Download Physics 110 Homework Set #9 (due Monday, April 10) 1) Two

Physics 110 Homework Set #9 (due Monday, April 10)
1) Two people are sitting 5 meters apart in the stands at the Yale Bowl, at points S and T as
shown below. On the opposite side of the Bowl, two entry tunnels are open to the street. The
distance across the stadium is 100 meters. A horn located at point X sounds a loud blare. The
person at T hears nothing. The principal wavelength of the sound waves from the horn is 1
meter. The person at T must be sitting at a minimum, perhaps the position of the first
interference minimum. If this is the case, calculate the distance between the tunnel openings at
the opposite side of the stadium. Note – the diagram below is not drawn to scale.
tunnel
T
5m
X
S
tunnel
100 m
2) The uncertainty in the position of a free electron is known to a precision of ∆x = 500 µm
(micro-meters). What is the uncertainty in its speed. The electron mass = 9.11 x 10-31 kg.
3-4) What is the de Broglie wavelength of
a) an electron in a TV tube with kinetic energy 104 electron volts?
b) a bacterium with a mass of 10-15 kg moving at a speed of 2 micro-meters per second?
c) an O2 air molecule (consisting of 2 atoms of oxygen with a total mass of 2 x 16atomic mass
units) moving at 100 m/s?
5-6) Two ferries depart from the same ferry port on the shore at the same time. One travels round
trip to a town located 20 miles due north of the ferry port, and the other travels round trip to a town
located 20 miles due west of the ferry port. There is a steady current from the east at a speed of 2
miles per hour over the water, and each ferry travels at a speed of 8 miles per hour across the
water.
a) How long does it take each ferry to make the round trip? What is the difference in time of
arrival of the ferries at the ferry port?
b) Draw an analogy between this problem and the Michelson-Morley experiment. What are the
primary differences?
7) Doesn’t Einstein’s theory of relativity state that the speed of light is constant? (If not, what does
it say about the speed of light?) How can you reconcile this with the fact that various materials
have indices of refraction which are greater than 1? (Please explain.)
8 - 9) Chapter 19, Challenge problem 3 - Suppose that an astronaut travels to a distant star and
returns to earth. Except for brief intervals of time when he is accelerating or decelerating, his
spaceship travels at the incredible speed of v = 0.995 c relative to the earth. The star is 30 lightyears away. (A light-year is the distance light travels in 1 year.)
a. Show that the factor γ for this velocity is approximately equal to 10.
b. How long does the trip to the star and back take as seen by an observer on the earth?
c. How long does the trip take as measured by the astronaut?
d. What is the distance traveled as measured by the astronaut?
e. If the astronaut left a twin brother at home on earth while he made this trip, how much younger is
the astronaut than his twin when he returns?
10) Cosmic rays bombard the earth from outer space at a very high rate (many per square meter
per second). A small particle called a muon is a product of cosmic ray interactions with molecules
in the upper atmosphere. The muon is best described as a heavy electron (with similar properties
as the electron, but 210 times the electron mass). Muons are unstable and decay to other particles
with a half-life of 2 microseconds. Classically, half-life is synonymous with lifetime. If the muon
is traveling near the speed of light, then classically it cannot travel more than c times its half-life
(or 300,000,000 m/s times 2 micro-seconds = 600 m) before decaying. However, cosmic ray
muons produced in the upper atmosphere reach the ground. How is this possible? How far can a
muon travel before decaying if it is traveling 99.9% of the speed of light? Hint – since the muon is
traveling near the speed of light include relativistic effects.