PJC H2 PHY 9646 Mid-Year Paper 2012

2012/PJC/PHYSICS/9646 [Turn over

PIONEER JUNIOR COLLEGE Mid-Year Examination

PHYSICS 9646/02 Higher 2 Paper 2 Structured Questions 27 June 2012 1 hour 45 minutes Candidates answer on the Question Paper. No Additional Materials are required.

READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.

This document consists of 22 printed pages.

Name Class Index Number

For Examiner’s Use

1 / 7

2 / 9

3 / 8

4 / 12

5 / 8

6 / 16

7 / 12

Total / 72

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2012/PJC/PHYSICS/9646

Data

speed of light in free space, 81000.3 c ms–1

permeability of free space, 70 104 Hm–1

permittivity of free space, 120 1085.8 Fm–1

910361 Fm–1

elementary charge, 191060.1 e C

the Planck constant, 341063.6 h Js

unified atomic mass constant, 271066.1 u kg

rest mass of electron, 311011.9 em kg

rest mass of proton, 271067.1 pm kg

molar gas constant, 31.8R JK–1 mol–1

the Avogadro constant, 231002.6 AN mol–1

the Boltzmann constant, 231038.1 k JK–1

gravitational constant, 111067.6 G Nm2 kg–2

acceleration of free fall, 81.9g ms–2

3


Formulae

uniformly accelerated motion, 2

2

1atuts

asuv 222

work done on/by a gas, VpW

hydrostatic pressure, ghp

gravitational potential, r

Gm

displacement of particle in s.h.m., txx sin0

velocity of particle in s.h.m., tvv cos0

22

0 xx

mean kinetic energy of a molecule kTE2

3

of an ideal gas,

resistors in series, ...21 RRR

resistors in parallel, .../1/1/1 21 RRR

electric potential, r

QV

04

alternating current/voltage, txx sin0

transmission coefficient, kdT 2exp where 2

28

h

EUmk

radioactive decay, )exp(0 txx

decay constant,

2

1

693.0

t

4


1 A ball bounces inelastically down a flight of steps in a plane perpendicular to the front edges of the steps, as shown in Fig. 1.1.

Fig. 1.1 Each step is 0.20 m high and 0.30 m deep. It is observed that the ball always bounces exactly in the middle of each step, and that after each bounce, it rises to the height of the previous step. Air resistance can be neglected.

(a) Calculate the vertical component of the ball’s velocity uy, immediately after impact.

uy = ........................................ ms−1 [2] (b) Show that the magnitude of the ratio of uy to the vertical component of the ball’s

velocity immediately before impact, is 0.71. [2]

0.30 m

0.20 m

5


(c) Calculate the horizontal component of the ball’s velocity. horizontal component = ........................................ ms−1 [3]

6


2 (a) Define the joule.

....................................................................................................................................... ....................................................................................................................................... ................................................................................................................................. [2]

(b) A light helical spring is suspended vertically from a fixed point, as shown in Fig. 2.1.

Fig 2.1

Different masses are suspended from the spring. The weight of the mass and the length L of the spring are noted.

The variation with weight W of the length L is shown in Fig. 2.2.

Fig. 2.2

Fig. 2.2

L / cm

W / N

spring

mass

7


(i) On Fig. 2.2, show clearly the area of the graph that represents energy stored in the spring when the weight on the spring is increased from zero to 5.0 N. [1]

(ii) For a spring undergoing an elastic change, the force per unit extension of the

spring is known as the force constant k.

Show that the energy E stored in the spring for an extension x of the spring is given by the expression

21

2E kx .

[2]

(c) The mass is pulled downwards and then released. The variation with time t of the

displacement y of the mass is shown in Fig. 2.3.

Fig. 2.3

Using information from Fig. 2.3,

(i) explain why the graph suggests that the oscillations are undamped,

.................................................................................................................................. ........................................................................................................................... [1]

t / s

y / cm

8


(ii) calculate the angular frequency of the oscillations, angular frequency = ........................................ rads−1 [2]

(iii) determine the maximum speed of the oscillations. maximum speed = ........................................ ms−1 [1]

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3 (a) A stationary electron experiences a force in the direction of the field in which it is placed. State, with a reason in each case, whether or not the field is magnetic, electric or gravitational.

(i) magnetic,

.................................................................................................................................. ........................................................................................................................... [1] (ii) electric,

.................................................................................................................................. ........................................................................................................................... [1]

(iii) gravitational.

.................................................................................................................................. ........................................................................................................................... [1]

(b) Fig 3.1 shows an electron travelling at right angles to a uniform magnetic field. The

electron travels at a linear speed of 73.4 10 ms−1, in a circle of radius 2.8 cm.

Fig. 3.1 The magnetic field is directed into the plane of the paper. (i) On Fig. 3.1, mark the direction of motion of the electron at point P. [1]

P region of uniform magnetic field into plane of paper

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(ii) Calculate the magnitude of the field strength. field strength = ........................................ T [2] (iii) A uniform electric field is now produced in the same region and in the same

direction as the magnetic field. Suggest and explain the shape of the resultant path of the electron.

.................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [2]

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4 (a) A coil of wire 1000 turns and resistance 23 Ω enclosing an area of 4.0 cm2 is rotated

from a position where its plane is parallel to the Earth’s magnetic field (Fig. 4.1) to one where it is perpendicular to the field (Fig. 4.2) in 5.0 ms.

Fig. 4.1 Fig. 4.2 Fig. 4.3

(i) Calculate the average induced e.m.f. if the Earth’s magnetic flux density at the

coil’s location is 56.0 10 T.

average induced e.m.f. = ........................................ V [3]

(ii) Calculate the average induced current flowing in the coil during the 5.0 ms.

average induced current = ........................................ A [2]

(iii) The coil is then rotated from the position in Fig 4.2 to Fig. 4.3 in 5.0 ms. State the difference, if any, between the average induced current now and in (a)(ii) for the current flowing in wire AB.

.................................................................................................................................. ........................................................................................................................... [1]

A

B

D

C

D

C B

A

B

A D

C

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(b) In Singapore, the transmission of electric power over long distances from the power station to the HDB flats is through the use of transformers. A transformer near the power plant steps up the plant’s output root-mean-square (r.m.s.) voltage from 12.0 kV to 240 kV and a series of step-down transformers near the flats reduces the r.m.s. voltage to a final value of 240 V to the flats.

(i) Calculate the turns ratio of the transformer that is located near the power plant.

s

p

N

N = ........................................ [1]

(ii) Explain why 1. the voltage is being stepped up near the power plant, and

.................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [2] 2. a.c. voltage is required to transmit the electrical energy. .................................................................................................................................. ........................................................................................................................... [1] (iii) An electric kettle is connected to a power socket in the flat. In Fig. 4.4 below,

sketch the variation with time t of the thermal power P generated by a kettle in a time interval of one period.

Fig. 4.4 [2]

P / W

t / s

13


5 Some of the energy levels in atomic hydrogen are shown in Fig. 5.1.

Fig. 5.1 (a) A photon of wavelength 91.4 nm interacts with atomic hydrogen. (i) Calculate the energy of the photon in electron-volt. energy = ........................................ eV [2] (ii) Hence, state the energy transition that will result from this interaction.

........................................................................................................................... [1] (b) The visible line emission spectrum of hydrogen is formed when electrons fall to the

−3.40 eV level. (i) Show that the wavelength of red light is 658 nm. [2]

−13.6 eV

−3.40 eV

−1.51 eV

−0.850 eV

−0.544 eV

energy

−0.378 eV

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(ii) On Fig. 5.2, sketch the pattern of the visible line emission spectrum of hydrogen. Mark the red and violet ends of the spectrum.

Fig. 5.2 [1]

(c) The momentum of a photon of the red light is related to its wavelength through the

de Broglie relation.

(i) State the de Broglie relation.

.................................................................................................................................. ........................................................................................................................... [1]

(ii) Use the equation in (i) to calculate the momentum of a photon of the red light. momentum = ........................................ kgms−1 [1]

increasing wavelength

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6 A serious hazard for fire-fighters is the explosion of containers of 'liquefied gas' (butane) that have been heated in a fire. When the butane suddenly burns in an explosion, the fire spreads very rapidly in the form of a spherical fireball of increasing radius that is at very high temperature.

In order to study such fireballs, a series of experiments is carried out. Some butane of

volume 312.5 10 m3 is put in a sealed container and is then heated until it explodes.

The variation with time t of the radius R of the fireball is determined. The results are shown in Fig. 6.1.

Fig. 6.1

(a) Use Fig. 6.1 to

(i) describe, without any calculation, the variation with time of the rate at which the

radius of the fireball increases,

.................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [2]

R / m

t / ms

16


(ii) suggest why, in a room of length 12 m, width 5 m and height 3 m, such an explosion would be very hazardous.

.................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [3]

(b) It is thought that, for a fixed volume of butane, the radius R of the fireball varies with

time t according to the expression n mR kt

where n and m are integers and k is a constant. Some corresponding values of Ig t and Ig R for the data in Fig. 6.1 are plotted on the graph of Fig. 6.2.

Fig. 6.2

(i) On Fig. 6.2,

1. plot the point corresponding to time t = 40 ms,

2. draw the best-fit line for all the plotted points. [2]

lg (R / m)

lg (t / ms)

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(ii) Determine the gradient of the line drawn in (b)(i)2.

gradient = ........................................ [2]

(iii) Using the values from (b)(ii), suggest values for the integers n and m. Explain your working.

n = ........................................ m = ........................................ [3]

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(c) The experiment is repeated using similar containers but with different volumes of butane. The results are shown in Fig. 6.3.

Fig. 6.3

Without drawing a further graph, use Fig. 6.3 to show that, at time t = 40 ms, the radius R of the fireball is related to the volume V of butane by the expression

cVR 5

where c is a constant. [3]

(d) The equation in (c) may also be applied to other exploding gases. Suggest one physical quantity on which the constant c will depend.

....................................................................................................................................... ................................................................................................................................. [1]

R / m

volume of container / m3

t / ms

19


7 When sound of a certain frequency is passed into a pipe closed at both ends, standing waves can be set up in the pipe. The standing waves can be made visible by sprinkling light powder along the inside length of the pipe. A possible shape (mode of vibration) set up in the pipe is shown in Fig. 7.1.

Fig. 7.1

The speed of the sound wave in the pipe is thought to depend on the pressure of the gas in the pipe.

You are provided with a loudspeaker connected to a signal generator which can generate a large range of unknown frequencies. You may also use any of the other equipment usually found in a Physics laboratory.

Design an experiment to find how the speed of sound in an enclosed pipe depends on the pressure of the gas in the pipe.

You should draw diagrams to show the arrangement of your apparatus. In your account you should pay particular attention to (a) the equipment you would use,

(b) the procedure to be followed,

(c) the control of variables,

(d) how the velocity of the sound would be measured,

(e) any precautions that you would take to improve the accuracy of the experiment. [12]

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Diagram

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End of paper

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PJC H2 PHY 9646 Mid-Year Paper 2012