Name : _______________________________
CT group: ________________
VICTORIA JUNIOR COLLEGE
2009 JC2 PRELIMINARY EXAMINATIONS
PHYSICS
Higher 2
9745/02
Paper 2
23 Sep 2009
WEDNESDAY
2 pm – 3.15 pm
(1 Hour 15 min)
This paper consists of 5 short structured questions
and 1 data analysis question. Attempt all
questions. Write your answers in the spaces
provided for each question.
For marker’s use
The intended marks for each question or part
question are given in brackets [ ].
3
N.B. You will hand in the whole question set issued
to you at the end of the examination. Do not
separate the question set into parts.
5
1
2
4
6 (data analysis)
Total (max. 60):
Percentage:
This question set consists of a total of 16 printed pages.
1
H2 Physics Papers, Notes at alevelphysics.co
Data
speed of light in free space,
c = 3.00 x 108 m s-1
permeability of free space,
µo = 4π x 10-7 H m-1
permittivity of free space,
εo = 8.85 x 10-12 F m-1
(1/(36π)) x 10-9 F m-1
elementary charge,
e = 1.60 x 10-19 C
the Planck constant,
h = 6.63 x 10-34 J s
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 J mol-1 K-1
the Avogadro constant,
NA = 6.02 x 1023 mol-1
the Boltzmann constant,
k = 1.38 x 10-23 J K-1
gravitational constant,
G = 6.67 x 10-11 N m2 kg-2
acceleration of free fall,
g = 9.81 m s-2
2
H2 Physics Papers, Notes at alevelphysics.co
Formulae
uniformly accelerated motion,
s = ut + (½) at2
v2 = u2 + 2as
work done on/by a gas,
W = p∆V
hydrostatic pressure,
p = hρg
gravitational potential,
φ =−
displacement of particle in s.h.m.,
x = xo sin ω t
velocity of particle in s.h.m.,
v = vo cos ωt
GM
r
= ±ω ( xo2 − x 2 )
resistors in series,
R = R1 + R2 + …
resistors in parallel,
1/R = 1/R1 + 1/R2+ …
electric potential,
V = Q/4πεor
alternating current/voltage,
x = xo sin ω t
transmission coefficient,
T = exp(-2kd)
where k =
8π 2 m(U − E )
h2
radioactive decay,
x = xoexp(-λt)
decay constant,
λ=
0.693
t1
2
3
H2 Physics Papers, Notes at alevelphysics.co
1. A ball is placed at the top of a slope as shown in Fig. 1.1. A block is fixed rigidly
to the lower end of the slope. The ball of mass 0.70 kg is released at time t = 0
from the top of the incline and v, the velocity of the ball down the slope, is found to
vary as shown in Fig. 1.2.
Fig. 1.1
v / m s-1
A
C
2.0
0
-2.0
2
t/s
1
3
4
Fig. 1.2
B
(a) Describe qualitatively the motion of the ball during the periods OA, AB and
BC.
[3]
OA: ___________________________________________________________
___________________________________________________________
AB: ___________________________________________________________
___________________________________________________________
BC: ___________________________________________________________
___________________________________________________________
___________________________________________________________
4
H2 Physics Papers, Notes at alevelphysics.co
(b) Calculate
(i) the acceleration of the ball down the inclined plane,
[2]
Acceleration = _____________ m s-2.
(ii) the length of the incline,
[2]
Length of incline = ____________ m
(iii) the average magnitude of the force experienced by the ball during its
impact with the block.
[3]
Mean force = ____________ N
5
H2 Physics Papers, Notes at alevelphysics.co
2. A particle of mass m is suspended from a point A by an inextensible string of
length L as shown in Fig. 2.1. It is projected from B with a velocity V,
perpendicular to AB, which is just sufficient for it to reach the point C.
C
v = (gL)1/2
Fig. 2.1
A
L
V
B
(a) Show that, if the string is to be just taut when the particle reaches C, its speed
there is (gL)1/2.
[2]
(b) Determine the speed V in terms of L with which the particle should be
projected from B.
[2]
(c) State and explain where the string is most likely to break when the particle
moves in a vertical circle.
[2]
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
6
H2 Physics Papers, Notes at alevelphysics.co
3. (a)
1.0 m s-2
Fig 3.1
A small sphere of mass 3.0 kg is attached to the ceiling of a lift via an
inextensible string as shown in Fig. 3.1. The length L of the string measured
from the point of suspension to the centre of the sphere is 1.0 m. The lift
accelerates upwards at 1.0 m s-2, and at the same time, the sphere is given a
slight displacement so that it performs small oscillations in a vertical plane.
L
Given that the period T of the pendulum is given by T = 2π
, where geff is
g eff
the effective acceleration of the sphere,
(i) explain why geff is not equal to 9.81 m s-2
[1]
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(ii) calculate the period of oscillations of the pendulum in the accelerating lift. [2]
Period = _____________ s
7
H2 Physics Papers, Notes at alevelphysics.co
(b) (i) A similar pendulum is attached to the ceiling of the cabin of a space-craft
orbiting the earth. Predict and explain what will happen to the subsequent
motion of the pendulum after the sphere is pulled aside and released. [3]
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(ii) The pendulum in the space-craft is now replaced by a spring-mass system
(a small object attached to a compressible spring). Predict and explain
what will happen to the subsequent motion of the spring-mass system after
the mass is pulled a short distance vertically downwards and released. [ the
m
period T of oscillation of a spring-mass system is given by T = 2π
k
where k is the restoring force constant.]
[2]
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
8
H2 Physics Papers, Notes at alevelphysics.co
4. The setup in Fig. 4.1 shows the top view of a 12 V DC supply connected in series
with a rod PQ of length 0.50 m. The rod has a resistance of 24 Ω. The frictionless
connecting rails are very long and have negligible electrical resistance. The rod lies
in a region of a uniform magnetic field. The magnetic field strength is 1.0 T and
the direction of the field is perpendicular to and acts into the plane of the page. The
two ends of the rod rest on the rails and are free to move in the plane of the rails.
The rod is initially at rest.
P
Z
Conducting rail
magnetic field
acts vertically
downwards
12 V
switch
rod
Fig. 4.1
Conducting rail
Y
Q
Fig. 4.2 shows the side view of the setup. The conducting rails are inclined at an
angle of 30o above the horizontal.
rod
I
Q
I
Conducting rail
Y
B = 1.0 T
30o
Fig. 4.2
The mass of the rod is 20 g.
(a) On Fig. 4.2, draw the forces acting on the rod.
[1]
(b) Calculate the initial acceleration of the rod when the switch is closed, and state
its direction.
[3]
Initial acceleration = ______________ m s-2 , (up / down) the slope
9
H2 Physics Papers, Notes at alevelphysics.co
(c) Calculate the circuit current when the rod reaches terminal velocity.
[2]
Current = ____________ A
(d) The moving rod PQ functions like a source of e.m.f. Identify the end of the rod
(P or Q) which is at the higher potential. Explain your answer.
[2]
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
10
H2 Physics Papers, Notes at alevelphysics.co
5. Two blocks of copper are maintained at the same positive electrical potential of
+4.00 V. If they are brought close together, until their separation is 5.00 × 10-10 m,
then there is a finite probability that an electron from either block will tunnel across
the gap between them and appear on the other side.
(a) Calculate the electrical potential energy of an electron in either of the two
blocks, expressing your answer in electron-volts. Take the potential energy of
the electron at an infinite distance away from the blocks to be zero.
[2]
Electric potential energy = _________ eV
(b) Draw a diagram to show how the electrical potential energy of an electron
varies as it moves from a point inside one block across the gap to a point
inside the other block. Take the potential energy of the electron in the gap to
be zero.
[1]
The transmission coefficient T for an electron to tunnel across a potential barrier
2m(V0 − E )
of width d is given by T ∝ exp(−2kd), where k =
, with m being

the mass of the electron, V0 being the height of the barrier and E being the total
energy of the electron.
(c) When electrons of energy 1.0 eV approach the gap from within the block, the
probability of successful tunnelling is T. If the width d of the gap is increased
by 10 %, determine the new value of the energy E of the electrons such that
the probability of successful tunnelling remains at the same value T.
[3]
E = ________ eV
11
H2 Physics Papers, Notes at alevelphysics.co
(d) A stream of electrons of the same energy hits the above barrier at a rate
equivalent to a current of 4.00 µA. If it is known that the probability of
successful tunnelling is 1.83 × 10-12, determine the rate of tunnelling of
electrons through the barrier.
[2]
Rate of tunnelling = _______________ s-1.
12
H2 Physics Papers, Notes at alevelphysics.co
6. A student investigated how the resistance R of a small semiconductor device X
varies with Celsius temperature θ. Fig. 6.1 shows the variation with temperature θ
of resistance R:
R/Ω
200
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30.0
Fig. 6.1
θ /0C
40.0
50.0
60.0
70.0
80.0
90.0
(a) (i) Assuming that the device X conforms to a relationship of the form
B
R = Ae T
where A and B are constants, calculate a value for A and for B , expressing
them with their units, by using values of R corresponding to temperatures
50.0 oC and 80.0 oC. Note that T represents the thermodynamic temperature.
[4]
A = __________
B = __________
(ii) Discuss whether there is a better method of determining the values of A and
B more reliably.
[1]
_______________________________________________________________
_______________________________________________________________
13
H2 Physics Papers, Notes at alevelphysics.co
(b) Determine a value for the resistance R at a temperature of 95.0 oC.
[1]
R = ___________ Ω
(c) Sketch a graph of the current I through device X against the potential
difference V across it.
[1]
I
V
(d) Device X is now connected to a fixed resistor of resistance 40.0 Ω as shown in
Fig. 6.2:
6.0 V
Fig. 6.2
40.0 Ω
X
Ideal voltmeter
V
(i) Calculate an estimated value for the voltmeter reading when device X is
immersed in water at temperature 30.0 oC.
[3]
V = __________ V
14
H2 Physics Papers, Notes at alevelphysics.co
(ii) The device X was then allowed to heat up. Explain whether the voltmeter
reading would increase or decrease.
[2]
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
(iii) Suggest how the circuit can be modified so that a buzzer will sound when
the temperature rises too high.
[2]
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
Energy band gap / eV
(e)
Fig. 6.3
Device
X
X
Temperature / K
Fig. 6.3 shows how the energy band gaps of some semi-conductors vary with
temperature. The energy band gap is thought to be a function of the
thermodynamic temperature T as given by the formula below:
αT 2
E g (T ) = E g (0) −
T +β
where Eg(0) is the energy band gap in electron-volts (eV) at 0 K and α and β
are positive constants for the semi-conductor concerned.
15
H2 Physics Papers, Notes at alevelphysics.co
It is known that Eg(0) is 0.744 eV for X. Calculate an estimated value for α
and for β for this semi-conductor, expressing them together with their units.
[4]
α = ______________
β = ______________
(f) Using the Band Theory and the graph in (e), suggest why the resistance of X
decreases with a rise in temperature.
[2]
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
End of Paper
16
H2 Physics Papers, Notes at alevelphysics.co