Name : ________________________________
CT group : ______________
VICTORIA JUNIOR COLLEGE
2013 JC2 PRELIMINARY EXAMINATIONS
9646/03
PHYSICS
20 Sep 2013
Higher 2
FRIDAY
Paper 3 Longer Structured Questions
2.30 pm – 4.30 pm
2 Hours
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your name and CT group at the top of this page.
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 staples, paper clips, highlighters, glue or correction
fluid.
Section A
Answer all questions.
Section B
Answer any two questions.
For Examiner’s Use
You are advised to spend about one hour on each section.
1
At the end of the examination, fasten all your work securely
together.
2
The number of marks is given in brackets [ ] at the end of each
question or part question.
4
3
5
6
7
8
9
10
This question set consists of a total of 20 printed pages.
1
Total
Data
speed of light in free space,
c = 3.00  108 m s-1
permeability of free space,
µo = 4  10-7 H m-1
permittivity of free space,
o = 8.85  10-12 F m-1
(1/(36))  10-9 F m-1
elementary charge,
e = 1.60  10-19 C
the Planck constant,
h = 6.63  10-34 J s
unified atomic mass constant,
u = 1.66  10-27 kg
rest mass of electron,
me = 9.11  10-31 kg
rest mass of proton,
mp = 1.67  10-27 kg
molar gas constant,
R = 8.31 J mol-1 K-1
the Avogadro constant,
NA = 6.02  1023 mol-1
the Boltzmann constant,
k = 1.38  10-23 J K-1
gravitational constant,
G = 6.67  10-11 N m2 kg-2
acceleration of free fall,
g = 9.81 m s-2
2
Formulae
uniformly accelerated motion,
s = ut + (½) at2
v2 = u2 + 2as
work done on/by a gas,
W = p V
hydrostatic pressure,
p = hg
gravitational potential,
 
displacement of particle in s.h.m.,
x = xo sin  t
velocity of particle in s.h.m.,
v  vo cos t
GM
r
v   ( xo2  x 2 )
resistors in series,
R = R1 + R2 + …
resistors in parallel,
1/R = 1/R1 + 1/R2+ …
electric potential,
V = Q/4or
alternating current/voltage,
x = xo sin  t
transmission coefficient,
T  exp(-2kd)
where k 
8 2 m(U  E )
h2
radioactive decay,
x = xo exp(-t)
decay constant,

0.693
t1
2
3
Section A
Answer all the questions in this section.
1. A student was tasked to determine the thickness of a cylindrical glass tube shown in Fig. 1.
He measured the internal and external diameters of the glass tube with a travelling
microscope and recorded his readings as follows:
Internal diameter of glass tube, d = 0.240 mm
External diameter of glass tube, D = 0.365 mm,
d
D
Fig. 1
(a) Assuming that his reading of the diameter was subject to an estimated uncertainty of
 0.001 mm, calculate the maximum percentage uncertainty in the thickness of the
glass tube.
[3]
Maximum percentage uncertainty = ……………… %
(b) Express the thickness of the glass together with its associated uncertainty.
[2]
Thickness = _________  ___________ m
4
2. A bullet of mass 10 g strikes a stationary block horizontally with a speed of 100 m s-1. The
block rests on a frictionless surface. The time that elapses from the instant the bullet
strikes the block to the instant it just emerges from the other side of the block is 0.030 s.
During this time, the bullet’s deceleration is 900 m s-2 and the block’s acceleration is
300 m s-2, both with respect to ground.
(a) Calculate the final speed of (i) the bullet and (ii) the block.
[2]
Final speed of bullet = …………….. m s -1
Final speed of block = …………….. m s-1
(b) Calculate the mass of the block.
[2]
Mass = ……………… kg
(c) Calculate the loss in kinetic energy of the system consisting of the bullet and block.
[1]
Loss in kinetic energy = ………………. J
5
3. A ball bearing of mass 5.00 g rests on a Hooke’s spring of elastic constant k = 500 N m-1.
The ball is pushed down 2.0 cm from its equilibrium position and then released as shown
in Fig. 3.1 and Fig. 3.2.
2.0 cm
Fig. 3.1
Fig. 3.2
(a) Calculate the maximum height H to which the ball bearing will rise from its lowest
position .
[2]
H = …………….. cm
(b)
(i) Explain clearly the transformation of energy of the ball bearing when it is
released from the depressed position of the spring until it reaches the
maximum height H. Include discussion of the energy transformation during the
time interval when the ball is rising.
[2]
…………………………………………………………………………………….
…………………………………………………………………………………….
(ii) Sketch the variations of the different energies in (b)(i) as a function of height
starting from the ball bearing’s lowest depressed position to its highest point.
Label the sketch appropriately.
[3]
Energy / J
height risen / m
6
4. A circus performer is riding his motorcycle with uniform speed such that its period is
20.0 s in a horizontal circle of radius 83 m on the inner surface of a cylindrical wall, as
shown in Fig. 4.1.
R
wall

wall
W
Fig. 4.1
Fig. 4.2
The orientation of his motorcycle is shown in Fig. 4.2. Two forces acting on the
motorcycle-man system are the reaction force R acting at an angle  with the vertical
and the weight W.
(a) Calculate the angle  with the vertical.
[3]
 = ………….. o
(b) Sketch a labelled free body diagram of the motorcycle-man system when  = 90o.
Hence explain why it is impossible for the system to achieve rotational equilibrium in
this position.
[3]
7
5. The p-V diagram in Fig. 5 shows a fixed mass of an ideal gas expanding isothermally
from state A to B.
p / Pa
p1
A
p2
B
V1
V2
3
V / cm
Fig. 5
(a) On Fig. 5, sketch a graph for an adiabatic expansion of the same gas from V1 to V2
from state A. Label the final state as C.
[1]
(b) State the First Law of Thermodynamics, and use it to explain why the final pressure at
state C is different from the pressure at state B.
[4]
…………………………………………………………………………………………..
…………………………………………………………………………………….…….
…………………………………………………………………………………….…….
…………………………………………………………………………………….…….
…………………………………………………………………………………….…….
…………………………………………………………………………………….…….
…………………………………………………………………………………….…….
…………………………………………………………………………………….…….
…………………………………………………………………………………….…….
…………………………………………………………………………………….…….
…………………………………………………………………………………….…….
8
6.
(a) A resistance wire 80.0 cm long has a uniform cross sectional area of 2.5 ×
10-8 m2. Given that its resistivity is 1.25 × 10-7 Ω m, calculate the resistance
across its ends.
[2]
Resistance = …………… 
(b)
(i)
5.0 V
2.0 Ω
P
X
jockey
3.0 V
1.0 Ω
Y
1.0 Ω
S
A
Fig. 6
The resistance wire XY in (a) is used to set up the circuit as shown in
Fig. 6. With the switch S open, the jockey is moved along the resistance
wire until the galvanometer indicates a null reading. Calculate the balance
length XP.
[2]
9
Balance length = …………………….. m
(ii) Switch S is now closed and the jockey is disconnected from the wire
XY. Calculate the current in the ammeter.
[1]
Current = ………………… A
(iii) Hence, or otherwise, calculate the new balance length when the jockey
is connected back to wire XY.
[1]
10
New balance length = ……………………. m
11
7. The radioactive nuclide
is used in radiotherapy. It has a half-life of 5.27 years
and, at each disintegration, two -rays are emitted, one of energy 1.17 MeV and the other
of energy 1.33 MeV.
(a) This nuclide is prepared by bombarding a suitable target (a stable nuclide) with an
appropriate particle. Possible projectiles are neutrons ( ) and deuterons ( ).
Write down the equations for three separate reactions, involving the target nuclei
,
and
respectively, and one or the other of the projectiles
and ,
by which
might be produced.
[3]
…………………………………………………………………………………….
…………………………………………………………………………………….
…………………………………………………………………………………….
(b) In a radiotherapy treatment, it is necessary to determine the amount of energy
absorbed from the radiation. A fresh 1.0 g sample of
, which may be treated as
a point source, is placed at a position 1.50 m from a patient. Calculate the intensity
of the radiation received by the patient.
[3]
Intensity = ………………. W m-2
12
Section B
Answer two questions from this section.
8. A small stone is dropped into a pool of calm water and this sets up ripples as shown in
Fig. 8.1.
B
A
Fig. 8.1
A progressive wave is set up from the centre A and it moves outwards passing point B,
which is at 0.90 m from A. A graph showing how the displacement y at A varies with
time t is shown in Fig. 8.2. Another graph, Fig. 8.3, shows how the displacement of the
wave at time t = 0 varies with distance x from point A.
y / cm
t/s
Fig. 8.2
y / cm
A
B
x/m
Fig. 8.3
(a) Calculate the speed of the ripple wave.
[2]
Speed = ……………… m s-1
13
(b) Write down the equation representing the oscillatory motion of point A.
[2]
…………………………………………………………………………………………
…………………………………………………………………………………………
(c) Calculate the phase difference between points A and B.
[2]
Phase difference = ………………….. rad
(d) Given that there is no energy loss from the wave travelling from A to B, explain the
wave profile shown in Fig. 8.3.
[2]
………………………………………………………………………………………….
………………………………………………………………………………………….
………………………………………………………………………………………….
(e) After an initial vertical displacement, an object floating on the water will bob up and
1 0.10
, where m is its
2
m
mass in kg. A small seed of mass 2.5 g and capable of floating drops into a pool of
calm water.
(i) Calculate the frequency of the seed’s oscillation if it is dropped into the pool of
calm water.
[2]
down with a frequency f given by the expression f 
Frequency = ………………… Hz
14
(ii) The waves due to the stone in (a) now pass through the region of water where the
seed is floating. Describe and explain how the seed would oscillate, paying
attention to its frequency response.
[3]
………………………………………………………………………………….…
……………………………………………………………………………….……
…………………………………………………………………………………….
……………………………………………………………………………….……
…………………………………………………………………………………….
(iii)
1. Describe and explain how the oscillation of the seed will change with time, if
it is taking in water.
[3]
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
2. Calculate the energy of the seed at the time when it is oscillating with a
maximum amplitude of 1.8 cm.
[4]
Energy = …………………… J
15
9.
v
A
Bo
A
Bo
P

𝑙
2
𝑙
2
Q
D
l
D
B
v
l
C
Isometric view
Plan view
Fig. 9.1
In the “zero-gravity” environment in a space station orbiting the Earth, a square
aluminium structure ABCD of side length l is given an initial torque that causes it to
undergo rotational motion about its vertical axis, as shown in Fig. 9.1. The structure has
a break PQ on its top side AD. A horizontal uniform magnetic field of uniform flux
density Bo is then directed across the structure.
(a) Given that the structure’s angular velocity is  , write down an expression for the
linear velocity v of each of its vertical sides.
[2]
………………………………………………………………………………………..
(b) Derive an expression for the e.m.f. induced along each of its vertical sides in terms
of l, , Bo and , where  is the angle between the structure’s normal and the
magnetic field at the instant shown in Fig. 9.1.
[2]
(c) State the direction of the e.m.f. induced in side AB at the instant shown in Fig. 9.1.
[1]
………………………………………………………………………………………..
(d) State which end, P or Q, of the structure across the break, would be at the higher
potential at the instant shown in Fig. 9.1.
[1]
………………………………………………………………………………………..
16
(e) If the angle  = 0o at time t = 0, derive an expression for the maximum e.m.f.
induced in the structure. Sketch a labelled graph to show the variation of the induced
e.m.f. in the structure with time.
[3]
The break in side AD is now mended such that the structure forms a complete circuit.
(f) Derive an expression for the current I in the structure at the instant shown in
Fig. 9.1, given that the electrical resistance of the structure is R. Give your answer in
terms of Bo, l,  and R.
[1]
(g) Draw a copy of the plan view of Fig. 9.1 in the space below. On your copy, draw
arrows to show the directions of the forces F acting on sides AB and CD as a result
of the induced current in them.
[1]
(h) Derive an expression for the torque  on the structure as a result of the forces on its
vertical sides, in terms of Bo, l, , R and .
[3]
(i) State the effect of the torque on the motion of the structure.
[1]
………………………………………………………………………………………..
17
(j) On the axes below, sketch a new graph to show the variation of the induced e.m.f. in
the mended structure with time, assuming that angle  = 0o at time t = 0. Explain the
shape of your graph.
[3]
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
(k) State the energy transformations in the structure over the entire course of its motion.
[2]
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
18
10.
𝜓4
𝜓
Fig. 10.1
𝜓
𝜓
L
Consider an electron in a one-dimensional box with infinitely high walls. Treat the
electron as a sinusoidal wave. Fig. 10.1 shows possible ways of fitting the wave into
the box of width L.
(a)
(i) Explain why the amplitude of the wave motion must vanish at the walls of the
box.
[1]
………………………………………………………………………………………
………………………………………………………………………………………
(ii)
Let there be n half-wavelengths in the box, where n = 1, 2, 3, 4… Write
down an expression relating n,  and L, where  is the wavelength.
[1]
19
(iii) Assuming that there is no potential energy, show that the energy of the electron
n2h2
is given by E n 
where h and m are the Planck constant and mass of the
8mL2
electron respectively.
[3]
(iv) The longest-wavelength photon that the electron in the ground state in the box
can absorb is of wavelength 1.0 × 10-7 m. Calculate a value for the width L of
the box.
[4]
L = ………………. m
(b) Electrons of de Broglie wavelength λ = 8.0 × 10-12 m hit a gold foil and cause X-rays
to be emitted. A plot of the intensity of emitted X-rays versus their wavelength yields
a smooth curve starting at a minimum wavelength and exhibiting some sharp peaks.
(i) Explain the origin of the smooth curve.
………………………………………………………………………………
………………………………………………………………………………
………………………………………………………………………………
………………………………………………………………………………
………………………………………………………………………………
………………………………………………………………………………
………………………………………………………………………………
20
[3]
(ii) Calculate the minimum wavelength of emitted X-rays.
[2]
Minimum wavelength = ……………………… m
(iii) With increasing wavelengths above this minimum wavelength, a first group of
sharp peaks is seen in the plot of X-ray intensity versus wavelength. State and
explain whether it corresponds to the K series or the L series.
[2]
…..……………………………………………………………………………….
…………………………………………………………………………………..
…………………………………………………………………………………..
…………………………………………………………………………………..
(iv) The characteristic X-rays in (iii) are due to incoming electrons kicking out
originally bound electrons from one of the innermost orbits of the gold atom.
Suggest what might be the effect/s of incoming electrons striking the electrons
from one of the outermost orbits of the atom.
[2]
…………………………………………………………………………………..
…………………………………………………………………………………..
…………………………………………………………………………………..
…………………………………………………………………………………..
(v) Explain why the minimum wavelength in (ii) is independent of the nature of the
target material while characteristic wavelengths are dependent on it.
[2]
…………………………………………………………………………………..
…………………………………………………………………………………..
…………………………………………………………………………………..
…………………………………………………………………………………..
…………………………………………………………………………………..
…………………………………………………………………………………..
21