Homework Assignment 6
Physics 55
Made available:
Due in class:
Wednesday, October 19, 2005
Monday, October 24, 2005
Problem 1: Problems from the Text
1. Do problem 19 on page 127 of the text.
2. Do problem 11, parts a, b, c, e, and f on page 223.
3. In the “Surprising Discoveries” list of questions on page 250, answer questions 3, 4, 5, 7, and 8. Make
sure to briefly justify your answers.
Problem 2: Temperature of A Moving Star
A certain remote star has a surface temperature of T = 3000 K and is moving toward our Sun at the enormous
speed of 0.1c (one-tenth the speed of light). Use Wien’s law and the Doppler shift formula to calculate the
surface temperature of this star as deduced by an astronomer on Earth, and explain why your numerical
answer makes scientific sense.
Problem 3: Traffic Ticket or Speeding Ticket?
A police officer gives you a traffic ticket because you failed to stop at a red light. Thinking quickly and
using your Physics 55 knowledge, you tell the policeman that, because you were approaching the light in
your car, the Doppler effect caused the red light (with wavelength 700 nm) to blueshift to the color green
(with wavelength 500 nm) so you saw a green light and drove right on through.
1. In order for your statement to be true, about how fast must your car have been traveling?
2. Should you have received a speeding ticket instead?
Problem 4: Number of photons striking your hand
Assume that all of the light emitted from the Sun (surface temperature of about 6,000 K) consists of
monochromatic photons with wavelengths equal to the wavelength λmax given by Wien’s law.
1. Using the Stefan-Boltzmann equation, calculate the approximate number of solar photons that strike
your hand each second. Assume that your hand has a surface area of about 16 cm×8 cm ≈ 1.3×10 −2 m2 ,
that you hold your hand perpendicular to the sunlight, and that all sunlight striking the Earth makes
it to the ground.
2. Assuming that you are wearing a black glove so that your hand absorbs all the photons that strike it
(the reflectivity of your hand is zero), estimate how much solar energy (in joules) your hand absorbs
each second.
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3. If your hand were not connected to your body so that solar heat were not removed by the flow of blood,
about how long would it take for the temperature of your hand to increase by 5 ◦ C? Assume that your
hand is mainly water, with a volume of about 16 cm × 8 cm × 1.7 cm, and use the fact that water has
a density of 1, 000 kg/m3 and a specific heat of about 4 × 103 J/(kg ◦ C). (The specific heat of water
means that it takes about 4,000 joules of energy to increase the temperature of one kilogram of water
by one degree Celsius.)
Problem 5: Should black spacesuits be ruled out of fashion?
If an astronaut goes for a spacewalk outside the International Space Station in a black spacesuit (zero
reflectivity), what will be the steady-state temperature of the surface of the space suit? Could this be a
dangerous situation for the astronaut?
For this problem, you can make a “spherical chicken” approximation and assume that the spacesuit has the
shape of a sphere with radius .8 m.
Problem 6: Origin of An Unusual Spectrum
An astronomer observing a remote star sees an unusual spectrum containing many absorption lines corresponding to the element hydrogen. Upon comparing these lines carefully with a laboratory emission spectrum
of hydrogen, the astronomer makes the following discoveries:
1. None of the spectral lines change over time.
2. All the observed spectral lines are identical in width to those observed in the laboratory emission
spectrum.
3. Some of the spectral lines are blueshifted compared to the laboratory spectrum.
4. Some of the spectral lines are even more strongly blueshifted compared to the laboratory spectrum.
5. Some of the spectral lines are redshifted compared to the laboratory spectrum.
Describe a single astronomical scenario that explains all of these five properties observed in a single spectrum.
(The problem is not asking for five different scenarios that explain each property in turn.)
Problem 7: Optional Extra Credit Problems
1. You are given two spheres that are identical in size, weight, appearance, and touch but one sphere is
hollow while the other is solid. (As an example, the solid sphere could be made out of a light wood
and the hollow sphere made out of a denser wood, then both spheres carefully painted to look and
feel the same.) Using only simple items that you might find at home (no fancy equipment, no drills),
determine which sphere is hollow.
2. A laser that emits monochromatic light with a wavelength of λ = 600 nm is attached to the bottom
of a 3 m long vertical heavy rigid rod such that the laser emits its beam of light vertically upward. A
high-precision spectrometer (a device that can measure wavelengths of light to high accuracy) is then
attached to the top of the same rod in such a way that it continously records the wavelength of the
light beam. If this device (laser plus rod plus spectrometer) is then dropped from the top of a tall
building:
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(a) Discuss qualitatively and conceptually whether a Doppler shift will be detected by the spectrometer and, if so, whether the light will be red- or blue-shifted.
(b) Derive a quantitative formula for the wavelength of light λ(t) measured by the spectrometer as a
funtion of time.
Problem 8: Comments about the Homework and Course
• About how long did it take you to complete this assignment?
• Do you feel that you are understanding the course material? If not, please indicate what topics or
ideas you would like to understand better.
• Comments or suggestions about other parts of the course such as reading, homeworks, lectures, or
observation sessions?
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