Download ia 96 - The University of Sydney

93/02 (a)
Semester 1, 1996
Page 1 of 7 pages
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THE UNIVERSITY OF SYDNEY
FACULTIES OF ARTS, EDUCATION, ENGINEERING
AND SCIENCE
PHYSICS 1 - ADVANCED
PAPER 1: June 1996
Time allowed: THREE Hours
MARKS FOR QUESTIONS ARE AS INDICATED
TOTAL: 100.
INSTRUCTIONS
• All questions are to be answered.
• Use a separate answer book for each section.
• All answers should include explanations in terms of physical principles.
DATA
Density of water

=
1.00  103 kg m-3
Free fall acceleration at earth's surface
g
=
9.81 m s-
Permittivity constant
0
=
8.85  10-12 F m-1
1/(40)
=
8.99  109 N m2 C-2
Gravitational constant
G
=
6.67  10-11 N m2 kg-2
Elementary charge
e
=
1.60 10
Speed of light in a vacuum
c
=
3.00 108 m s-1
2
-19
C
93/02 (a)
Semester 1, 1996
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SECTION A
(Please use a separate book for this section)
Question 1
A horizontal disk rotates freely about its vertical axis with angular speed  . A
o
small lump of chewing gum, mass m , is dropped onto the disk, landing at a radial
distance r from the centre and sticking to the disk.
(a)
As a result of this collision, does the angular speed increase or decrease?
Explain the physical reasoning behind your answer.
(b)
Will the magnitude of the change in angular speed depend on r ? Explain.
(5 marks)
Question 2
Explain why the following reasoning is wrong.
"The Sun attracts all bodies on the Earth. At midnight, when the Sun is directly
below, it pulls on an object in the same direction as the pull of the Earth on that
object; at noon, when the Sun is directly above, it pulls on an object in the direction
opposite to the pull of the Earth. Hence all objects should be heavier when weighed
on a set of scales at midnight (or during the night) than at noon (or during the day)".
(5 marks)
Question 3
During the latest Easter holiday period many people were killed in cars involved in
traffic accidents. Many of those killed were not wearing seat belts. It is claimed that
seat belts save lives. Provide an explanation in terms of the concepts and principles
of physics which supports this claim.
(5 marks)
93/02 (a)
Semester 1, 1996
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Question 4
An armada of spaceships that is 1.0 light years long (in its rest system) moves with
speed 0.80 c relative to ground station S. A messenger travels from the rear of the
armada to the front with speed 0.95 c relative to S.
(a)
What is the speed of the messenger according to an observer at rest in the frame
of the armada?
(b)
Find the Lorentz factors
(i) for the armada according to an observer in S,
(ii) for the messenger according to an observer in S, and
(iii) for the messenger according to an observer in the rest frame of the armada.
(c)
What is the length of the armada according to an observer (i) in system S, (ii) in
the rest frame of the messenger.
(d)
Determine how long the trip takes as measured by an observer
(i) in the messenger's rest system,
(ii) in the armada's rest system, and
(iii) in system S.
(10 marks)
Question 5
Two identical blocks each of mass M , are connected by a massless string over a
pulley of radius R and rotational inertia I , as shown in the figure. The string does
not slip on the pulley. It is not known whether or not there is friction between the
table and the sliding block; the pulley's axis is frictionless.
When this system is
released it is found that the pulley turns through an angle  in time t and the
acceleration of the blocks is constant.
(a)
What is the angular acceleration of the pulley?
93/02 (a)
Semester 1, 1996
Page 4 of 7 pages
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(b)
What is the acceleration of the blocks?
(c)
What are the tensions in the upper and lower sections of the string? All
answers are to be expressed in terms of M, I ,R ,  , g and t .
(10 marks)
SECTION B
(Please use a separate book for this section)
Question 6
An airship filled with helium is able to hover above a fixed point on the ground, while
an aeroplane must keep moving. Explain why, including a brief explanation of how
each one stays aloft.
(5 marks)
Question 7
Briefly explain the difference between conductors and insulators. Give an argument
to show that, in electrostatic equilibrium, the electric field inside a conductor must
be zero.
(5 marks)
Question 8
Water is held in a sealed tank under 2.0 atm pressure. The tank is 5.0 m high and
the water reaches a level 50 cm from the top. The tank stands on legs 1.0 m high.
A plug (diameter 10 cm) is pulled from the bottom of the tank.
When the plug is first pulled out
(a)
What is the rate of flow of water out of the plug hole?
(b)
What is the speed of the water as it hits the ground?
(10 marks)
93/02 (a)
Semester 1, 1996
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Question 9
A metal spherical shell of outer radius 20 cm as shown in the diagram above carries
8
a net charge of 4  10 C .
(a)
If the reference potential is V  0 at infinity, what is the electric potential at the
centre of the sphere.
Now consider the situation where a charge of 3 10
charged shell.
8
C lies inside the above
(b)
What is the electric field at a distance of 60 cm from the centre of the sphere?
(c)
Does your answer depend on where the charge is placed inside the sphere?
Briefly explain your answer.
(d)
What is the total electric flux through a spherical gaussian surface centred at O,
and with radius a , as shown in the diagram. Give a brief reason for your
answer.
(10 marks)
93/02 (a)
Semester 1, 1996
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SECTION C
(Please use a separate book for this section.)
Question 10
Shown in the figure below is the relation between the angular frequency  and the
angular wave number k for a wave propagating through diamond.
14
1
(a)
Calculate the wave speed at   10
(b)
What can you conclude about the wave speed as a function of frequency from
the fact the relation between  and k is not a straight line?
(5 marks)
rad s
.
Question 11
(a)
Explain, using diagrams and examples as appropriate, what is meant by the
phase space of a dynamical system. (Write no more than about 10 lines of
text.)
(b)
Explain briefly why a deterministic system must have more than two
independent physical parameters if it is to exhibit chaotic behaviour.
(5 marks)
93/02 (a)
Semester 1, 1996
Page 7 of 7 pages
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Question 12
A cylindrical buoy, sitting in water, has a counterweight attached in order to keep it
vertical. The total mass of buoy plus counterweight is 50 kg. The mean density of
3
the buoy is 550 kg m , and its dimensions are: height = 0.8 m, cross-sectional
radius = 0.15 m.
(a)
If the buoy is displaced vertically, what forces act on it?
(b)
Write the total force acting on the buoy as a function of the displacement.
State any assumptions you make.
(c)
Ignoring damping, if the buoy is displaced vertically and released, does it
undergo simple harmonic motion? State any assumptions you make.
(10 marks)
Question 13
13
An optical pulse with a peak intensity of 2  10 W m
optical fibre.
2
propagates through an
(a)
Explain what is meant by a non linearity in the context of the propagation of
optical pulses.
(b)
What is the refractive change due to the non linearity at the peak of pulse.
(2)
20 2 1
 2. 310 m W .
Recall that for glass n
(c)
Over what distance approximately must the pulse propagate, in order for the non
linear contribution to the phase to amount to roughly 2  . Consider only the
peak of the pulse.
(15 marks)
93/02 (a)
Semester 1, 1996
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