Download ph103 principles of physics iii spring 2009

PH103 PRINCIPLES OF PHYSICS III SPRING 2009
EXAM II – RELATIVITY AND QUANTUM – A
All work on this exam must be your own. You may use a calculator, and a 3"X5" card of
equations. Clearly indicate your final answer for each question.
Section 1: Multiple choice. No partial credit for this section. Circle one answer for each
question. (2 pts each)
1) What experiment could be done to distinguish whether you were in an accelerating reference
frame or an inertial frame?
a) See if the velocity of an object relative to you accelerates as if in a gravitational field.
b) Place an object at rest relative to you, and see if it begins to move relative to you.
c) Both of the above.
d) None of the above.
2) According to the photon theory, very little UV light is only given off by very hot objects
because
a) only very hot object have atoms that vibrate quickly enough to make high frequency
photons.
b) only very hot objects have enough energy to produce high energy photons.
c) only very hot objects can accelerate UV to the speed of light
d) only very hot objects have enough momentum to produce long wavelengths of light
3) A spaceship is traveling away from the Andromeda galaxy toward the Milky Way galaxy.
Relative to this ship, the light from the Andromeda galaxy travels _______ light from the
Milky Way galaxy.
a) faster than
b) slower than
c) the same speed as
d) The answer cannot be deduced without more information.
4) Two stars go supernova simultaneously in a frame at rest relative to the two stars, and at rest
relative to the earth. A spaceship is traveling at near-light speed relative to earth. Which of
the following must be true?
a) The light from the two supernovae reach earth at the same time.
b) The light from the two supernovae reach the spaceship at the same time.
c) The spaceship observers conclude that the supernovae were not simultaneous.
d) all of the above.
5) One star, whose surface is at temperature T (in Kelvin) emits light most strongly at a
wavelength . Another star emits light most strongly at a wavelength 2. The temperature
of the 2nd star is
a) 2T
b)
2T
c) T/2.
d) T/4.
6) Daria is travelling from Earth to planet Vulcan. As she travels, she observes two events to
happen at the same time, one on Earth, one on Vulcan. Which of the following must be
true?
a) Daria measures the proper time between the events.
b) Daria measures the proper length (distance) between the events.
c) All other observers will agree that the two events happen at the same time.
d) None of the above.
7) An electron at rest in a region of zero potential energy has
a) zero momentum and zero energy.
b) zero momentum and positive energy.
c) zero momentum and negative energy.
d) positive momentum and positive energy.
8) Which of the following is a consequence of the uncertainty principle?
a) An electron’s wavefunction exists at only one point in space.
b) The position of any particle cannot be measured more accurately than about h/2.
c) Conservation of energy can be violated as long as it occurs for a short enough period of
time.
d) All of the above.
9) A red light source and a green light source each emit 1.2 mW of light.
Which of the
following must be true?
a) The red light source gives off more-energetic photons, but fewer of them per second than
the green source.
b) The red light source gives off less-energetic photons, but the same number of them per
second as the green source.
c) The red light source gives off less-energetic photons, but more of them per second than
the green source.
d) The red light source gives off more-energetic photons, but the same number of them per
second as the green source.
10) Linda and Laura are in spaceships moving past each other at near-light-speed. Each has a
properly-working clock. Because of time dilation, Laura observes Linda's clock to run
slowly. When Linda observes Laura's clock, she will see
a) Laura's clock runs slowly.
b) Laura's clock runs fast.
c) Laura's clock runs at an appropriate rate -- neither fast nor slow.
d) The answer depends on the direction of relative motion of the ships.
11) A fast train is traveling north, which we will take as the positive direction. A bird in front of
the train is flying north, but not as fast as the train. A squirrel is scampering south along the
tracks, headed toward the train (Look out, little squirrel!) The velocity of the squirrel
relative to the train is __, the velocity of the train relative to the bird is __, and the velocity of
the train relative to the squirrel is __.
a) -, -, +
b) +, +, +
c) -, +, d) -, +, +
Section 2: Long-answer problems and questions. (20 pts each) Partial credit will be given for
this section. Show all work and justify all answers.
12) Darth Sidious heads toward the planet Naboo at 0.65c. Queen Amidala leaves Naboo
intending to intercept Darth Sidious before he reaches her planet.
a) How fast must she go relative to Naboo, so that her speed relative to Darth Sidious is
0.95 c
b) If Queen Amidala’s ship has a rest mass of 8.2X104 kg, what is its kinetic energy as
measured by Darth Sidious?
c) Does Queen Amidala measure the proper length for the distance between her and
Darth Sidius? Does Darth Sidius? Does an Earth or Naboo observer? As always,
justify.
13) Ten points for each part:
a) At one time, a beam of electrons is determined to have a speed of 1.2 ± 0.03 km/s.
Find the minimum uncertainty in the electrons' position at that time.
b) Suppose you have determined the interference pattern that occurs when a beam of
neutrons with wavelength  is sent through a double-slit. Describe clearly and
completely what you would expect to see if a single neutron with wavelength  were
sent through the same double-slit.
14) A Cthulu makes a trip from the planet Cthu to Earth. According to the travelling Cthulu,
the trip is 22 light-years long and takes 51 years.
a) How fast is the Cthulu traveling relative to Earth?
b) How long does the trip take according to observers on Earth?
15) 425-nm light falls on a metal, which has a work function of 1.07 eV.
a) Find the kinetic energy of the most energetic electrons.
b) Find the wavelength of the most energetic electrons.
1 yr = 3.16X107 s
electron mass = 0.511 MeV/c2
1 ly = 9.46X1015 m
proton mass = 938 MeV/c2
km = 103 m, nm = 10-9 m
h = 4.136X10-15 eVs
= 9.11 X10-31 kg
-19
1 eV = 1.602 X10
J
= 1.67 X10-27
kg
h = 6.626 X10-34 Js
hc = 1240 eVnm