SCORE: ________ / 100 = ___________ 1 Name_____________________________________ Alpha ____________ USNA Physics Department LCDR Shivok’s SP211 2015 Third Exam PRACTICE VERSION A Chapters 13 17 (with no intentional review) Gravitation, Kepler’s Laws, Fluids at rest, Pressure, Pascal’s principle, Buoyancy, Bernouli’s Eqn, Simple Harmonic Motion, Pendulums, Damped Oscillations, Resonance, Types of waves, Methods waves move, Waves on a String, Engergy and Power of a wave, Wave Equation, Interference of Waves, Standing Waves, Sound waves, Intensity, Beats, Doppler Effect, and supersonic shock waves. If you use these problems to help you determine the areas in which you are weak, I believe they will help you prepare for the Third Examination. DO NOT confine your study to just these problems. This is a REVIEW PROBLEM exercise, NOT an all encompassing gouge! The submarine “dives” because it takes on water into tanks to overcome the buoyant force. Exam III, breakdown Takehome Pts Inclass Pts CH-13 4Q’s 9 2Q’s 14 CH-14 5Q’s 11 2Q’s 16 CH-15 5Q’s 11 2Q’s 16 CH-16 4Q’s 9 2Q’s 14 Total 22 Q’s 40 8 Q’s 60 CH17 is only covered on Final Exam. Note: No intentional review questions, but the course builds on topics. There just won’t be a specific question from previous chapters on this exam.
The submarine “dives” because it takes on water into tanks to overcome the buoyant force.
Exam III, breakdown
Takehome Pts Inclass Pts
CH-13 4Q’s 9 2Q’s 14
CH-14 5Q’s 11 2Q’s 16
CH-15 5Q’s 11 2Q’s 16
CH-16 4Q’s 9 2Q’s 14
Total 22 Q’s 40 8 Q’s 60
CH17 is only covered on Final Exam. Note: No intentional review questions, but
the course builds on topics. There just won’t be a specific question from previous
chapters on this exam.
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Chapter 13 (20 points)
1. (4 points) The figure here shows the observed orbit of the star S2 as the star moves
around a mysterious and unobserved object called Sagittarius A* (pronounced “A star”),
which is at the center of the Milky Way galaxy. S2 orbits Sagittarius A* with a period of
15.2T yrs and with a semimajor axis of 5.50a light‐days 14(1.42 10 )x m . What is
the mass M of Sagittarius A* in terms of our sun mass of our Sun (MSun = 1.99 × 1030 kg).?
By the way, Sagittarius A* is a black hole. (Movies of the stars orbiting Sagittarius A* are available on the Web;
search under “black hole galactic center.”)
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2. (2 points) A particle of mass m1 = 5.00 × 10-6 kg is 4.78 m from the center of a uniform spherical shell of mass m2 = 4.00 kg, outer radius R0 = 3.14 m, and inner radius Ri = 3.12 m. What is the magnitude of the gravitational force on the particle due to the spherical shell? A) zero B) 1.8 x 10-17 N C) 8.5 x 10-17 N D) 8.5 x 10-11 N E) 5.8 x 10‐17 N
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3. (3 points) Planet A has mass M = 3.00 × 1024 kg and radius R = 2.00 × 107 m, and it completes a full rotation in time T = 35.0 h. What is the free-fall acceleration g on its equator? A) zero B) .500 m/s2 C) .450 m/s2 D) .0500 m/s2 E) 5.8 x 10‐3 m/s2
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4. (4 points) In Fig. below, what is the gravitational potential energy of three particles that form the corners of a right triangle? The masses are m1 = 2.5 kg, m2 = 4.5 kg, and m3 = 6.2 kg. The distances are 3.0 m, 4.0 m, and 5.0 m.
A) zero B) ‐8.8 x 10-10 J C) +8.8 x 10-10 J D) ‐5.8 x 10-10 J E) +5.8 x 10‐10 J
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5. (3 points) Two particles with mass m1 = 3.0 × 10-13 kg and m2 = 5.0 × 10-13 kg are separated by distance r = 2.6 × 10-3 m. How much work do we do if we double the separation?
A) +1.9 x 10-33 J B) ‐1.9 x 10-33 J C) +3.8 x 10-33 J D) ‐3.8 x 10-33 J E) zero
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6. (2 points) A planet travels in an elliptical orbit about a star as shown. At what pair of points is the speed of the planet the same?
A) W and S B) P and T C) P and R D) Q and U E) V and R
Explain:
7. (2 points) A small satellite is in elliptical orbit around Earth as shown. If L denotes the magnitude of its angular momentum and K denotes kinetic energy:
A) L2 > L1 and K2 > K1 B) L2 > L1 and K2 = K1 C) L2 = L1 and K2 = K1 D) L2 < L1 and K2 = K1 E) L2 = L1 and K2 > K1
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Chapter 14 (20points)
8. (2 points) Figure below shows how the stream of water emerging from a faucet “necks down” as it falls. This change in the horizontal cross-sectional area is characteristic of any laminar (nonturbulant) falling stream because the gravitational force increases the speed of the stream. Here the indicated cross-sectional areas are A0 = 1.2 cm2 and A = 0.35 cm2. The two levels are separated by a vertical distance h = 45 mm. What is the volume flow rate from the tap?
A) 24 cm3/s B) 34 cm3/s C) 11 cm3/s D) 14 cm3/s E) 3.4 cm3/s
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9. (2 points) Figure below shows two containers filled to the same water depth h = 50 cm and each having a bottom surface that is circular with a radius of 1.5 cm. What is the pressure on each bottom surface?
A) 4.3 x 10-3 Pa B) 4.3 x 103 Pa C) 2.3 x 10-3 Pa D) 2.3 x 103 Pa E) zero
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10. (2 points) In the hydraulic lever of Fig. below, the input force of magnitude Fi = 50.0 N is applied to an area Ai = 0.040 m2. The area at the output is A0 = 0.800 m2. What is the magnitude F0 of the output force? If the input piston moves downward by distance di = 0.010 m, through what distance d0 does the output piston move ?
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11. (2 points) Two identical blocks of ice float in water as shown. Then:
A) block A displaces a greater volume of water since the pressure acts on a smaller bottom area B) block B displaces a greater volume of water since the pressure is less on its bottom C) the two blocks displace equal volumes of water since they have the same weight D) block A displaces a greater volume of water since its submerged end is lower in the water E) Block B displaces a greater volume of water since its submerged end has a greater area
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The next three questions apply to the following initial conditions and diagram: In Fig. below, a rectangular block floats in a liquid. A block of mass m = 0.500 kg and density ρ = 0.700 kg/m3 floats facedown in a liquid of density ρf = 1200 kg/m3.
12. (2 points) What is the magnitude of the buoyant force on the block from the liquid, the weight of the liquid displaced by the block (the liquid that would be in the space now occupied by the block).
13. (2 points) What is the mass of that displaced liquid?
14. (2 points) What fraction of the block's volume is submerged?
15. (2 points) What fraction of its height is submerged?
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16. (2 points) Which of the following statements about Pascal's principle is true?
A) It is valid only for incompressible fluids B) It explains why light objects float C) It explains why the pressure is greater at the bottom of a lake than at the surface D) It is valid only for objects that are less dense than water E) None of the above are true
17. (2 points) Water ( = 1000 kg/m3) and then oil (water and oil don't mix) are poured into one end of a Ushaped tube. They come to equilibrium as shown in the accompanying figure. The density of the oil is closest to (HINT: The pressures at points a and b are equal.)
A. 345 kg/m3 B. 654 kg/m3 C. 1530 kg/m3 D. 2890 kg/m3 E. Cannot be determined from the data given.
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Chapter 15 (20 points)
18. (4 points) Figure below is a graph of the position x(t) of a block in a spring‐block oscillator undergoing simple harmonic motion. What is the equation x(t) for the block's position as a function of time?
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19. (2 points) In Fig. below, a spring with spring constant K = 400 N/m hangs from a ceiling. A block with mass m = 2.00 kg is attached to the lower end and then released. The block undergoes simple harmonic motion. What is the angular frequency ω of the oscillations?
A) 28.2 rad/s B) .071 rad/s C) 14.1 rad/s D) .141 rad/s E) 4.1 rad/s
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20. (2 points) In Fig. below, two springs with spring constants k1 = 400 N/m and k2 = 400 N/m act on a block with mass m = 8.00 kg. The springs are said to be (or act) in parallel. (They could be on opposite sides of the block as shown or on the same side of the block.) What is the angular frequency ω of the oscillations?
A) 5.0 rad/s B) 10.0 rad/s C) 2.0 rad/s D) 20.0 rad/s E) .200 rad/s
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21. (3 points) In Fig. below, a small bob of mass m = 1.2 kg is attached at the lower end of a string of negligible mass and length L = 0.15 m. The other end is tied to a ceiling. The bob and string then swing as a simple pendulum, with the string making only small angles with the vertical. What is the period of the motion?
A) 24.0 s B) 78.0 s C) 28.0 s D) 2.8 s E) 0.78 s
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22. (2 points) Fig. below, a stick of length L = 1.85 m oscillates as a physical pendulum. What value of distance x between the stick's center of mass and its pivot point O gives the least period?
A) 0.53 m B) 0.35 m C) 0.70 m D) 0.86 m E) 0.33 m
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23. (2 points) The amplitude of oscillation of a simple pendulum is increased from 1° to 4°. Its maximum acceleration changes by a factor of:
A) 1/4 B) 1/2 C) 2 D) 4 E) 16
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24. (2 points) Five particles undergo damped harmonic motion. Values for the spring constant k, the damping constant b, and the mass m are given below. Which leads to the smallest rate of loss of mechanical energy
A) k = 100N/m, m = 50g, b = 8g/s B) k = 150N/m, m = 50g, b = 5g/s C) k = 150N/m, m = 10g, b = 8g/s D) k = 200N/m, m = 8g, b = 6g/s E) k = 100N/m, m = 2g, b = 4g/s
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25. (3 points) A mass of 1.2 kg is attached to a spring and undergoes simple harmonic motion with a period of T 2.5 s . The motion is along a frictionless horizontal surface and the total energy of the spring-mass system is 3.7 J. What is the amplitude of oscillation?
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Chapter 16 (20 points)
26. (3 points) Seismic waves are waves that travel either through Earth's interior or along the ground. Seismology stations are set up mainly to record seismic waves generated by earthquakes, but they also record seismic waves generated by any large release of energy near Earth's surface, such as an explosion. As the seismic waves travel past a station, they oscillate a recording pen and the pen traces out a graph. Part a of the figure here is one of the graphs created by seismic waves from the mysterious sinking of the Russian submarine Kursk in August 2000. The first oscillations of the pen are marked with an arrow and were of small amplitude. Much stronger oscillations began about 134 s later.
(a) Graph made by a recording device as seismic waves from the Kursk passed the device. Amplitude is plotted vertically; time increases rightward. (Courtesy of Jay Pulli/BBN Technologies) (b) With the submarine sitting at depth D, the large explosion sent pulses both into the ground and up through the water.
From this, analysts concluded that the first seismic waves were generated by an onboard
explosion, possibly a torpedo that failed to launch when fired. The explosion presumably
breached the hull, started a fire, and sank the submarine. The later, much stronger seismic
waves were generated after the submarine was sunk and were possibly generated when the
fire caused several of the powerful missiles on board to explode simultaneously. These stronger
waves arrived at seismology stations as pulses separated by a time interval Δt of about 0.11 s.
To what depth D did the submarine sink?
A) 1500m B) 42 m C) 38.5 m D) 83 m E) none of these
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27. (3 points) A wave traveling along a string is described by
( , ) 0.00327 (72.1 2.72 ),y x t Sin x t
in which the numerical constants are in SI units (0.00327 m, 72.1 rad/m, and 2.72 rad/s).
What is u, the transverse velocity of the string element at x = 22.5 cm and at t = 18.9
s? (This velocity, which is associated with the transverse oscillation of an element of the
string, is in the y direction. Do not confuse it with v, the constant velocity at which the
wave form travels along the x axis.)
A) 24.0 mm/s B) 8.0 mm/s C) 2.8 mm/s D) 7.2 mm/s E) .270 mm/s
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28. (3 points) A uniform cord has mass m = 5.00 × 10-5 kg and length L = 2.00 m, and it is under tension τ = 160 N. What is the speed v of transverse waves along the cord? A) 2.0 x 10-3 m/s B) 2.5 x 10-3 m/s C) 3.5 x 10-3 m/s D) 1.5 x 10-3 m/s E) zero
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29. (4 points) A sinusoidal wave moving along a string in the positive direction of an x axis was recorded on video. The curves in Fig. below present the wave in two freeze‐frames of the video, first as the solid curve and then, 1.0 ms later, as the dotted curve. The grid lines along the x axis are 1.0 cm apart. Each string element oscillated vertically (perpendicular to the x axis) a total distance of 4.0 mm as the wave passed through it. The wave moved a distance d = 3.16 cm to the right in the 1.0 ms time interval. Write an equation for this wave in the general form
( , ) ( ),my x t y Sin kx t
where ± indicates that the proper sign must be determined.
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30. (2 points) Fully destructive interference between two sinusoidal waves of the same frequency and amplitude occurs only if they:
A) travel in opposite directions and are in phase B) travel in opposite directions and are 180° out of phase C) travel in the same direction and are in phase D) travel in the same direction and are 180° out of phase E) travel in the same direction and are 90° out of phase
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31. (3 points) A transverse wave on a taut string is described by ( , ) 3.0 (5.0 7.0 )y x t Sin x t in SI units. What is the wavelength of this wave?
A) 1.3 m B) 2.1 m C) 0.9 m D) 5.0 m E) 3.0 m
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32. (2 points) A wave on a string is reflected from a fixed end. The reflected wave:
A) is in phase with the original wave at the end B) is 180° out of phase with the original wave at the end C) has a larger amplitude than the original wave D) has a larger speed than the original wave E) cannot be transverse
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Chapter 17 (20 points)
33. (3 points) What is the bulk modulus B in granite, in which the speed of sound is v = 6000 m/s and the density is ρ = 2.70 g/cm3?
A) 4.3 x 10-9 Pa B) 4.3 x 109 Pa C) 9.7 x 1010 Pa D) 2.2 x 109 Pa E) None of these
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34. (3 points) The largest number of beats per second will be heard from which pair of tuning forks?
A) 200 and 201 Hz B) 256 and 260 Hz C) 534 and 540 Hz D) 763 and 774 Hz E) 8420 and 8422 Hz
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35. (3 points) A source emits sound with a frequency of 1000 Hz. It and an observer are moving toward each other, each with a speed of 100 m/s. If the speed of sound is 340 m/s, the
observer detects sound with a frequency of:
A) 545 Hz B) 294 Hz C) 1000 Hz D) 3400 Hz E) 1830 Hz
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36. (2 points) The rise in pitch of an approaching siren is an apparent increase in its: A) speed B) amplitude C) frequency D) wavelength E) number of overtones
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37. (5 points) A French submarine and a U.S. submarine move toward each other in motionless water. The French sub moves at a speed of 5 knots and the U.S. submarine moves at a speed of 8 knots. The French sub sends out a sonar ping (sound wave in water) at 1000 Hz. Sonar waves travel at 5470 km/h.
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(a) What is the signal’s frequency as detected by the U.S. submarine? (b) What is the signal’s frequency as detected by the French submarine after reflection from the U.S.
submarine?
38. (4 points) A column of midshipmen, marching at 120 paces per minute, keep in step with the beat of a drummer at the head of the column. The midshipmen in the rear are striding forward with the left foot when the drummer is advancing with the right foot. What is the approximate length of the column if the speed of sound in air is 343 m/s?
Make sure you showed all your work for all problems! Do the idiot check on your math… Does 50 – 30 = 20 or did you fat finger the calculator?
