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THE UNIVERSITY OF SYDNEY
FACULTY OF SCIENCE
INTERMEDIATE PHYSICS
PHYS 2001 PHYSICS 2A
JUNE 2003 TIME ALLOWED: 3 HOURS
ALL QUESTIONS HAVE THE VALUE SHOWN
INSTRUCTIONS:
This paper consists of 4 sections.
Section A Special Relativity 25 marks Section B Optics 45 marks Section C Nuclear and Particle Physics 40 marks Section D Introduction to Stellar Astrophysics 40 marks
Candidates should attempt all questions.
USE A SEPARATE ANSWER BOOK FOR EACH SECTION.
In answering the questions in this paper, it is particularly important to give rea- sons for your answer. Only partial marks will be awarded for correct answers with inadequate reasons.
No written material of any kind may be taken into the examination room. Calcu- lators are permitted.
Table of constants
Avogadro’s number =
speed of light =
electronic charge = C
electron rest mass = kg
electron rest energy energy = 511 keV
electron volt 1 eV = J
protron rest mass = kg
neutron rest mass = kg
Planck’s constant = J.s
Planck’s constant (reduced) = J.s
Boltzmann’s constant =
Stefan’s constant =
gravitational constant =
atomic mass constant =
astronomical unit AU =
parsec pc =
light year ly =
Please use a separate book for this section.
Answer ALL QUESTIONS in this section.
- (a) Two events occur at the same position in inertial frame , separated by a time interval. Inertial frame is moving at constant speed relative to , in a direction along the axis of. The origins of the two frames coincided at.
(i) Draw a spacetime (Minkowski) diagram to show that these events do not occur at the same position in. Label your axes clearly.
(ii) If the two events had occurred simultaneously and at the same position in frame , is it possible they may not be simultaneous in another inertial frame , moving relative to? Briefly explain your answer.
(iii) Frame has a speed of relative to , along the axis of. An event occurs at sec and m in. Where and when does it occur in?
(iv) If another event occurs in frame at sec and m, what is the time interval between the events in frame (moving as in part (iii) above)?
(b) A car has an ellipse painted on its side such that the longer axis of the ellipse is along the direction of motion. The longer axis is 1.6 times the length of the shorter axis. How fast does the car have to travel, relative to observers on the ground, for the ellipse to appear circular to the observers? (15 marks)
- A particle whose kinetic energy is 3 times its rest energy decays into two photons, which are emitted in opposite directions.
(a) What are the energies of the two photons, in terms of the rest mass of the particle?
(b) Can both photons be emitted in the same direction? Briefly justify your answer. (10 marks)
SECTION B
OPTICS
FORMULAS
where
(b) A HeNe laser with a wavelength of 633 nm is used to illuminate two narrow slits in an opaque screen. The slits are 1.0 mm apart, and the light from them falls on a screen placed 2.0 m from them. Draw a dia- gram showing the distribution of intensity you would expect to see on the screen and give a numerical value for the distance between minima in intensity. (10 marks)
- (a) Briefly describe a simple experimental result which supports the propo- sition that light is a transverse wave. Explain why the experimental observation supports the proposition.
(b) Four sheets of polaroid are arranged one behind the other. Unpolarised light is incident on the first sheet, which has its transmission axis ver- tical. The transmission axis of each subsequent sheet is rotated in the same sense with respect to the transmission axis of the preceding sheet.
(i) What fraction of the incident intensity is transmitted by this com- bination?
(ii) What is the direction of polarisation of the light leaving the last sheet?
(c) Polaroid sunglasses are effective at removing glare when the sun is reflected from a wet road.
(i) Explain briefly why this is so.
(ii) Would the glare reduction still be effective if you viewed the wet road with your head on its side (so the glasses are rotated by about )? (10 marks)
- (a) Oil ( ) leaking from a damaged tanker creates a large oil slick on the harbour ( ). In order to determine the thickness of the slick, an aircraft is flown when the sun is overhead. The sunlight re- flected from directly below the aircraft is found to have intensity max- ima at 450 nm and 600 nm, and at no wavelengths in between. What is the thickness of the oil slick? Explain your reasoning.
(b) The diagram shows an insulating window made from two identical sheets of 3 mm glass separated by a 12 mm air gap. Coloured fringes are seen when viewing a white-light source through the window. The fringes are created by interference between the pair of ray paths marked A.
glass
glass
air
A B Briefly explain why pair A can account for the observed fringes, but pair B cannot. (10 marks)
- The most common isotope of copper is Cu. The measured mass of the neutral atom is 62.929601 u.
(a) From the measured mass determine the mass defect, and use it to find the total binding energy and binding energy per nucleon.
(b) The total binding energy is also given by the equation
where MeV MeV MeV MeV MeV Explain why the fifth term in this equation must be zero for Cu.
(c) Calculate the binding energy from this equation, and compare with the result you obtained in part (a). What is the percentage difference? What do you conclude about the accuracy of the formula given in part (b) above? (10 marks)
SECTION D
INTRODUCTION TO STELLAR ASTROPHYSICS
FORMULAS
- (a) Draw a Herzsprung-Russell (HR) diagram, clearly labelling the axes appropriately. On your diagram sketch the position of the Main Se- quence (MS) and the Zero Age Main Sequence (ZAMS). In no more than two or three lines, explain the relationship between the MS and ZAMS.
(b) Where on the main sequence would you expect to find a 10 solar mass star? Indicate this point on your diagram and sketch the post-main se- quence evolutionary track for this star, clearly indicating the important phases in the star’s evolution. (10 marks)
0
50
100
150
200
250
350 450 550 650 750 850 Wavelength (nm)
- The plot of intensity versus wavelength shown above represents the visible spectrum of a star.
(a) Describe the most important features of this low resolution spectrum. What physical properties of the star can you deduce from these fea- tures?
(b) Estimate the spectral class of this star (in the form such as M7). What
spectral features lead to this conclusion?
(c) Name three further properties of this star that you could deduce from a much higher resolution spectrum. For each of these properties, use one sentence to explain how you would deduce the property from the spectrum.
(d) If this is a young star, just recently arrived on the Main Sequence, briefly describe how you would expect its spectrum to change
(i) in 5 million years from now
(ii) in 5 billion years from now (10 marks)
THERE ARE NO MORE QUESTIONS.
