EXAM III, PHYSICS 1408-001, November 28, 2007
Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
1. PLEASE put your name on every sheet of paper you use and write on one side of the paper
only!! PLEASE DO NOT write on the exam sheets, there will not be room!
2. PLEASE show all work, writing the essential steps in the problem solution. Write
appropriate formulas first, then put in numbers. Partial credit will be LIBERAL, provided
that essential work is shown. Organized, logical, easy to follow work will receive more credit
than disorganized work.
3. The setup (PHYSICS) of a problem will count more heavily than the math of working it out.
4. PLEASE write neatly. Before handing in your solutions, PLEASE: a) number the pages and
put the pages in numerical order, b) put the problem solutions in numerical order, and c)
clearly mark your final answers. If I can’t read or find your answer, you can't expect me to
give it the credit it deserves.
NOTE!!! I HAVE 51 EXAMS TO GRADE!!! PLEASE
HELP ME GRADE THEM EFFICIENTLY BY
FOLLOWING THE ABOVE SIMPLE INSTRUCTIONS!!!
FAILURE TO FOLLOW THEM MAY RESULT IN A
LOWER GRADE!! THANKS!!
A 3’’ x 5’’ card with anything on it & a calculator are allowed. Problem 1 (Conceptual
Questions) IS REQUIRED! Answer any two (2) of the remaining problems for a total of three
(3) problems required. Problem 1 is worth 34 points. Problems 2, 3, 4 & 5 are equally weighted &
worth 33 points each.
1. REQUIRED CONCEPTUAL QUESTIONS!!! Answer these briefly. Most answers should
be a few complete, grammatically correct English sentences. Keep formulas to a minimum.
Use WORDS instead! If you use a formula, DEFINE EVERY SYMBOL you use. (Note:
Answers using ONLY symbols, with no explanation about what they mean, will receive NO credit!)
a.
b.
c.
d.
State Newton’s Universal Law of Gravitation.
State ANY ONE of Kepler’s 3 Laws (for planetary orbits).
State Pascal’s Law (for confined fluids).
State Archimedes’ Principle (for the buoyant force on an object partially or completely
submerged in a fluid).
e. In Ch. 13, I emphasized that Newton was first to do Gravitation theory. I said many times that
this led to his “Greatest Triumph” (or “Greatest Achievement”). Tell me, as briefly as
possible, exactly what his “Greatest Triumph” was. [Note: Answers which ONLY state that he
developed the Universal Gravitation Law (which is obvious from Ch. 13!) are NOT sufficient & will get
ZERO credit. Correct answers should give some details of the problem he successfully applied this to.]
f. 5 Point Bonus! Mon., Nov. 26, when discussing Archimedes’ Principle, I briefly told the story
of the “Archimedes’ Bath Legend”, which is supposedly the story of how & when Archimedes
found the answer to a problem his king asked him to solve. Tell me, as briefly as possible, the
main ideas about the “Archimedes’ Bath Legend”. [Note: Answers which ONLY state that he took a
bath & found the answer (which is in Ch. 14!) are NOT sufficient & will get ZERO credit. Correct answers
should give a few details of the problem the king gave him and how & when he found the answer. If you
were in class when I talked about this, you likely will be able to answer this. If you “cut” class that day, as
many of you often do, you probably won’t be able to!]
NOTE: Answer any two (2) of problems 2, 3, 4, & 5!!!
circular orbit!
2. See figure. Note: YOU MUST use scientific (power of 10) notation to solve
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this. PLEASE be careful of large & small numbers! A satellite of mass
m = 3,725 kg, is in a circular orbit at constant speed v around planet X,
which is assumed to be a sphere of constant density. (The resemblance to Earth
is coincidental!) The orbit radius (measured from the planet’s center) is
r = 7.3  107 m. Planet mass M = 7.8  1024 kg. G = 6.67  10-11 N m2/kg2.
a. The satellite’s orbit is circular, so it experiences centripetal acceleration.
Using words (not equations, which will get ZERO credit!) tell me the cause of this acceleration.
(Hint: See part b!)
b. Calculate the gravitational force between the satellite & the planet. (Hint: This should be a
few hundred Newtons in size. If your result is much smaller or much larger than this, you’ve done
something wrong!) What is the “centripetal force” on the satellite? (Hint: This should be
consistent with the answer to part a! You don’t need the satellite’s speed to answer this!).
c. Calculate the centripetal acceleration experienced by the satellite. What is the direction of
this acceleration? (Hint: This will be very much smaller than the gravitational acceleration g =
d.
9.8 m/s2 on the Earth’s surface! If your result is much larger than this or if it is similar in size to g,
you’ve done something wrong! You don’t the satellite’s speed to answer this!).
Calculate the speed of the satellite in orbit. (Hints: Einstein taught us that the largest speed
possible for anything is the speed of light c = 3 × 108 m/s! If your v is larger than c, or even a
significant fraction of it, you’ve done something wrong! v should be large enough for the satellite
to go the HUGE distance around the orbit in a reasonable time. Depending on the orbit radius,
Earth satellites make 2 or more orbits per day. If your v is as slow as that of ordinary objects moving
on Earth’s surface, such as, for example, 100 m/s, that’s much too slow & you’ve done something wrong!).
e. Calculate the period T of the satellite’s orbit. (Hint: This should be a reasonable period for a
satellite around a planet similar in size to Earth. If your T is either very much larger or very much
smaller than this, you’ve done something wrong! For a typical period, see the hint for part d.)
3. See figure. Note: YOU MUST use scientific (power of 10) notation to solve this!
PLEASE be careful of large & small numbers ! A mass m = 3,725 kg, is initially
sitting on the surface of planet X, which is assumed to be a sphere of constant
density. (The resemblance to Earth is coincidental!) Planet radius R = 8.5  106 m.
Planet mass M = 7.8  1024 kg. Gravitational constant G = 6.67  10-11 N m2/kg2.
a. Calculate gravitational acceleration g on the planet surface. (Hint:
Answering g = 9.8 m/s2 will receive ZERO credit! But, g should be reasonable &
similar in size to g on the Earth’s surface! If your result is either very large or very small, you’ve
done something wrong!).
The mass m is launched off of the planet’s surface into outer space.
b. Calculate the gravitational force of attraction between the mass & the planet when m
has reached an altitude h = 1.5  106 m above the planet’s surface. (Hint: This should be
c.
several thousand Newtons in size. If your result is much smaller or much larger than this, you’ve
done something wrong!).
Calculate the gravitational acceleration g the mass experiences at this altitude. (Hint: See
hint for part a!)
d. Calculate the gravitational potential energy when m has reached the altitude in part b.
(Hint: Answering U = mgh will receive ZERO credit!)
e. Calculate the minimum escape speed vi required to launch m from the surface of the
planet so that it will move an infinite distance away from the planet’s surface. (Hint:
Einstein taught us that the largest speed possible for anything is the speed of light c = 3 × 108 m/s!
If your vi is larger than c, or even a significant fraction of it, you’ve done something wrong! vi
should be similar in sie to the escape speed from Earth’s surface, which is vE = 1.12  104 m/s.)
NOTE: Answer any two (2) of problems 2, 3, 4, & 5!!
4. See Figures. A rectangular block, mass m = 15 kg, is suspended by a wire from a
scale & immersed in oil (oil density ρo = 1.8  103 kg/m3). It’s free body diagram is at
the far right. B is the buoyant force on the block due to the oil & T is the wire
tension. The block’s horizontal faces have area A = 0.022 m2 & it’s vertical
dimension is L = 0.12 m, so it’s volume is V = AL = 2.64  10-3 m3. It’s top face is
a distance y = 0.1 m below the oil surface. The system is static.
a. Calculate the density ρB of the block.
b. Neglecting the effect of atmospheric pressure, calculate the oil pressure P1 on the
top face of the block & the oil pressure P2 on it’s bottom face. Use these results to
calculate the downward force F1 due to the oil on the block’s top face & the upward force
F2 on it’s bottom face. (Hint: Use the definition of pressure in terms of force).
Note: To answer the following, you MUST use some combination of 1) Archimedes’ Principle,
2) Newton’s 2nd Law in the vertical direction with a = 0, AND the definition of density in terms of
mass & volume! Answers attempting to use ONLY the definition of density in terms of mass &
volume will be given ZERO credit! Calculate:
c. The upward buoyant force B exerted by the oil on the block. What physical principle did
you use to calculate this force?
d. The tension T in the wire. What physical principle did you use to calculate this force? The
magnitude of T is the same as the scale reading. This is true because of what physical principle?
5.
See figures (illustrating how Archimedes supposedly determined
whether his King’s crown was really gold or not). A crown is hung by a
masseless cable attached to a scale & weighed twice. At left, it is
weighed in air & the scale reads the true weight w = Fg = mg = 9.5 N.
At right, it is submerged in water & weighed. The scale then reads
the apparent weight w′ = m′g = 8.2 N. Water density: ρw = 1,000 kg/m3.
The free body diagrams for the two cases are at the left of the figures. Fg is
the gravitational force on the crown, T1 & T2 are the cable tensions in the
two cases, B is the buoyant force on the crown at the right. Neglect
atmospheric pressure & assume that the crown is static.
a. At the right, the vertical distance from the top water surface to the point where the crown
is attached to the cable is h = 0.2 m. Calculate the pressure in the water at that point.
Suppose a sheet of thin plastic of cross sectional area A = 0.025 m2 is submerged in the
water at the right to the same depth, h = 0.2 m, as in part a. If its surface is parallel to the
top water surface, calculate the force on this sheet produced by the water pressure. (Hint:
Use the definition of pressure in terms of force.)
Note: To answer the following, you MUST use some combination of 1) Archimedes’ Principle,
2) Newton’s 2nd Law in the vertical direction with a = 0, AND the definition of density in terms of
mass & volume! Answers attempting to use ONLY the definition of density in terms of mass &
volume will be given ZERO credit!
b. Calculate the buoyant force B, that the water exerts on the crown. What physical
principle did you use to calculate this force?
c. Calculate the crown volume V. What physical principle did you use to calculate V?
d. Calculate the crown density ρc.
e. In the weighing experiments discussed above, the scale reading is equal & opposite to
the tension in the wire (T1 at the left & T2 at the right) in both cases. What Physical
Principle causes the preceding sentence to be true?
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
B T



mg
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