Download Spring Physics of Astronomy– Quiz on Ch

Physics of Astronomy – Spring midterm –.Thus.4.May.2006
This is a CLOSED-BOOK exam to be taken in class. You have TWO hours, so pace
yourself. SHOW YOUR WORK, to receive full credit, and include units.
Please circle or underline your answers, on problems with considerable calculation.
Keep answers in simplest exact form or make order-of-magnitude estimates.
(sign legibly)_______________________________________________________________
I affirm that I have worked this exam with WITHOUT using a calculator, text, HW,
quizzes, computer, classmates, or other resources.
Math-A students – do Parts I through III
Math-B students – do the whole exam
Possibly useless information (please ask if you need more info)
G = 6.67x10-11 N m2/kg2
0 = 8.85 x 10-12 C2/N.m2
g=9.8 m/s2
parsec~3 ly
-8
 = 5.67 x 10 W/m2.K4
c=3x108 m/s h = 6.63 x 10-34 J.s
k = 1.38 x10-23 J/K
F=mg
F=-GmM/r2 F = -qQ/(40r2)
F = -kx
F = -dU/dx
F = dp/dt = ma
p = mv
s=r v=r a=r
T = dL/dt = I
L = I = mvr
=d/dt
=d/dt
2
2
2
K= ½ I
K= ½ mv
I = miri
(m)T(K) ~ 3x10-3 F = T4 = L / area
I = dq/dt
V=IR
P=IV
W=qV
E=-dV/dx
F=qvxB=ILxB
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p=1/d
pc ~ 3 x 10 m
m-M = 5 log (d/10 pc)
M-Msun = 5/2 log(Lsun/L)
Msun = 4.76 Lsun = 3.826 x 1033 erg/s
Sun
Earth
Moon
5
3
Radius
7 x 10 km
6.4 x 10 km
1.74 x 103 km
30
24
Mass
2 x 10 kg
6 x 10 kg
7.35 x 1022 kg
Distance between them: 1.5 x 108 km
3.84 x 105 km
Charge
Mass
Electron
1.6 x 10-19 C
9.11 x 10-31 kg
proton
1.6 x 10-19 C
1.67 x 10-27 kg
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I. ASTRO-A – Everyone do this part of the exam. (10-15 minutes)
1. Describe the evolution of the Sun in time, in terms of its temperature, size, and color.
(a) What was it like 3 billion years ago?
(b) What will it be like 3 billion years from now?
(c) How will the Sun end its life?
2. The solar neutrino problem refers to
the difficulty of detecting any neutrinos at all from the Sun.
the observed underabundance of neutrinos from the Sun compared to the number
predicted theoretically.
the observed overabundance of neutrinos from the Sun compared to the number
predicted theoretically.
3. What are neutrino oscillations, and why are they important?
Neutrinos oscillate like photons, but much more rapidly. These oscillations allow
neutrinos to escape from the core of the Sun without being stopped.
Neutrinos passing through the convective outer layers of the Sun cause these layers
to oscillate with an approximate five-minute period. These oscillations allow us to probe
deep layers for which we would otherwise have no information.
Neutrinos change type enroute to Earth, because they have nonzero mass. This
oscillation solves the solar neutrino problem.
4. If a solar flare produces an X-ray outburst and also triggers a coronal mass
ejection (CME), what will be the arrival times of these components with reference to
the time of occurrence of the flare upon the Sun?
Disturbances upon the Earth from each of these components occur a few days after
the flare.
The X rays arrive after about 8 minutes, while the CME material arrives after a few
days.
The disturbances upon the Earth from these outbursts occur almost simultaneously,
about 8 minutes after the flare because the CME material travels almost at the speed of
light.
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5. Why are sunspots dark?
6. A star is observed to move back and forth with a period of exactly 1 year against
a background galaxy that appears close to it in our sky. What is the most likely cause of
this observed motion?
The star has an unseen companion star and the observed motion is due to the star's
orbital motion around its companion star with a period of exactly 1 year.
The observed motion is simply the motion of the star around the center of the
adjacent galaxy.
The star is relatively close to the solar system, and the Earth's orbital motion
produces an apparent change in the star's position against the background (i.e., the
galaxy) because of motion of the observer.
7. A particular star is found to have a stellar parallax of 1/6 arcsec. What is the
distance to this star?
1/6 pc
12 pc
6 pc
8. According to the inverse-square law, if two stars have the same luminosity and if
one star is 10 times farther away than the other, then
the more distant one would be 100 times fainter.
the more distant one would be 10 times fainter.
the more distant one would be 100 magnitudes fainter.
9. The color of a nearby but isolated star appears to be redder than that of the Sun.
Which of the following conclusions is the most likely?
The star is moving very rapidly away from the Sun.
The star's temperature is lower than that of the Sun.
Dust and gas between the star and Earth has absorbed or scattered much of the
blue light of the star.
10. A certain star is seen to have a relatively low surface temperature but a very
high luminosity. What can we conclude from these observations?
The star must be very large.
The star is a main sequence star, about the size of the Sun.
The star is a brown dwarf.
10.b Explain your reasoning.
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II. PHYS-A: Electrostatics and magnetism: Everyone do this part (20-25 minutes)
1. Conductors are conductors of electricity because they
(a) are metal
(b) have free protons
(c) are not insulators
(d) have free electrons
2. When the distance between two charges increases, the force between them
(a) increases directly with the distance
(b) increases inversely with the distance
(c) increases directly with the square of the distance
(d) increases inversely with the square of the distance
3. The direction of the electric field halfway between an electron and a proton is
(a) toward the electron
(b) toward the proton
(c) perpendicular to the line between the particles
(d) undefined since the field at this point is zero
4. Electric field lines can cross only if equal numbers of positive and negative charges are
involved.
True
False
5. Explain your reasoning:
6. If a particle with a charge of 2 coulombs moves through a potential difference of 12 volts, its
change in kinetic energy will be
(a) 12 J
(b) 24 J
(c) 6 J
(d) 1/6 J
7. Volts per meter are equivalent to Newtons per coulomb.
True
False
8. Electric field lines
(a) start on positive charges
(b) start on negative charges
(c) start on positive charges and end on negative charges
(d) are not vectors
9. Equipotential lines
(a) start on positive charges
(b) start on negative charges
(c) start on positive charges and end on negative charges
(d) are not vectors
10. Equipotential lines
(a) are always parallel to electric field lines
(b) are always perpendicular to electric field lines
(c) may curve at different angles to electric field lines
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11. Write the fundamental defining relationship between electric fields and potentials:
12. a) Draw some electric field lines for a positive charge.
+q
b) Then draw some equipotential lines with dotted lines.
13. If a 10 A current flows for two minutes, how much charge passes through the circuit?
(a) 10 C
(b) 12 C
(c) 20 C
(d) 1200 C
14. Current flows through a resistor
(a) from high potential to low potential
(b) from low potential to high potential
(c) can flow from any potential to a different potential, since V=0 is arbitrary
(d) with no fixed direction
15. Write the fundamental relationship between potential difference, current, and resistance:
16. If a 3 V potential difference causes a 0.6 A current to flow through a resistor, its resistance
is
(a) 0.20 
(b) 1.8 
(c) 5.0 
(d) 15 
17. Write the fundamental relationship between power, voltage, and current:
18. When a 60 W light bulb operates on a 120-V household line, what current does it draw?
(a) 0.5 A
(b) 1.4 A
(c) 2.0 A
(d) 120 J/C
19. What kind of units are kilowatt-hour (kwH)?
(a) energy
(b) power
(c) voltage
(d) luminosity
20. If a house uses 2400 kWh in a month, what will the electric bill be at a rate of 10 cents per
kWh?
21. Draw a series circuit with two resistors and a battery.
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22. In a series circuit, all elements have, in general, (choose all that apply)
(a) the same voltage
(b) the same current
(c) different voltage
(d) different current
23. Draw a parallel circuit with two resistors and a battery.
24. In a parallel circuit, all elements have, in general, (choose all that apply)
(a) the same voltage
(b) the same current
(c) different voltage
(d) different current
25. Christmas tree lights should be wired how?
(a) in parallel
(b) in series (c) doesn’t matter
26. Why?
27. Consider two light bulbs in a simple circuit with a battery. One has greater resistance than
the other (R1 > R2). The bulb with greater resistance (R1)
(a) burns brighter in a parallel circuit
(b) burns brighter in a series circuit
(c) burns just as bright as the other bulb in either circuit
28 Explain your reasoning.
MAGNETISM:
29. Draw the magnetic field of a bar magnet.
30. Cutting a bar magnet in two could yield two magnetic monopoles, one purely north and one
purely south.
True
False
31. Explain your reasoning:
32. The direction of the magnetic force on a current is (circle all that apply)
(a) parallel to the current
(b) perpendicular to the current
(c) parallel to the magnetic field
(d) perpendicular to the magnetic field
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III. Quantitative ELECTROSTATICS – Everyone do this part (10-15 minutes)
A water droplet of radius r remains stationary in the air. If the electric field E of
the Earth is known, you can find how many excess electron charges the water droplet
must have.
(a) Draw a diagram. Indicate the direction of the Earth’s electric field, and all the forces on the
floating water droplet.
(b) Use Newton’s second law to find an expression for the charge q on the droplet, in terms of
its mass and known quantities.
(c) How many (N) electrons would it take to make up this much charge? Get an expression in
terms of the fundamental unit of electron charge, e. (No numbers yet.)
(d) Find an expression for the mass m of the droplet, in terms of its density .
(e) Finally, put this all together to ESTIMATE the number of electrons in a droplet of radius
r = 0.020 mm with density  = 103 kg/m3 suspended in Earth’s field of E = 150 N/C.
Take care with units.
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IV. ASTROPHYSICS: Only Math-B students need do this part. (20-30 minutes)
1. Describe how you can find each of these things about a star from observations.
Use (i) words and (ii) a simple equation (or a diagram)
(a) Temperature
(b) Radiant Flux
(c) apparent magnitude (no equation)
(d) absolute magnitude
(e) distance
(f) luminosity
(g) radius
2. Consider a model of a star consisting of a spherical blackbody with a surface
temperature of 10,000 K and a radius of 3 Rsun. Let this model star be located at a distance
of 200 pc from Earth. Determine the following for this star.
(a)
(b)
(c)
(d)
(e)
Peak wavelength
Radiant flux at the star's surface
Luminosity
Radiant flux at Earth's surface (compare this with the solar constant)
What kind of star would this be?
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3
 m  2  mv2 2 kT 2
3. Maxwell-Boltzmann distribution function: f = nv dv  4 n 
v dv
 e
 2 kT 
a) What physical situation does the Maxwell-Boltzmann distribution describe?
b) Sketch the function f versus speed v, and label the axes.
c) Briefly explain the physical meaning of the beginning (v ~ 0), middle, and end (v  ) of your
plot.
d) How could you find the most probable speed in this distribution? Describe your strategy.
e) Carry out your strategy and find the most probable speed in the distribution. (Hint: group
constants.)
f) Which particles in the distribution contribute most to fusion in the Sun ? Explain briefly.
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