Download reg95 - School of Physics

THE UNIVERSITY OF SYDNEY
FACULTIES OF ARTS, EDUCATION, ENGINEERING,
MEDICINE AND SCIENCE
PHYSICS I - REGULAR
PAPER 1 : June 1995
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 ice
=
920 kg/m3
Density of water
=
1000 kg/m3
g
=
9.81 m/s2
0
=
8.85  10-12 F/m
1/(40)
=
8.99  109Nm2/C2
G
=
6.67  10-11 Nm2/kg2
e
=
1.60 10-19 C
SECTION A
(Please use a separate book for this section)
Question 1
The velocity-time graph shown represents a virtual reality "race" between two different
futuristic vehicles code-named XR-3000 and 450-BC.
50
45
40
ve locity [m/s]
35
30
XR-30 00
25
45 0-BC
20
15
10
5
0
0
50
10 0
tim e [s]
(a)
Describe the motion of the two vehicles, using the terminology of physics.
(b)
One car crosses the finish line 100 seconds after the start. Which car is it?
your answer.
(c)
Briefly discuss how realistic the performance of the XR-3000 vehicle is, considering
fundamental principles of physics.
Explain
[5 marks]
Question 2
A 5.0g bullet moving at a speed of 1000 ms-1 strikes a 0.80 kg block at rest on a frictional
surface. The bullet emerges from the block at a speed of 700 ms-1.
(a)
(b)
Find the resulting speed of the block.
Determine the change in the total kinetic energy.
[5 marks]
Question 3
Due to global warming all the ice in the arctic and the antarctic melts.
(a)
State what happens to the sea level when all the arctic ice which is floating melts.
(b)
By how much will the oceans rise when all the antarctic ice which rests on land melts?
The antarctic ice has an average thickness of 2 km and covers 2.8% of the earth’s
surface. (Assume that the oceans cover 70% of the surface and the density of ice is 920
kg·m-3.)
[5 marks]
Question 4
(a)
An aeroplane in flight has air flowing over the top of its wings with an effective speed
vµ, and over the bottom of its wings with speed vl . Describe how you would use these
speeds to calculate an estimate of the lift force F on the aeroplane.
(b)
The aeroplane climbs with constant velocity at an angle of 30 to the horizontal. Draw
a diagram giving the directions of the four forces acting on the aeroplane, labelling each
force.
[5 marks]
Question 5
Briefly explain, in terms of relevant physics principles, how a communications satellite can
stay apparently suspended in the same position high above the earth's surface, while other
objects simply fall straight down towards the earth.
[5 marks]
Question 6
A wave propagates through a piece of silicon. For this wave  = 1.5  1014s-1, while k =
1.25  1010m-1.
(a)
(b)
(c)
(d)
Calculate the wavelength of the wave.
How does the answer in (a) compare to the wavelength of visible light?
Calculate the wave speed of the wave.
How does the wave speed compare to the speed of light in vacuum?
[5 marks]
Question 7
A person jumps from a bridge with a long rubber cord attached to their ankles ("bungee
jumping"). After the initial fall, it is found that the person oscillates vertically suspended by
the cord and that the motion is approximately simple harmonic.
(a)
(b)
(c)
What two things does this tell you about the net force acting on the person during the
oscillatory motion?
When is the person's kinetic energy a maximum?
Why does the person eventually come to rest?
[5 marks]
Question 8
(i)
Explain what is meant by the term resonance, giving an example of its occurrence in a
real physical system.
(ii)
In your chosen system, describe the factors which control the resonant frequency.
[5 marks]
SECTION B
(Please use a separate book for this section)
Question 9
A uniform cylinder of mass m and radius b is released from rest at height h above the
ground, and it rolls without slipping along the track shown in the figure above.
(a)
If the velocity of the cylinder's centre of mass is v at a particular instant, show that the
corresponding total kinetic energy of the cylinder is
3
4
(b)
mv
2
Show, with the aid of a free-body diagram, that the cylinder will stay on the track, and
loop the loop, if it has a velocity vA at point A given by
 
A
gR ,
where R is the radius of the loop-the-loop track and b is assumed to be much less than
R.
(c)
Using an energy argument, determine the minimum height h for releasing the cylinder
so that it does not leave the track at the top of the loop (A).
[10 marks]
Question 10
A block of brightly painted, School of Physics wood is sliding down an inclined plane
at constant velocity. The plane makes an angle to the horizontal

(a) Draw a free-body diagram showing the forces acting on the block, and hence determine
k, the coefficient of kinetic friction.
(b)
Karl, who is waiting patiently for the block to reach him, then kicks the block straight
back up the slope. If this impulse gives the block an initial speed v0, how far up the
incline will it slide before coming to rest?
As before, you should draw a free-body diagram for the block.
(c)
Will the block slide down the incline again? Give an explanation in terms of the
forces acting on the block.
[10 marks]
Question 11
(a) Explain why all points in a conductor in electrostatic equilibrium have the same electric
potential and why the electric field inside the conductor is zero.
(b)
A point charge q = 1.0 10-7 C is at the centre of a spherical cavity of radius 30 mm in
a metal conductor. What is the magnitude of the electric field
(i)
(ii)
at a point 15mm from the centre of the cavity; and
at a point 40 mm from the centre of the cavity and inside the metal?
[10 marks]
Question 12
Suppose that a tunnel is drilled through the centre of the earth. Assuming that the density of
the earth is constant and independent of radius, derive (stating what assumptions you make):
(a)
the magnitude of the gravitational force acting on a mass m at a distance r from the
centre of the earth;
(b)
the potential energy of the mass at the same point.
[10 marks]
Question 13
A small body of mass 0.12 kg, hanging from the end of a vertical spring, is undergoing
simple harmonic motion of amplitude 85 mm and period 0.20 s.
(a)
Sketch graphs of:
displacement vs time,
velocity vs. time,
acceleration vs time
in a way that clearly shows the phase differences between the curves.
On the graphs, indicate amplitude and period.
(b)
Draw a picture of the small body and the spring at an instant when the force acting on
the small body is a maximum.
Indicate the equilibrium position of the body in your picture.
(c)
Calculate the maximum value of the force acting on the small body.
[10 marks]
Question 14
(a)
A point sound source produces sound energy at a rate of 1.0 kilowatt.
(i)
Describe (in words) how the intensity varies with distance from
the source.
(ii)
Calculate the intensity in W.m-2 at a distance of 50 m from the
source.
(iii)
(b)
Calculate the sound level in decibels at this position.
Two musical instruments are playing together. Source 1 has a fundamental
frequency of 555 Hz and source 2 has a fundamental frequency of 565 Hz.
(i)
Describe what you hear.
Now show this mathematically by answering the following questions.
(ii)
Write down expressions for the displacement at some position
due to source 1 alone and source 2 alone and add them. Assume
the displacement amplitudes are equal.
(iii)
Why can you simply add the displacements?
(iv)
Manipulate this result to explain what you hear.
[The following information may prove useful:
standard reference intensity is 1012 W.m2
that
( ) ( )
( ) ( )
sinA + sinB = 2 sin
cosA + cosB = 2 cos
A B
2
A B
2
cos
cos
AB
2
AB
2
]
[10 marks]