0 2 4 6 8

0.20

0.40

0.60

0.80

Fig 3

8

4 Fig 4.1 below shows the variation of binding energy per nucleon with nucleon number.

Consider the following nuclear reaction:

Fission reaction:

(a) Define binding energy.

[2]

(b) Explain, with reference to Fig 4.1, why the fission reaction is possible.

[1]

(c) Estimate the energy released in the fission of a uranium-235 nucleus.

Energy released = ____________ J [3]


9

8

7

6

5

4

3

2

1

0

Binding Energy per nucleon / MeV

Nucleon number

235U

144Ba

90Kr

4He

3H

2H

Fig 4.1

9

4 (d) Suggest two forms of energy produced during the fission of a single uranium 235 nuclide.

[2]

5 (a) Emission spectra are often produced in the laboratory using a discharge lamp containing the gas to be investigated. Draw a sketch of the experimental setup and explain the physical processes occurring within such a lamp which lead to the excitation of the gas atoms and the emission of light.

[4]


10

5 (b) Fig 5.1 below shows the energy level diagram for mercury atoms.

(i) Draw a transition arrow on Figure 5.1 that will result in the emission of visible light photons. Show your working.

[2]

(iii)

In the process of photo-ionisation, a photon interacts with the atom causing the ejection of the electron. Find the maximum wavelength of the radiation required to ionise the electron from the ground state. State the region of the electromagnetic spectrum in which this radiation lies.

Minimum wavelength = ____________ m

Region of the EM spectrum ___________ [2]


ground state - 10.43 eV

- 5.50 eV- 4.94 eV

- 3.70 eV

- 2.67 eV

- 1.56 eV

0 eV

Energy

Fig 5.1

11

NATIONAL JUNIOR COLLEGEPRELIMINARY EXAMINATIONSHigher 2

CANDIDATE NAME

SUBJECT CLASS

REGISTRATION NUMBER

PHYSICSPaper 3 Longer Structured Questions

Candidate answers on the Question Paper.No Additional Materials are required.

9646/03 14 Sep 2011

2 hours

Section BAnswer any two questions.

You are advised to spend one hour on each section.

The number of marks is given in brackets [ ] at the end of each question or part question.

Circle the questions you attempted.

Submit Section A and B separately.

For Examiner’s Use

6

7

8

Total


12

Section BAnswer two questions in this section.

6 (a) Explain the following situation:

(i) As a ball falls towards the Earth, the ball’s momentum increases because its speed increases. Suggest and explain if momentum is conserved in this situation.

[2]

(ii) Consider 5 identical balls shown in Fig 6.1. Suggest if it is possible that when ball 1 is released, balls 4 and 5 will swing out on the opposite side and travel with half the speed of ball 1, as shown in Fig 6.1. You may assume that the collision is elastic.

[2]

(iii)

A raw egg dropped to a floor breaks but when it is dropped to a thick foam rubber cushion, it does not break. Explain.

[2]


Fig 6.1 2

vv

13

6 (a) (iv)

An iceberg floating in seawater is extremely dangerous because much of the ice is below the surface. This hidden ice can damage a ship that is still a considerable distance from the visible ice. Determine the fraction of the iceberg that lies below the water level. Assume density of ice and seawater are 917 kgm-3 and 1030 kgm-3 respectively.

Fraction = ________ [2]

(b) Fig 6.2 shows two blocks of masses M and 3M, placed on a horizontal, frictionless surface. A light spring is attached to one of them. A cord initially holding the blocks together is burnt. Mass 3M moves to the right at 2.0 ms-1.

(i) State the Principle of Conservation of Linear Momentum.

[1]

(ii) Since no external force acts on the system, explain why the momentum of mass 3M is not conserved.

[1]

(iii)

Determine the original elastic potential energy in the spring if M is 0.350 kg.

Elastic potential energy = _______ J [3]


Fig 6.2

v 2.0 ms-1

14

6 (c) Distinguish the difference between the torque of a couple and the moment of a force.

[2]

(d) A model, shown in Fig 6.3, is built to represent the action of a human arm. The elbow behaves like a simple hinge. The mass, m = 8.0 kg, represents a load held in the hand and the forearm is assumed to be uniform with mass of 1 kg. Neglect the mass of the upper arm and the thickness of the forearm.

(i) Calculate the tension in the muscle when the forearm is horizontal and the muscle itself is vertical as shown in Fig 6.3A

Tension = _______ N [3]


Fig 6.3A Fig 6.3B

m = 8.0 kg

forearm

300 mm

30 mm elbow

muscle300 mm

Upper arm

15

6 (d) (ii) The mass is now lifted, with the muscle vertical and in the final state of equilibrium as shown in Fig 6.3B. State how the tension in the muscle and the compressive force acting along the forearm changes, if at all? Explain your answer.

[3]

7 (a) A small conducting sphere carries a charge of +5.0 x 10-9 C.

(i) Fig 7.1 shows the sphere held at the midpoint between two parallel plates. The plates are initially uncharged. When the sphere was inserted, charges were induced on both plates.

Draw at least six electric field lines between the sphere and the plates. [3]

(ii) The plates, which are 4.0 cm apart, are now connected to a 50 000 V DC supply. Calculate

1. the magnitude of the electric field strength E between the plates assuming that this electric field is uniform.

E = ____________ NC-1 [2]


Fig 7.1

16

7 (a) (ii) 2. the magnitude F of the electric force acting on the sphere, treating the sphere as a point charge of +5.0 x 10-9C

F = _____________ N [2]

(b) Fig 7.2 shows a linear particle accelerator or linac used to accelerate protons. Such a linac consists of a series of cylindrical electrodes. These electrodes are attached alternately to the terminals of an alternating voltage source of a fixed frequency so that the protons accelerate each time they cross the gap between two electrodes. Each time a proton crosses the gap, it is accelerated by a potential difference of 100 kV.

Protons from the source enter electrode 1 with 50 keV of energy.

(i) State the energy of one of these protons after being accelerated 10 times.

energy = ____________keV [1]

(ii) Calculate the speed of this proton (after being accelerated 10 times).

speed = ____________ms-1 [2]


Cylindrical electrodes

Proton source

Proton beam

Fig 7.2

ac voltage source

17

7 (b) (iii) If electrons are used instead of protons, calculate the speed of an electron after being accelerated 10 times.

speed = ___________ms-1 [2]

(iv) Comment on your answer in (iii).

[1]

(v) The lengths of the electrodes in a proton linac increase along the path of the particles (as shown in Fig 7.2). However a high-energy electron linac has electrodes which are all of the same length. Suggest why this is so.

[2]

(c) Fig 7.3 shows a beam of potassium ions passing through a region of uniform magnetic field of flux density 0.84T directed into the plane of paper. The ions are travelling at a speed of 5.0 x 105 ms-1.

The ions that make up the beam are produced at a rate of 5.4 x 107 per second and the charge on each ion is +1.6 x 10-19 C.

(i) Calculate the electric current of the beam

current = _____________ A [1]


Source of potassium ions

Path of potassium ions

Region of uniform magnetic field

Fig 7.3Vacuum Chamber

18

7 (c) (ii) If the mass of each potassium ion is 6.5 x 10-26 kg, calculate the radius of the path of the ions within the magnetic field

radius = _____________ m [2]

(iii)

In an actual experiment, it was found that 93% of all potassium ions emitted from the source followed the path with the radius calculated in (ii). The remaining 7% followed a different path with a slightly larger radius. Suggest why this happens.

[2]

8 (a) Using appropriate diagram(s) and the concepts of population inversion and stimulated emission, explain the action of a laser.

[5]


19

(b) (i) 1. State two conditions for the superposition of two waves to give rise to a well-defined interference pattern.

[2]

2. Explain why these conditions are necessary.

[2]

(ii) A red laser beam of wavelength 628 nm illuminates two narrow vertical slits. The interference fringes produced is observed on a screen parallel to and 1.5 m from the slits. The distance between the centres of the fourth order maxima on either side of the central maximum is 6.0 cm.

1. Calculate the separation of the slits.

Separation = __________ m [2]

2. If the whole apparatus was submerged in water of refractive index 1.33, determine the new fringe separation given that

Refractive index of water

Separation = ___________m [3]


20

8 (c) Explain why the aperture(s) of a diffraction grating for visible light should be

(i) narrow compared to the wavelength of the visible light

[1]

(ii) close together

[1]

(d) The same laser beam is now incident normally on a diffraction grating with vertical slits that has 5.5 x 105 lines per metre as shown in Fig 8.1 below. The distance between the grating and the screen is 1.5 m.

(i) Sketch on Fig 8.2, the pattern produced on the screen (X corresponds to the central fringe indicated in Fig 8.1). Label the distances in your sketch and show your working clearly.

[3]


lasergrating

screen

X

Fig 8.1

X

5 m

5 m

Fig 8.2

21

8 (d) (ii) The grating is now replaced by a crossed diffraction grating with both vertical and horizontal slits. Sketch on Fig 8.3, the possible pattern produced on the screen when the laser light is sent through such a grating.

[1]


End of Paper

X

5 m

5 m

Fig 8.3

2011 njc prelim h2 physics paper 3 .qp final

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