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a.12b. 0.50c. 0.01d. 1.9

e. 0.08

Oscillatory MotionMultiple Choice

2. A body oscillates with simple harmonic motion along the x-axis. Its displacement varies with time according to the equation x = 5.0 sin (t). The acceleration (in m/s2) of the body at t = 1.0 s is approximately

a. 3.5b. 49c. 14d. 43e. 4.3

3. A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = 5 sin (t + /3). The phase (in rad) of the motion at t = 2 s is

a. 7/3 b. /3 c. d. 5/3e. 2

6. The amplitude of a system moving with simple harmonic motion is doubled. The total energy will then be

a. 4 times larger b. 3 times larger c. 2 times largerd. the same as it wase. half as much

7. A mass m = 2.0 kg is attached to a spring having a force constant k = 290 N/m as in the figure. The mass is displaced from its equilibrium position and released. Its frequency of oscillation (in Hz) is approximately

18. Three pendulums with strings of the same length and bobs of the same mass are pulled out to angles1, 2 and 3 respectively and released. The approximation sin = holds for all three angles, with 3 >2 > 1. How do the angular frequencies of the three pendulums compare?

a. 3 > 2 > 1

b. Need to know amplitudes to answer this question.c. Need to knowd. 1 > 2 > 3

e. 1 = 2 = 3

g / L to answer this question.

20. An object of mass m is attached to string of length L. When it is released from point A, the object oscillates between points A and B. Which statement about the system consisting of the pendulum and the Earth is correct?

a. The gravitational potential energy of the system is greatest at A and B.b. The kinetic energy of mass m is greatest at point O.c. The greatest rate of change of momentum occurs at A and B.d. All of the above are correct.e. Only (a) and (b) above are correct.

21. A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown below. A point or points at which the object has positive velocity and zero acceleration is(are)

a. B b. C c. Dd. B or De. A or E

22. A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown below. The point at which the object has negative velocity and zero acceleration is

a. A b. B c. C d. D e. E

23. A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown below. The point at which the object has zero velocity and positive acceleration is

a. A b. B c. C d. D e. E

32. When a damping force is applied to a simple harmonic oscillator which has angular frequency 0 in the absence of damping, the new angular frequency is such that

a. .0

. b.

0 c. .

0

d. T T .0 0

e. T T .0 0

33. When a damping force is applied to a simple harmonic oscillator which has period T0 in the absence of damping, the new period T is such that

a. T T .0

b. T T .0

c. T T .0

d. T T .0 0

e. T T .0 0

34. To double the total energy of a mass oscillating at the end of a spring with amplitude A, we need to

a. increase the angular frequency by 2 .b. increase the amplitude by 2 .c. increase the amplitude by 2.d. increase the angular frequency by 2.

e. increase the amplitude by 4 and decrease the angular frequency by 1

.2

Wave MotionMultiple Choice

1. The wavelength of light visible to the human eye is on the order of 5 10–7 m. If the speed of light in air is 3 108 m/s, find the frequency of the lightwave.

a. 3 107 Hz b. 4 109 Hz c. 5 1011

Hz d. 6 1014 Hz e. 4 1015 Hz

2. The speed of a 10-kHz sound wave in seawater is approximately 1500 m/s. What is its wavelength in sea water?

a. 5.0 cm b. 10 cm c. 15 cm d. 20 cm e. 29 cm

4. Ocean waves with a wavelength of 120 m are coming in at a rate of 8 per minute. What is their speed?

a. 8.0 m/s b. 16 m/s c. 24 m/s d. 30 m/s e. 4.0 m/s

6. A piano string of density 0.0050 kg/m is under a tension of 1350 N. Find the velocity with which a wave travels on the string.

a. 260 m/s b. 520 m/s c. 1040 m/s d. 2080 m/s e. 4160 m/s

8. Transverse waves are traveling on a 1.00-m long piano string at 500 m/s. If the points of zero vibration occur at one-half wavelength, (where the string is fastened at both ends), find the frequency of vibration.

a. 250 Hz b. 500 Hz c. 1000 Hz d. 2000 Hz e. 2500 Hz

16. Write the equation of a wave, traveling along the +x axis with an amplitude of 0.02 m, a frequency of440 Hz, and a speed of 330 m/sec.

a. y = 0.02 sin [880 (x/330 – t)]b. y = 0.02 cos [880 x/330 – 440t]c. y = 0.02 sin [880(x/330 + t)] d. y = 0.02 sin [2(x/330 + 440t)] e. y = 0.02 cos [2(x/330 + 440t)]

2 The figure below shows a sine wave at one point of a string as a function of

Which of the graphs below shows a wave where the amplitude and the frequency are doubled?

2 The figure below shows a sine wave at one point of a string as a function of

Which of the graphs below shows a wave where the amplitude and frequency are each reduced in half?

2 The figure below shows a sine wave on a string at one instant of

Which of the graphs below shows a wave where the frequency and wave velocity are both doubled?

2 The figure below shows a sine wave on a string at one instant of

Which of the graphs below shows a wave where the wavelength is twice as large?

29. Superposition of waves can occur

a. in transverse waves.b. in longitudinal waves.c. in sinusoidal waves.d. in all ofthe above.e. only in (a) and (c) above.

3 Two pulses are traveling towards each other at 10 cm/s on a long string at t = 0 s, as shown

Which diagram below correctly shows the shape of the string at 0.5 s?

31. Suppose that you were selected for a “Survivor”-type TV show. To help keep your group connected, you suggest that long vines can be tied together and used to transmit signals in cases of emergency. To get the signals to travel faster, you should

a. select lighter vines.b. increase the tension on the vines.c. hang weights from the vines at evenly spaced intervals.d. do all of the above.e. do (a) and (b) above only.

35. Ariel claims that a pulse is described by the equation

y( x, t) 2

x 2 6.0xt 9t 2 9where x and y are measured in cm and t in s. Miranda says that it is not possible to represent a pulsewith this function because a wave must be a function of

and why?x vt or x vt. Which one, if either, is correct,

a. Ariel, because x 2 6.0xt 9t 2 ( x 3.0t)2.b. Ariel, because a pulse is not an infinite wave. c. Miranda, because (x 3.0t)2 is the same as (3.0t x)2 .d. Miranda, because a pulse is not an infinite wave.

2 e. Miranda, because x 2 6.0 xt 9t 2 x 21

6.00 t 9 t

is infinite when x=0. x

x 2

40. Four wave functions are given below. Rank them in order of the magnitude of the wave speeds, from least to greatest.

I.

II.

III.

IV.

y( x, t) 5sin(4 x 20t 4)

y( x, t) 5sin(3x 12t 5)

y(x, t) 5cos(4 x 24t 6) y(x, t) 14 cos(2x 8t 3)

a. IV, II, I, IIIb. c.

IV = II, I, III III, I, II, IV

d. IV, I, II, IIIe. III, IV, II, I

41. Four wave functions are given below. Rank them in order of the magnitude of the frequencies of the waves, from least to greatest.

I.

II.

III.

IV.

y( x, t) 5sin(4 x 20t 4)

y( x, t) 5sin(3x 12t 5)

y(x, t) 5cos(4 x 24t

6) y(x, t) 14 cos(2x 8t

3)


IV = II, I, III III, I, II, IV

d. IV, I, II, IIIe. III, IV, II, I

42. Four wave functions are given below. Rank them in order of the magnitude of the wavelengths, from least to greatest.

I.

II.

III.

IV.

y( x, t) 5sin(4 x 20t 4)

y( x, t) 5sin(3x 12t 5)

y(x, t) 5cos(4 x 24t

6) y(x, t) 14 cos(2x 8t

3)


IV, I, II, III I, II, III, IV

d. IV, II, III = Ie. I = III, II, IV

Electric FieldsMultiple Choice

2. A particle (charge = +40 µC) is located on the x axis at the point x = –20 cm, and a second particle (charge = –50 µC) is placed on the x axis at x = +30 cm. What is the magnitude of the total electrostatic force on a third particle (charge = –4.0 µC) placed at the origin (x = 0)?

a. 41 N b. 16 N c. 56 N d. 35 N e. 72 N

3. In the figure, if Q = 30 µC, q = 5.0 µC, and d = 30 cm, what is the magnitude of the electrostatic force onq?

a. 15 N b. 23 N c. zero d. 7.5 N e. 38 N

4. A charge of +80 µC is placed on the x axis at x = 0. A second charge of –50 µC is placed on the x axis at x= 50 cm. What is the magnitude of the electrostatic force on a third charge of 4.0 µC placed on the x axis at x = 30 cm?

a. 13 N b. 77 N c. 39 N d. 25 N e. 45 N

7. A point charge Q is placed on the x axis at x = 2.0 m. A second point charge, –Q, is placed at x = 3.0 m.If Q = 40 µC, what is the magnitude of the electrostatic force on a 30-µC charge placed at the origin?

a. 7.2 N b. 3.9 N c. 1.5 N d. 14 N e. 8.1 N

11. If a = 3.0 mm, b = 4.0 mm, Q1 = –60 nC, Q2 = 80 nC, and q = 30 nC in the figure, what is the magnitude of the total electric force on q?

a. 1.4 N b. 1.0 N c. 1.7 N d. 2.0 N e. 0.50 N

13. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 32 nC in the figure, what is the magnitude of the total electric force on q?

a. 1.6 N b. 1.3 N c. 1.9 N d. 2.2 Ne. 0.040 N

20. If Q = 25 µC, q = 10 µC, and L = 40 cm in the figure, what is the magnitude of the electrostatic force onq?

a. 28 N b. 22 N c. 20 N d. 14 N e. 10 N

21. If Q = 20 µC and L = 60 cm, what is the magnitude of the electrostatic force on any one of the charges shown?

a. 25 N b. 19 N c. 15 N d. 9.1 N e. 14 N

22. If a = 60 cm, b = 80 cm, Q = –4.0 nC, and q = 1.5 nC, what is the magnitude of the electric field at pointP?

a. 68 N/C b. 72 N/C c. 77 N/C d. 82 N/C e. 120 N/C

23. If a = 60 cm, b = 80 cm, Q = –6.0 nC, and q = 4.0 nC, what is the magnitude of the electric field at pointP?


24. If a = 60 cm, b = 80 cm, Q = –6.0 nC, and q = 6.0 nC, what is the magnitude of the electric field at point Pin the figure?


25. If a = 60 cm, b = 80 cm, Q = –6.0 nC, and q = 3.0 nC in the figure, what is the magnitude of the electric field at point P?


30. A +20-nC point charge is placed on the x axis at x = 2.0 m, and a –25-nC point charge is placed on the yaxis at y = –3.0 m. What is the direction of the electric field at the origin?

a. 209 b. 61 c. 29 d. 241 e. 151

31. A charge Q is placed on the x axis at x = +4.0 m. A second charge q is located at the origin. If Q = +75 nC and q = –8.0 nC, what is the magnitude of the electric field on the y axis at y = +3.0 m?


32. A 40-µC charge is positioned on the x axis at x = 4.0 cm. Where should a –60-µC charge be placed to produce a net electric field of zero at the origin?

a. –5.3 cm b. 5.7 cm c. 4.9 cm d. –6.0 cme. +6.0 cm

Gauss’s LawMultiple Choice

1. Two charges of 15 pC and –40 pC are inside a cube with sides that are of 0.40-m length. Determine the net electric flux through the surface of the cube.

a. +2.8 N m2/C b. –1.1 N m2/C c. +1.1 N m2/C d. –2.8 N m2/C e. –0.47 N m2/C

2. The total electric flux through a closed cylindrical (length = 1.2 m, diameter = 0.20 m) surface is equal to–5.0 N m2/C. Determine the net charge within the cylinder.

a. –62 pC b. –53 pC c. –44 pC d. –71 pC e. –16 pC

3. Charges q and Q are placed on the x axis at x = 0 and x = 2.0 m, respectively. If q = –40 pC and Q = +30 pC, determine the net flux through a spherical surface (radius = 1.0 m) centered on the origin.

a. –9.6 N m2/C b. –6.8 N m2/C c. –8.5 N m2/C d. –4.5 N m2/C e. –1.1 N m2/C

5. A uniform charge density of 500 nC/m3 is distributed throughout a spherical volume (radius = 16 cm).Consider a cubical (4.0 cm along the edge) surface completely inside the sphere. Determine the electric flux through this surface.

a. 7.1 N m2/C b. 3.6 N m2/C c. 12 N m2/C d. 19 N m2/C e. 970 N m2/C

6. A point charge +Q is located on the x axis at x = a, and a second point charge –Q is located on the x axis at x = –a. A Gaussian surface with radius r = 2a is centered at the origin. The flux through this Gaussian surface is

a. zero because the negative flux over one hemisphere is equal to the positive flux over the other.b. greater than zero.c. zero because at every point on the surface the electric field has no component perpendicular to the

surface.d. zero because the electric field is zero at every point on the surface.e. none of the above.

9. Charge of uniform surface density (4.0 nC/m2) is distributed on a spherical surface (radius = 2.0 cm).What is the total electric flux through a concentric spherical surface with a radius of 4.0 cm?

a. 2.8 N m2/C b. 1.7 N m2/C c. 2.3 N m2/C d. 4.0 N m2/C e. 9.1 N m2/C

11. A charge of 0.80 nC is placed at the center of a cube that measures 4.0 m along each edge. What is the electric flux through one face of the cube?

a. 90 N m2/C b. 15 N m2/C c. 45 N m2/C d. 23 N m2/C e. 64 N m2/C

15. Two infinite parallel surfaces carry uniform charge densities of 0.20 nC/m2 and 0.60 nC/mthe magnitude of the electric field at a point between the two surfaces?


2 . What is

31. A solid nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/m3) distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the center of the sphere.


32. A 5.0-nC point charge is embedded at the center of a nonconducting sphere (radius = 2.0 cm) which has a charge of –8.0 nC distributed uniformly throughout its volume. What is the magnitude of the electric field at a point that is 1.0 cm from the center of the sphere?

a. 1.8 105

N/C b. 9.0 104 N/C c. 3.6 105 N/C d. 2.7 105 N/C e. 7.2 105 N/C

33. A charge of 5.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of –2.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the electric field 3.0 cm from the center of the two surfaces.


34. A charge of 8.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of –3.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the electric field 5.0 cm from the center of the two surfaces.


46. An astronaut is in an all-metal chamber outside the space station when a solar storm results in the deposit of a large positive charge on the station. Which statement is correct?

a. The astronaut must abandon the chamber immediately to avoid being electrocuted.b. The astronaut will be safe only if she is wearing a spacesuit made of non-conducting materials.c. The astronaut does not need to worry: the charge will remain on the outside surface.d. The astronaut must abandon the chamber if the electric field on the outside surface becomes

greater than the breakdown field of air.e. The astronaut must abandon the chamber immediately because the electric field inside the

chamber is non-uniform.

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