First Name:	Last Name:	Student ID:	Section:

December 23, 2004

PHYSICS 207: Final

Print your name and section clearly on all pages. (If you do not know your section number, write your TA's name.) Show all work in the space immediately below each problem. Your final answer must be placed in the box provided. Problems will be graded on reasoning and intermediate steps as well as on the final answer. Be sure to include units wherever necessary, and the direction of vectors. In doing the problems, try to be neat. Check your answers to see that they have the correct dimensions (units) and are the right order of magnitudes. You are allowed four 8½ x 11" sheet of notes and no other references. The exam lasts exactly 120 minutes.

NOTE: For the purposes of this exam you may assume:

1. $g=10$ m/s$^2$
2. $I_{cylinder}=\frac{1}{2} MR^2$
3. $I_{sphere}=\frac{2}{5} MR^2$
4. $I_{hoop}=~~MR^2$
5. $I_{hollow~cylinder}=\frac{1}{2} M (R_1^2+R_2^2)$
6. $I_{bar}=\frac{1}{12} M R^2$

Do NOT write below this point.

SCORE [PROBLEMS 3-5, 8-11++ are multiple choice.]

PROBLEM 1:	PROBLEM 9:
PROBLEM 2:	PROBLEM 10:
PROBLEM 3:	PROBLEM 11:
PROBLEM 4:	PROBLEM 12:
PROBLEM 5:	PROBLEM 13:
PROBLEM 6:	PROBLEM 14:
PROBLEM 7:	PROBLEM 15:
PROBLEM 8:	PROBLEM 16:

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PROBLEMS 1-2: (24 pts.) A professor, not on this Earth, is lecturing to his class in a monotone at a frequency of 100 Hz The velocity of sound in the atmosphere is 400 m/s.

P1 (12 pts.) What is the wavelength of the sound?

P2 (12 pts.) At what minimum speed and direction must the students move in order to Doppler shift the professor's voice to a frequency too low for them to hear the lecture (in this case below 40 Hz)?

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PROBLEM 3: (12 pts.)
$\parbox{0.50\linewidth}{ \noindent The velocity of an object as a fu... ...ow best represents the net force {\it vs} time relationship for this object? }$ $\parbox{0.30\linewidth}{~~ \begin{center} \includegraphics[width=1.3in]{f3_1.eps} \end{center}}$

PROBLEM 4: (12 pts.) A 50 kg person, starting at rest, falls vertically ($g=10$m/s$^2$), and lands squarely onto a vertically mounted Hookes' Law spring ($k= 2000$ N/m). The spring compresses 2 m before the person comes momentarily to a rest.

What was the initial height of the person above the uncompressed spring?

1. [(A)]  1 m
2. [(B)]  2 m
3. [(C)]  3 m
4. [(D)]  4 m
5. [(E)]  6 m

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PROBLEMS 5 (12 pts.)

A merry-go-round is spinning horizontally at 1.0 revolutions per second with a rotational moment of inertia of 400. kg-m$^2$ (of just the merry-go-round). On the merry-go-round and spinning with it is a 50. kg person standing initially at 2.0 m from the axis of rotation. The person then walks 1.0 m to a position 1.0 m from the axis of rotation and rotates with the merry-go-round.
What is the final angular velocity?

1. [(A)]  8.0 rad/sec
2. [(B)]  8.4 rad/sec
3. [(C)] 16.0 rad/sec
4. [(D)] 16.8 rad/sec
5. [(E)] None of the above

PROBLEMS 6-7: (24 pts., 12 pts. each)

P6

A pipe is 15 m long and open at both ends, what is the fundamental frequency if the speed of sound is 340 m/s

P7

How far from the end is the first node (with respect to displacement) when the pipe is resonating at the third harmonic? (Draw sketches of the first and second harmonics.)

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PROBLEM 8: (12 pts.)

$\parbox{0.59\linewidth}{ \noindent A 40 kg block rests on a horizont... .... \\ What is the horizontal velocity of the two objects after the collision? }$ $\parbox{0.40\linewidth}{ \begin{center} \includegraphics[width=1.8in]{final_04_2.eps} \end{center}}$

1. [(A)] 4.54 m/s
2. [(B)] 6.65 m/s
3. [(C)] 9.12 m/s
4. [(D)] 30.1 m/s
5. [(E)] None of the above

PROBLEM 9: (13 pts.)

An aluminum bar (1.000000 m long, 0.10 m$^2$ cross-sectional area) just slides into the 1.000000 m gap of a press. The temperature is now raised 10 $^\circ$C. How much pressure must be applied to keep the gap at exactly 1.000000 m. (Possibly useful information: Linear expansion coefficient $20. \times 10 ^{-6}$ $/^\circ$C, Young's Modulus $7.0 \times 10. ^{10}$ N/m$^2$ and $10 \times 10^{10}$ Bulk Modulus )

1. [(A)] 2.0 $\times 10^6$ N/m$^2$
2. [(B)] 2.0 $\times 10^7$ N/m$^2$
3. [(C)] 2.0 $\times 10^8$ N/m$^2$
4. [(D)] 1.4 $\times 10^6$ N/m$^2$
5. [(E)] 1.4 $\times 10^7$ N/m$^2$

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PROBLEM 10: (13 pts.)

$\parbox{0.45\linewidth}{ \noindent A thin bar 2 meters long and mass... ...from rotating? (The acceleration due to gravity is assumed to be 10 m/s$^2$.) }$ $\parbox{0.50\linewidth}{~~ \begin{center} \includegraphics[width=1.8in]{final_04_3.eps} \end{center}}$

1. [(A)] 15 N
2. [(B)] 16 N
3. [(C)] 20 N
4. [(D)] 25 N
5. [(E)] 30 N

PROBLEM 11: (13 pts.)
$\parbox{0.45\linewidth}{ \noindent A person pulls a block across a r... ...among the force magnitudes $W$, $f$, $N$\ and $F$\ {\bf must be true}? \vfill }$ $\parbox{0.30\linewidth}{~~ \begin{center} \includegraphics[width=2.5in]{f_4.eps} \end{center}}$

1. [(A)] $F = f$ and $N = W$
2. [(B)] $F = f$ and $N > W$
3. [(C)] $F > f$ and $N < W$
4. [(D)] $F > f$ and $N = W$
5. [(E)] None of the above

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PROBLEM 12-13: (26 pts., 13 pts each)

$\parbox{0.39\linewidth}{ \noindent Five moles of an ideal monoatomic... ...or the purposes of this problem use R, the gas constant, to be 8.3 J/K mol.) }$ $\parbox{0.50\linewidth}{ \begin{center} \includegraphics[width=3.2in]{final_04_1.eps} \end{center}}$

1. [P12] What is the internal energy of the gas at point C (in joules)?
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
2. [P13] What is work done in moving from A to B (in joules)?
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

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PROBLEM 14: (13 pts.) Two uniform spheres of mass M and radius R are initially held at rest and (from center to center) 8R apart. If they are released, how fast will they be going when they collide (in terms of R, M, G or any combination)?

PROBLEM 15: (13 pts.) An adiabatic two compartment container, each container having a 10 liter capacity, is filled with 0.5 mole (per compartment) of an identical monoatomic idea gas with temperatures of 200 $^\circ$K and 600 $^\circ$K respectively. By how much does the entropy change if the gas in each chamber is allowed to mix and reestablish thermodynamic equilibrium? (Hint: Mixing and thermal equilibrium may be done separately.)

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PROBLEM 16: (13 pts.) A tub with 2 kg of water at 0 $^\circ$C is connected through a silver rod, 1 meter long and 0.25 m$^2$ in cross sectional area, to a thermal reservoir at -50 $^\circ$C. How long it will take the water to freeze?
(The latent heat of fusion for water, $3.33 \times 10^5$ J/kg and the thermal conductivity for silver is 400 W/m $^\circ$C)