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Document # 9356531

Physical Sciences Self-Assessment: Physics Test

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e t u b i r t s i D t o MCAT® is a program of the Association of American Medical Colleges

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Copyright Infringement Reminder Please note that your usage of this test is governed by the terms and conditions of your purchase. You may review the terms and conditions at https://www.aamc.org/publications/274794/mcatpracticetesttermsconditions.htm.

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Taking Your Test Offline The full length test may be taken online, printed and taken offline, or a combination of both methods. If you started a test online, the answer sheet provided at the end of this printout does not include the answers you entered online. Your online answers will appear on the online answer sheet used to submit your answers for scoring. Once you have completed your offline test, follow these steps to enter your answers and submit them for scoring.  Sign in to the web site.  If this is a new test, click the "Start on Paper" link provided in the "Start a New Test" table of your home page.  If you want to continue entering answers for an in-progress test, click the "Restart on Paper" link provided in the “Resume a Test" table of your home page.  Click the "Score Paper Test" link.  Enter your answers in the provided form. Any answers previously entered using your online practice test or this answer sheet will appear in the form.  Once you have finished entering your answers be sure to save them by clicking "Save", "Save and Exit", or "Review Online". If you close the answer sheet page without clicking one of these links, your answers will not be saved.  You may return to the answer sheet to enter or review answers as many times as you like.  When you are ready to submit your final answers for scoring, click the "Update and Submit for Score" link. Once you submit your final answers for scoring, you will not be able to review or modify your answers using the entry form.  After your answers have been submitted for scoring, you will automatically return to your home page. To view your analytic summary, click the link provided in the "Completed Tests" table.  From the score report you can review your answers and the solution for each question.  Additional support for scoring a paper test offline is available by contacting [email protected]

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Printing Guide Use this printing guide as a reference to print selected sections of this test. To print, click the PRINTER icon located along the top of the window and enter one of the following options in the PRINT RANGE section of the print dialog window: To Print

Enter Print Range Options

Complete Test

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Commitment Self-Assessment Pre-test Confidence Self-Assessment Periodic Table Test questions

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Post-test Confidence Self-Assessment Answer Sheet

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Click PAGES FROM radio to and enter page 5 to 5 Click PAGES FROM radio to and enter pages 6 to 7 Click PAGES FROM radio to and enter page 8 to 8 Click PAGES FROM radio to and enter pages 10 to 49 Click PAGES FROM radio to and enter pages 50 to 51 Click PAGES FROM radio to and enter pages 52 to 53

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Commitment Self-Assessment How committed are you to completing this test and using the results to prepare for the MCAT? 1=Not committed , 2=Somewhat committed, 3=Committed If answer is 1, --- Completing the test requires a commitment of time and energy. If you do not feel you can commit the time to complete it, you may be better off waiting to take the test until you can commit the time. The test must be completed to receive the feedback to guide your study. If answer 2,--- It’s okay if you are unsure about your confidence to use the results to prepare for the MCAT. The unknown can be daunting. However, it is important that you feel motivated to complete the test since you need to answer all the questions to receive feedback. The Official MCAT® Self- Assessment Package will show your relative strengths and weaknesses to help you determine in what areas you should focus your preparation. The entire test will take a few hours to complete, but you don’t need to complete it all at once. It doesn’t matter how long it takes you to finish the test, but you do need to finish to receive feedback!

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If answer 3,-- You’ve taken an important step in preparing for the MCAT by committing your time and energy to completing the Self-Assessments. It is okay if you don’t know all the answers. This time spent on preparation and practice will help you figure out your relative strengths and weaknesses in the content of the MCAT so that you can plan your study most effectively.

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Pre-test Confidence Self-Assessment One of the factors that can influence both your preparation and performance on the actual MCAT exam is your confidence. This questionnaire will help you assess your confidence on the topics in this section of the exam so that you can use the information to decide where you should focus your study time. You will be asked to rate your confidence again after completing the test to help you gauge how your experience with actual MCAT questions influences your perception of your ability in these content areas so that you can decide if you were overconfident, under confident or on target and why this may be. Confidence: Using the 5-point scale below in the table, how confident are you are in your ability to perform well on this section of the MCAT exam as well as for each content category?

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Test/Content Categories 1. Physics Overall 2. Atomic and Nuclear Structure

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A=1-Not Confident at all

B=2Somewhat Confident

C=3Moderately Confident

D=4-Very Confident

E=5Extremely Confident

4. Electronic Circuit Elements 5. Equilibrium and Momentum 6. Fluids and Solids

7. Force and Motion, Gravitation

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8. Light and Geometrical Optics 9. Sound 10. Translational Motion 11. Waves and Periodic Motion 12. Work and Energy

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Periodic Table of the Elements

1

H

2

He

1.0 3

4

Li

Be

B

C

N

O

F

Ne

6.9

9.0

10.8

12.0

14.0

16.0

19.0

20.2

5

6

7

8

9

4.0 10

11

12

13

14

15

16

17

18

Na

Mg

Al

Si

P

S

Cl

Ar

23.0

24.3

27.0

28.1

31.0

32.1

35.5

39.9

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

K

Ca

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga

Ge

As

Se

Br

Kr

39.1 37

40.1 38

45.0 39

47.9 40

50.9 41

52.0 42

54.9 43

55.8 44

58.9 45

58.7 46

63.5 47

65.4 48

69.7 49

72.6 50

74.9 51

79.0 52

79.9 53

83.8 54

Rb

Sr

Y

Zr

Nb

Mo

Tc

Ru

Rh

Pd

Ag

Cd

In

Sn

Sb

Te

I

Xe

85.5 55

87.6 56

88.9 57

91.2 72

92.9 73

95.9 74

(98) 75

101.1 76

102.9 77

106.4 78

107.9 79

112.4 80

114.8 81

118.7 82

121.8 83

127.6 84

126.9 85

131.3 86

Cs

Ba

La*

Hf

Ta

W

Re

Os

Ir

Pt

Au

Hg

Tl

Pb

Bi

Po

At

Rn

132.9 87

137.3 88

138.9 89

178.5 104

180.9 105

183.9 106

186.2 107

190.2 108

192.2 109

195.1 110

197.0 111

200.6 112

204.4

207.2 114

209.0

(209) 116

(210)

(222)

Fr

Ra

Ac†

Rf

Db

Sg

Bh

Hs

Mt

Ds

(223)

(226)

(227)

(261)

(262)

(266)

(264)

(277)

(268)

(281)

Uuu Uub

Uuq

Uuh

(272)

(289)

(289)

(285)

58

59

60

61

62

63

64

65

66

67

68

69

70

71

* Ce

Pr

Nd

Pm

Sm

Eu

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu

140.1 90

140.9 91

144.2 92

(145) 93

150.4 94

152.0 95

157.3 96

158.9 97

162.5 98

164.9 99

167.3 100

168.9 101

173.0 102

175.0 103

232.0

(231)

† Th

Pa

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U

Np

Pu

Am

Cm

Bk

Cf

Es

Fm

Md

No

Lr

238.0

(237)

(244)

(243)

(247)

(247)

(251)

(252)

(257)

(258)

(259)

(260)

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Document # 9356531

Physical Sciences Self-Assessment: Physics Test Number of Questions: 109 Approximate Time to Complete: 2-3 hours Welcome to the Physical Sciences Self-Assessment: Physics Test. The goal of this test is to analyze your knowledge in the content of the MCAT. In order to obtain an accurate assessment of your strengths and weaknesses, you must answer every question. Because the test is lengthy, you are encouraged to take breaks as needed. Good luck!

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Passage I A large amount of energy is released when the nucleus of an atom disintegrates. Nuclear fission of 1 kg of U produces approximately 8.0  1013 J, an amount of energy equal to that produced by burning 2.3  106 kg of coal. A simple model of nuclear disintegration can be used to explain the source of this large amount of energy. The nucleus of a U atom contains 92 protons and 146 neutrons in a sphere with a radius of approximately 7.6  10–15 m. There is a large repulsive force between the positive charges in the nucleus. This force is balanced by a short-range attractive force, the strong nuclear force. By using a simple model, calculations can be done to find the amount of energy released when a uranium atom fissions. The model assumes that the uranium nucleus disintegrates into two spherical fragments, as shown in Figure 1.

kQ2/(2r), which is the energy available from this disintegration. A value of 3.2  10–11 J per atom is obtained by making a calculation for the model uranium atom. This value is very close to the experimentally determined value. 1. According to the passage, the energy released when an atom splits comes from: A) fast-moving electrons. B) the short-range attraction of the nucleons. C) mutual attraction of the fragments. D) mutual repulsion of the fragments. 2. Based on the passage, why are there no naturally occurring elements that have more protons in their nucleus than uranium does? A) All of the heavier elements have radioactively decayed.

e t u b i r t s i D t o B) All of the heavier elements are stable.

C) The range of the strong nuclear force is too short to hold them together.

D) The heavier elements can be made only in nuclear reactors.

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Figure 1 Nuclear disintegration model

The fragments each have radius r, mass m, and charge Q. Immediately after separation, their centers are separated by 2r. There is a large electrical repulsion between these two fragments that causes them to move apart and gain kinetic energy. The repulsive force between the two nuclei is kQ2/d2, where k is Coulomb’s constant and d is the distance between the centers of the nuclei. The potential energy of the system of charged nuclear fragments is

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3. Which of the following graphs best illustrates how the force between fragments from the fission of a uranium nucleus varies as the fragments move away from each other? A)

4. A nucleus splits into two fragments that have equal charge but unequal mass. Which of the following is equal for the two fragments as they move apart? A) Magnitude of the force of one fragment on the other B) Magnitude of acceleration C) Speed D) Kinetic energy

B)

C)

D)

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Passage II The Global Positioning System or “GPS” is based on satellite radio ranging. A transmitter aboard each of the 24 satellites sends out a radio signal that specifies the precise position of the satellite and the precise time the signal was sent. The position is known from accurate tracking by ground stations and the laws of orbital mechanics, while synchronized cesium clocks aboard each GPS satellite provide very accurate timing. Each satellite has a mass of 1000 kg and orbits Earth in a circle = 1.8 × 107 m above the surface of Earth (2.4 × 107 m from the center of Earth). It takes 12.4 hours to complete this orbit.

6. How much current from a Ni-Cd battery is drawn by a radio transmitter that requires 3.96 W? A) 1/9 A B) 1/3 A C) 3 A D) 9 A 7. What beat frequency is detected in a receiver on Earth from the two GPS radio signals used to correct for atmospheric effects? A) 0.7 × 106 Hz B) 1.4 × 106 Hz

The atomic clock is powered with a 5-g radioactive Cs source. The transmitter is powered by a 1.32-V nickel-cadmium battery. A radio receiver on Earth can be used to calculate the distance to the satellite by measuring the time difference between the broadcast and reception because the signal travels at the speed of light (3.0 × 108 m/s). When the distances to several different satellites have been measured–at least four satellites are visible from anywhere on Earth at all times–the receiver position can be determined by triangulation. Timing corrections due to atmospheric effects are usually accounted for by broadcasting the GPS signals at two frequencies, one at 102.1 MHz and another at 104.9 MHz.

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D) 5.6 × 106 Hz 8. How many years will pass before there are 0.625 grams of Cs remaining in the source, if Cs has a half-life of 175 years?

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5. A high-altitude GPS satellite is kept in a circular orbit because Earth’s gravitational force: A) supplies the centrifugal force.

C) 2.8 × 106 Hz

A) 525 years B) 650 years C) 700 years

D) 1400 years

9. For a GPS satellite that is at an angle of 40o from Earth’s horizon, it takes 0.07 s for the radio signal to reach a receiver. The distance between the transmitter and the receiver is:

B) offsets the atmospheric drag force.

A) 2.1 × 107 sin 40° m.

C) offsets the moon’s gravitational force.

B) 2.1 × 107 m.

D) supplies the centripetal force.

C) 2.1 × 1011 cos 40° m. D) 2.1 × 1011 m.

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Passage III

10. The fundamental notes of a violin’s strings are at:

The physics of stringed instruments has been studied for almost as long as the instruments themselves have been played. The most studied stringed instruments are in the violin family. This family consists of four instruments: the violin, the viola, the cello, and the bass. Each of these instruments has four strings. The fundamental tones of these strings are separated by a perfect fifth, which means the fundamental frequency of each string is 2/3 that of the next higher frequency string. The tones are created when the bow is dragged across the strings, a move called bowing.

A) 98 Hz, 65 Hz, 43 Hz, 29 Hz.

The violin is the most popular instrument in the family. Its strings are tuned with decreasing frequency to the notes E, A, D, G, where A has a frequency of 440 Hz. The strings of the viola are at A, D, G, C. The cello is tuned one octave below the viola, which means the frequencies of the cello strings are half that of the viola strings. Finally, the bass is tuned two perfect fifths below the cello.

C) 440 Hz, 293 Hz, 196 Hz, 130 Hz. D) 660 Hz, 440 Hz, 293 Hz, 196 Hz. 11. A good violin body is one that has good resonance at the fundamental frequencies of: A) the middle strings. B) the highest frequency string. C) the lowest frequency string. D) all the strings. 12. The fundamental frequency of the A string on a cello is: A) 110 Hz.

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The fundamental frequency f of a string is given by its length L, tension T, and mass per unit length ρ as f= (T/ρ)1/2/(2L).

Scientists have studied in great detail how violins produce sound. The best violins produce loud tones over the full frequency range of the instrument, whereas poor instruments do not. Minor changes in the thickness and density of the wood can produce significant differences in an instrument’s sound. Despite much research, scientists have not been able to create violins that sound as pure and clear as those of the great violinmaker Stradivarius. It seems that despite all our scientific advances, there is still much to learn about these musical instruments.

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B) 220 Hz, 147 Hz, 98 Hz, 65 Hz.

B) 220 Hz. C) 440 Hz.

D) 880 Hz.

13. A way to make lower-toned instruments would be to use: A) heavier wood in the violin. B) thicker wood in the violin.

C) heavier strings on the violin. D) denser wood in the violin.

14. By what factor would a string’s tension need to be changed to raise its fundamental frequency by a perfect fifth? A) 2/3 B) (2/3)1/2 C) 3/2 D) 9/4

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Passage IV The detection of low-frequency pressure waves in stars, infrasonic waves, offers astronomers an insight into stellar structure. Such waves are observed in the Sun (with frequencies around 3.3 × 10–3 s–1) and are now being detected in large, bright nearby stars. In one method of detecting them, one looks for Doppler shifts in light emissions; the Doppler-shifted light shows periodicities typical of the pressure waves producing the motion. The pressure waves can be likened to standing waves in a pipe open at both ends, and an inner layer of the star can be taken as a large number of neighboring, outwardly directed columns of gas— much like a collection of pipes. The relationships derived for ordinary pipes are then useful. In a gas of density  and bulk modulus B, the harmonic frequencies fn for a pipe of length L are given by

15. In the newer observational technique discussed, one makes use of the fact that: A) the hydrogen gas in the observed stellar atmospheres is completely ionized. B) stellar atmospheres are open to space, so that pressure and temperature are independent of volume. C) pressure waves in stars propagate upward very slowly, generally at about 1 m/s. D) light is absorbed or emitted whenever electrons move from one energy level to another. 16. A collection of an unspecified number of neighboring gas columns, or pipes, can reasonably be used to represent the layer of a star in which pressure waves occur because the:

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where n = 1, 2, 3, . . . , the speed of sound vs is

and the constant B is defined in terms of pressure and volume changes

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level 3, which is associated with light of wavelength 0.6563 × 10–6 m.

A) harmonic frequencies of a pipe are independent of its diameter. B) harmonic frequencies of a pipe are independent of its length. C) speed of sound in gas confined to a pipe is independent of gas density.

D) speed of sound propagating upward against gravity decreases with height.

Observations are difficult because of the small velocity changes in the gas, about 1 m/s, associated with the pressure waves. One needs abundant data (large, bright stars) to separate the Doppler shifts due to pressure waves from those of thermal origin. A new, different observational technique may help. Stellar atmospheres are mostly hydrogen atoms, and many are in an excited state—the electron in energy level 2. The fraction in level 2 is extremely temperature sensitive, increasing as T 6. So slight pressure changes vary the intensity of light at the wavelengths associated with transitions into or out of level 2. These, in fact, are mostly from level 2 to

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17. As an aid in identifying the various resonant pressure-wave frequencies in the Sun and stars, one can use the fact that: A) the Doppler-shifted light is easily recognized, being polarized in a way that is characteristic of hydrogen. B) the Doppler-shifted light stands out, being steadier in intensity than the unshifted light emissions that accompany it. C) resonant frequencies are always separated by increments that are equal to a basic number multiplied by an integer. D) resonant frequencies in hydrogen gas depend strongly on its degree of gas ionization, which, in turn, depends on temperature.

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Passage V The eye can detect wavelengths that range from 400 nm to 700 nm, where 1 nm = 10–9 m. The color of this visible light ranges from violet at 400 nm to red at 700 nm. This range closely matches the wavelength range of maximum emission from the sun. The relationship between the wavelength of light and the energy of each quantum is E = hc/λ, where h is Planck’s constant, c is the speed of light in a vacuum, and λ is the wavelength. Another form of this equation is E = 1,240/λ, where λ is in nm and E is in eV (electron volts). Light can be emitted when atoms make transitions from excited states to lower-energy states. Each quantum of emitted light carries energy equal to the difference between the energies of the states involved. For the emitted light to be visible, it is necessary that the states involved be separated by the proper energies. Visible light arises from atomic transitions between energy levels separated by approximately 1.78 to 3.10 eV. For example, assume that the energy levels of a hypothetical atom are the following: Energy Level 5 Energy Level 4 Energy Level 3 Energy Level 2 Energy Level 1

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18. The most intense wavelength emitted by the sun is 480 nm. What is the approximate temperature of a blackbody that emits its most intense radiation at the same wavelength? A) 4,100 K B) 6,000 K C) 7,200 K D) 9,000 K 19. A blackbody appears white when its temperature is approximately 6,000 K. Which of the following statements explains the color of light emitted at this temperature? A) The object is not hot enough to emit red light. B) The object is too hot to emit blue light. C) White light is the most common wavelength being emitted.

e t u b i r t s i D t o –0.8 eV –1.5 eV –4.1 eV –6.3 eV –15.6 eV

Energy will be emitted when an atom makes a transition from a higher to a lower energy level, but visible light will result only when those energies fall within the prescribed range.

Light is also emitted from a hot object by a process called blackbody radiation. The most intense wavelength of blackbody radiation is given by Wien’s displacement law, λ = 2.9 × 106/T, where T is in kelvins and λ is in nm.

D) The object is emitting some light from all colors of the visible spectrum.

20. What is the maximum number of emission lines of visible light that could be observed in the spectrum of the hypothetical atom described in the passage? A) 1 B) 2 C) 5

D) 6 21. As the power input to a light bulb decreases, the brightness decreases. How does the color of the emitted light change? A) The emitted spectrum shifts to longer wavelengths. B) The emitted spectrum shifts to shorter wavelengths. C) The spectrum narrows around the original predominant color. D) The spectrum does not change.

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These questions are not based on a descriptive passage and are independent of each other. 22. Suppose that a ball is thrown vertically upward from earth with velocity v, and returns to its original height in a time t. If the value of g were reduced to g/6 (as on the moon), then t would: A) increase by a factor of 6.

24. Which of the following statements best explains why the intensity of sound heard is less when a wall is placed between a source of sound and the listener? A) Sound travels more slowly in a solid than in air. B) The frequency of sound is lower in a solid than in air. C) Part of the sound energy is reflected by the solid.

B) increase by a factor of 61/2.

D) The wavelength of sound is shorter in a solid than in air.

C) decrease by a factor of 6. D) decrease by a factor of 61/2. 23. A solid body can be in rotational equilibrium only when: A) it has zero angular momentum.

25. When a downward force is applied at a point 0.60 m to the left of a fulcrum, equilibrium is obtained by placing a mass of 10–7 kg at a point 0.40 m to the right of the fulcrum. What is the magnitude of the downward force?

B) it is in free fall.

A) 1.5 × 10–7 N

C) its external forces sum to zero.

B) 6.5 × 10–7 N

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D) its external torques sum to zero.

C) 9.8 × 10–7 N

D) 1.5 × 10–6 N

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Passage VI Retroreflecting arrays consist of spherical beads. Light is refracted as it enters a bead, then reflected off the back of the bead. Arrays of retroreflectors are attached to flexible sheets used as safety reflectors on clothing and bicycles. Ideal retroreflectors return a beam to its source regardless of the angle of incidence of the beam to it. Each light ray is returned on a path no farther than the diameter of a bead from the source ray. Thus, if a distortion that changes the path of light is placed in front of the retroreflecting array, the incident and the reflected rays will pass through the same distortion. When this occurs, the ray perfectly retraces itself, thereby canceling the distortion. An experiment is conducted with the setup illustrated in Figure 1. A light source covered by a screen with a pinhole in it provides a point source of light. A glass pane acts as a beam splitter. Some of the source light is reflected out of the experiment; the remainder of the light is incident upon the array. Some of the light returning from the array is reflected, at a right angle, to a viewing screen by the beam splitter. The wave front reflected from a retroreflecting array will be irregular. However, a pinhole image will still appear on the screen because the human eye cannot perceive the separation of the wave fronts.

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e t u b i r t s i D t o Figure 1

26. The beam splitter in Figure 1 is set at what angle to the incident beam? A) 15° B) 30° C) 45°

D) 60°

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27. Which of the following figures shows a possible path for a ray of light passing through a retroreflecting bead? (Note: Assume that the index of refraction of the bead is greater than that of air.)

28. The glass that is used as a beam splitter is replaced with glass that is identical except that it has a 10% higher index of refraction. Which of the following changes will occur to the pinhole image?

A)

A) It will move. B) It will become larger. C) It will become smaller. D) It will become more clear.

B)

29. What is the approximate number of wavelengths of light that can travel in 1 direction within a retroreflecting bead that has a diameter of 5 × 10–5 m? (Note: The speed of light = 3 × 108 m/s, and its frequency is approximately 1015Hz.)

C)

A) 0.6

D)

e t u b i r t s i D t o B) 1.7 × 102 C) 1.5 × 104

D) 3.3 × 106

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Passage VII A capacitor is a device that stores charge. The voltage V across a capacitor and the charge q on the capacitor are related by q = CV, where C is the capacitance measured in farads, F (1.0 F = 1.0 coulomb per volt). A student sets out to measure the capacitance using the circuit of Figure 1.

30. Which circuit elements store energy? I. Capacitors II. Resistors III. Batteries A) I only B) I and II only C) I and III only D) II and III only 31. The resistance of the variable resistor, R, at the beginning of the discharge process is: A) 2000 Ω. B) 3000 Ω.

Figure 1 Circuit for measuring capacitance

C) 4000 Ω.

In this circuit, the capacitor will be fully charged soon after switch S is closed to the left, as current passes through the small fixed resistor r in series with the capacitor C. Then, when S is switched to the right, the capacitor discharges through the variable resistor R. R is adjusted so that the discharge current, as measured by the ammeter, is constant during the discharge time.

D) 6000 Ω. 32. To keep the current constant during the discharge cycle:

e t u b i r t s i D t o A) the resistance R must be continually increased.

B) the resistance R must be continually decreased. C) the resistance r must be continually increased. D) the resistance r must equal R.

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Figure 2 The discharge current versus time

Figure 2 shows the current-versus-time plot during the discharge. The voltage of the battery used in the measurement was 12.0 V. The total charge q transferred to the capacitor can be estimated from the constant current value during the discharge time.

33. When switch S is closed to the left, charge begins to accumulate on the capacitor. Charge cannot accumulate indefinitely because: A) the variable resistor inhibits the current flow. B) the battery continually loses charge. C) successive charges brought to the plates are repelled by charges accumulated earlier. D) the fixed resistor loses energy to heat.

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34. As the capacitor is charged, the electrical potential energy that it gains: A) equals the work done by the battery throughout the charging process. B) is less than the work done by the battery throughout the charging process. C) is greater than the work done by the battery throughout the charging process. D) equals the potential energy stored in resistor r.

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Passage VIII

35. The frequency and period of the oscillatory motion:

To model thermal motion of atoms in solids, let us assume that each atom can oscillate about its equilibrium position. Interactions with neighboring atoms hold it in place allowing most motion in a single preferred direction marked by x in Figure 1. The effect of the neighboring atoms is described, for small oscillations, by two springs of length l as shown. We denote the atom’s mass by M. Each spring is characterized by the spring constant K, so that the restoring force it applies on the atom is K|x| in magnitude, and is opposite in direction to the displacement x. The potential energy of each spring is given by Kx2/2. An atom oscillates back and forth between its maximal displacements x = –A and A, with frequency f, where A is the amplitude of the motion. The time to complete one oscillation is the period T. Experimentally, such solids have internal energy nR(t + 273), where n is the number of moles in the sample, R = 8.3 J/(mol·oC) is the gas constant, and t is the temperature in oC. Usually, A < l; the solid melts when the amplitude increases to l. (Avogadro constant is N = 6 x 1023 per mole.)

A) have the same units. B) are proportional to each other. C) are equal. D) are the inverse of each other. 36. In the oscillatory motion of an atom described by the model, what quantity is conserved? A) Total energy B) Potential energy C) Linear momentum D) Angular momentum 37. The motion for small displacements × is characterized by two dimensional constants, K and M. Identify by dimensional argument the correct formula from which the period T can be calculated.

e t u b i r t s i D t o A) (T/π)2 = 4K/M B) (T/π)2 = 4K·M C) (T/π)2 = 4M/K

D) (T/π)2 = 4/(K·M)

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Figure 1 Model of an atom in a solid

38. What is the effective spring constant of the system of two springs shown in Figure 1? A) K

B) 2K C) K/2 D) 0

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Passage IX Scientists have recently discovered that a natural, uranium-powered fission reactor was in operation for approximately 300,000 years about 1.8 billion years ago. They estimated that 15,000 megawatt-years of energy was released, representing the consumption of 6 tons of the fissionable isotope 235U. The scientists first detected this phenomenon from a lower-thanusual 235U concentration in uranium ore in the natural reactor’s locale. The percentage of 235U to 238U presently averages 0.72% throughout the solar system. Since the half-life of 235U is shorter than that of 238U, this percentage decreases in time. The percentage was 3% 1.8 billion years ago. The minimum percentage of 235U to 238U for the operation of a plausible natural reactor is about 1%. Other important conditions for the operation of a natural reactor are concentration of uranium in the soil, size, and shape of the deposit; presence of low atomic mass elements (e.g., those in water) with which higherenergy fission neutrons may collide; and absence of elements that strongly absorb neutrons.

A) 100% B) 50% C) 33% D) 25% 41. Neutrons emitted during a fission event will either escape from the reactor assembly or be absorbed by reactor materials. Some of the absorbed neutrons may induce other fissions. A self-sustaining fission reaction requires that: A) no neutrons escape the reactor assembly. B) the reactor assembly have the optimum size and shape.

e t u b i r t s i D t o

The process of fission for a 235U nucleus begins with the absorption of a low-energy neutron. The nucleus then distorts, breaks into 2 unequal fragments and several neutrons, and releases energy. The radioactive fission fragments then decay, with halflives ranging from seconds to decades. The array of stable isotope fission products detected in the uranium ore, along with the corresponding depletion of the 235 U isotope, provided conclusive evidence of the existence of the ancient natural reactor.

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40. A fission neutron loses its kinetic energy through collisions. When a neutron in motion collides with a particle, what is the maximum percentage of its kinetic energy that can be transferred?

39. Modern nuclear reactors typically have several boron rods that can be inserted varying distances into the reactor. These rods control the rate of reaction by:

C) each fission produce at least 2 neutrons.

D) on average, 1 neutron per fission induce another fission.

42. A nuclear reactor operates most efficiently if its shape contains the minimum surface area for neutrons to escape for any specific volume. The most efficient reactor would be in the shape of a: A) cube.

B) sphere.

C) cylinder. D) slab.

A) producing neutrons. B) speeding up neutrons. C) reflecting neutrons. D) absorbing neutrons.

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Passage X Unlike other stars, the Sun is available for closeup examination. The density at the center of the Sun is 1.6 × 105 kg/m3, and the pressure is 1.4 × 1016 N/m2. These conditions give protons sufficient energy to overcome their mutual electrostatic repulsion. When the protons are ~1.0 × 10–16 m apart, they can undergo fusion: the conversion of two protons into deuterium followed by additional reactions that produce helium nuclei. The energy produced in this series of reactions gives the Sun a luminosity L =4 × 1026 J/s. In the conversion of 1000 kg of hydrogen, 993 kg of helium is produced, and 7 kg of matter is transformed into radiant energy (E = mc2) that eventually escapes the surface of the Sun as visible light. Thus, hydrogen fusion has an efficiency of η = 0.007. Satellites are used to observe the movement’s of the Sun’s surface. Doppler-shift analysis of light from the surface shows that the Sun vibrates in a variety of frequencies and modes, with the most common solar vibration having a period of 5 min. The speed of sound at a point in the Sun is proportional to the square root of the quotient of the local pressure divided by the local density.

A) Friction with the atmosphere heats it and causes an infrared glow. B) The flares carry light from the Sun and release it into the air. C) Solar flares cause lightning. D) Kinetic energy from the flare excites air atoms, which then emit visible light. 44. An electron of mass m and charge q in a solar flare bends in a circle while in Earth’s magnetic field B. What is the expression for the radius of the circle if the electron has a velocity v perpendicular to B. A) (mv)/(qB)

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Eruptions from the surface of the Sun can blast vast amounts of matter into space as solar flares. When protons and electrons from a flare arrive at Earth’s atmosphere, they produce a shimmering aurora.

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43. Which of the following statements best explains why solar flares produce auroras in Earth’s atmosphere?

5

(Note: The radius of the Sun is 7.0 × 10 km, its mass is 2.0 × 1030 kg, and the magnetic field at the surface is ~0.5mT. The speed of light in a vacuum is c = 3.0 × 108 m/s.)

B) (mq)/(vB)

C) (mv2)/(qB)

D) (mq2)/(vB)

45. If the pressure at the center of the Sun increases by a factor of 4 while the density decreases by a factor of 2, how will the speed of sound change? A) Increase by 21/2

B) Decrease by 21/2 C ) Increase by 81/2

D) Decrease by 81/2

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Passage XI The effectiveness of a tire is determined by its coefficients of kinetic and static friction under different road conditions. The coefficient of static friction is defined by µS = F(max static)/F(normal), and for kinetic friction µK = F(kinetic)/F(normal). The forces refer to the maximum static frictional force required to start a tire moving, the normal force exerted by the road supporting the tire, and the kinetic frictional force on a rolling tire. These coefficients are properties of the road and tire surfaces. The coefficients are measured in two experiments.

coming to rest. During the skid the speed decreases steadily for 2.00 s before the tire comes to rest. (Note: Approximate the acceleration due to gravity as 10 m/s2.) 46. What is the coefficient of static friction in Experiment 1? A) 1.5 B) 1500 C) 6000 N D) 7500 N

Experiment 1 A tire is mounted on a wheel whose axle is locked so that the tire cannot roll on the road. The axle carries weights to a total mass of 500 kg (axle plus wheel and tire) to simulate the load the tire would experience during normal use. A light rope pulls horizontally on the axle. During the experiment, the force on the rope is steadily increased until the tire begins to skid along the road without rotating. Once the tire starts to skid, the dragging force is reduced to the minimum needed to maintain a steady speed. Table 1 shows the pulling force versus time data for a measurement made on a dry road.

47. The initial translational kinetic energy of the wheel system in Experiment 2 (just before applying the brakes): A) is less than the magnitude of work required to stop the tire from skidding.

e t u b i r t s i D t o B) is equal to the magnitude of work required to stop the tire from skidding. C) is greater than the magnitude of work required to stop the tire from skidding.

D) cannot be determined from the information given.

Table 1 Data from Experiment 1

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Force (N) 0 1500 3000 4500 6000 7500 6000 6000 6000 6000

Experiment 2 The road conditions are the same as for Experiment 1 but the tire is now allowed to roll. At some instant the axle of the rolling tire is locked as if brakes were applied. The tire skids 24.0 m before

48. If a tire with a radius of 0.5 m is rolling with an angular frequency of 30 rad/s, how far will the axle travel in 2 s? A) 5 m

B) 10 m C) 20 m

D) 30 m 49. In Experiment 1, the acceleration of the hub of the tire during the first 4 s is: A) a nonzero constant in the direction of the frictional force. B) a nonzero constant in the direction of the pulling force. C) increasing steadily as the pulling force increases. D) constant and zero.

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These questions are not based on a descriptive passage and are independent of each other. 50. A 0.5 kg ball accelerates from rest at 10 m/s2 for 2 sec. It then collides with and sticks to a 1.0 kg ball that is initially at rest. After the collision, approximately how fast are the balls going?

52. Consecutive resonances occur at wavelengths of 8 m and 4.8 m in an organ pipe closed at one end. What is the length of the organ pipe? (Note: Resonances occur at L = nλ/ 4, where L is the pipe length, λ is the wavelength, and n = 1, 3, 5,…) A) 3.2 m

A) 3.3 m/s

B) 4.8 m

B) 6.7 m/s

C) 6.0 m

C) 10.0 m/s

D) 8.0 m

D) 15.0 m/s 51. A vertically oriented spring is stretched by 0.15 m when a 100 g mass is suspended from it. What is the approximate spring constant of the spring?

53. Suppose that a stream of fluid flows steadily through a horizontal pipe of varying crosssectional diameter. Neglecting viscosity, where is the fluid pressure greatest?

A) 0.015 N/m

A) At the intake point

B) 0.15 N/m

B) At the point of maximum diameter

C) 1.5 N/m

C) At the point of minimum diameter

D) 6.5 N/m

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e t u b i r t s i D t o D) At the point of maximum change in diameter

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Passage XII Three balls with the same volume of 1.0 x 10–6 m3 are in an open tank of water that has a density (ρ) of 1.0 x 103 kg/m3. The balls are in the water at different levels, as shown in the figure below. Ball 1 floats in the water with a part of it above the surface, Ball 2 is suspended in the water, and Ball 3 rests on the bottom of the tank. Any movement of the water obeys Bernoulli’s equation:

where P1 and P2 are the pressures, and v1 and v2 are the speeds of the water at elevations y1 and y2. (Note: Assume acceleration due to gravity (g) equals 9.8 m/s2. Unless otherwise noted, the water and balls are stationary.)

55. Ball 2 is in the water 20 cm above Ball 3. What is the approximate difference in pressure between the 2 balls? A) 2 × 102 N/m2 B) 5 × 102 N/m2 C) 2 × 103 N/m2 D) 5 × 103 N/m2 56. Assume that the side of the water tank is punctured 5.0 m below the top of the water, and that atmospheric pressure is 1.0 × 105 N/m2. What is the approximate speed of the water flowing from the hole? A) 10 m/s B) 12 m/s C) 14 m/s D) 17 m/s

e t u b i r t s i D t o 57. Assume that the density of Ball 1 is 8.0 × 102 kg/m3. Ignoring the atmospheric pressure, what fraction of Ball 1 is above the surface of the water? A)

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54. The densities of the balls, D1, D2, and D3, are related by which of the following? A) D1 < D2 < D3 B) D1 < D2 = D3

B) C)

D)

C) D1 = D2 < D3

D) D1 = D2 > D3

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Passage XIII The speed (v) of blood flowing through an artery can be measured by the electromagnetic flowmeter shown in Figure 1.

59. An artery is constricted at one location to 1/2 its normal cross-sectional area. How does the speed of blood past the constriction compare to the speed of blood flow in the rest of the artery? (Note: Assume ideal fluid flow.) A) It is 1/4 as fast. B) It is 1/2 as fast. C) It is 2 times as fast. D) It is 4 times as fast. 60. Which of the following describes the direction of the magnetic force on an ion moving in an artery past a flowmeter?

Figure 1 Electromagnetic flowmeter The flowmeter utilizes a magnet to apply a magnetic field (B) across an artery. This field produces magnetic forces (Fm) that cause the positive and negative ions in the blood to move to opposite sides of the artery. The segregation of charges creates an electric field (E) within the artery. The artery acts like a parallel plate capacitor with plate separation equal to the diameter (d) of the artery. The voltage across the artery (V) is measured by the meter in Figure 1 and is equal to Ed. The electric field produces an electric force (Fe) on the ions that acts in the direction opposite of Fm. Charges continue to accumulate until an equilibrium condition occurs when Fe = Fm. At equilibrium v = V/Bd.

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A) Parallel to both the direction of v and the direction of B B) Parallel to the direction of v and perpendicular to the direction of B C) Perpendicular to the direction of v and parallel to the direction of B

e t u b i r t s i D t o

58. Which of the following will occur when the magnet used in the flowmeter discussed in the passage is replaced with a stronger magnet?

D) Perpendicular to both the direction of v and the direction of B

61. What is the volume flow rate of blood that moves at 0.20 m/s through an artery with a diameter of 1.0 × 10–2 m? A) 5.0 × 10–6 m3/s B) 5π × 10–6 m3/s C) π × 10–5 m3/s

D) 2π × 10–5 m3/s

A) The electric field will reverse polarity. B) The electric field will decrease. C) The voltage will increase. D) Blood will flow faster.

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Passage XIV A scientist uses an apparatus as sketched in Figure 1 to measure the relative amounts of different nuclear isotopes in a sample. Atoms are ionized by removing electrons. A short pulse of ionized atoms is injected into the region between two accelerating plates. The plates are separated by a distance d, and have a voltage V between them. When an ion of charge Q and mass M is accelerated in this region, it acquires a kinetic energy equal to the product of its charge and the accelerating voltage Mv2/2 = QV with v being the ion velocity.

e t u b i r t s i D t o Figure 1 Isotope spectrometer

The ion then travels a distance to the end of the apparatus where a detector records its arrival time relative to the injection time. Isotopes of an element have different velocities and consequently arrive at the detector at different times. A sample of lithium atoms was measured. Figure 2 shows a spectrum of the number of ions detected versus their time of flight. The location of each peak depends on the mass and charge of the ion. Peaks 3 and 4 are the peaks expected for the two, singly-ionized isotopes of lithium, 6Li+ and 7Li+, respectively.

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Figure 2 Time-of-flight spectrum

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62. The 6 in 6Li refers to:

64. In order to accelerate the ions in the correct direction, the electric field in the region between the two plates of the device in Figure 1 should be directed toward:

A) the number of protons. B) the number of neutrons. C) the number of protons plus the number of neutrons.

A) the top of the figure.

D) the number of protons minus the number of neutrons.

C) the left of the figure.

B) the bottom of the figure. D) the right of the figure.

63. Which peaks in Figure 2 correspond to the doubly-ionized lithium isotopes? A) 2, 3 B) 2, 4

65. A decrease in the voltage between the two plates in the device would cause what change in the measured times-of-flight? A) Measured times would increase for each peak.

C) 1, 3

B) Measured times would decrease for each peak.

D) 1, 2

C) Times for some peaks would increase; times for others would decrease. D) Measured times would not change.

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Passage XV Three common types of radioactive decay are discussed below. Alpha Decay

66. Which of the following describes the direction of motion of alpha, beta, and gamma rays in the presence of an external magnetic field? A) They all travel straight. B) They are all bent in the same direction.

Some heavy nuclei can spontaneously emit alpha particles (α), which are helium nuclei that consist of 2 neutrons and 2 protons. The process for decay of plutonium-238 to uranium-234 is written schematically as

C) Gamma rays travel straight; alpha and beta rays are bent in the same direction. D) Gamma rays travel straight; alpha and beta rays are bent in opposite directions. 67. A radioactive series begins with

and has an

intermediate product of . Which of the following describes a possible sequence of particle emissions that occurs between these two atoms?

The alpha particle has a mass of 4 atomic mass units (amu), or 6.6 × 10–27kg, and carries a charge of +2 electronic charge units. Beta Decay

A) Beta, beta, beta, beta

A beta particle (β) is an energetic electron. A typical beta decay is illustrated by the decay of chlorine to argon.

B) Alpha, beta, beta, beta

e t u b i r t s i D t o C) Alpha, alpha, beta, beta D) Alpha, beta beta

where is an antineutrino, an additional particle created in the decay.

Beta particles are emitted over a range of energies. The maximum energy is called the endpoint energy and is determined by the relative energies of the states of the nuclei involved. For beta particles less energetic than the endpoint energy, the excess energy is carried away by the antineutrino. The net effect of beta decay in the nucleus is to replace a neutron with a proton.

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68. A sample of radiosodium ( ) has a half-life of 15 hr. If the sample’s activity is 100 millicuries after 24 hr, approximately what must its original activity have been? A) 200 millicuries B) 300 millicuries C) 600 millicuries

D) 1,000 millicuries

Gamma Rays Gamma rays are very high energy photons that have no rest mass and no charge. They are emitted by excited nuclei in their transition to lower-energy nuclear levels. (Note: proton mass = 1.0073 amu; neutron mass = 1.0087 amu; electron rest mass = 9.11 × 10–31 kg; energy equivalent of 1 amu = 931 MeV (million electron-volts); 1 eV = 1.6 × 10–19 J)

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69. In a radioactive series, a nucleus decays through several steps. The thorium series starts with a atom, then emits 1 alpha, 2 beta, 4 alpha, 1 beta, 1 alpha, and 1 beta, in succession. The final product of the series is:

70. When a nucleus emits a 2.5 MeV gamma ray, by how much does the nuclear mass decrease? A) 2.8 × 10–28 kg B) 1.2 × 10–28 kg

A)

C) 4.4 × 10–30 kg

B)

D) 8.6 × 10–31 kg

C) D)

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Passage XVI

72. What is the post-collision speed of cars A and B after the no-spring inelastic collision?

Cars are subjected to many forces as they move: air drag, tire-road friction, engine motive force, gravity, and other factors. Unfortunately, collisions occasionally occur. During such accidents, a (potentially large) fraction of the kinetic energy is rapidly and irreversibly converted to thermal energy and deformation of the car structure. Test crashes with dummy drivers and passengers and other experiments help designers develop safer vehicles. In one test, two 1000-kg cars, A and B, are initially 100 m apart. They are traveling on a highway in the same direction: car A at 30 m/s, car B at 20 m/s with car B ahead of car A. Eventually they collide. In one case the collision is cushioned by a spring (with constant k = 105 N/m) on the front of car A. In a second case there is no spring and the body deformation of the two cars absorbs the collision energy. (Assume g = 10 m/s2 when needed.)

A) 0 m/s B) 20 m/s C) 25 m/s D) 50 m/s 73. Two cars, each of mass 1000 kg traveling at 20 m/s in opposite directions, have a head-on inelastic collision. How much heat and deformation energy is produced? A) 2 × 105 J B) 4 × 105 J C) 8 × 105J D) 16 × 105 J 74. Consider the difference in crash deceleration on a test dummy in two test cases.

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71. How long before test car A overtakes car B? A) 2 s B) 3.33 s C) 5 s D) 10 s

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Case I: The dummy hits the steering wheel at 20 m/s and stops in 0.1 s. Case II: The dummy hits an air bag at 20 m/s and stops in 0.25 s. What is the ratio of the average acceleration in Case II to that in Case I?

A) 0.25 B) 0.40 C) 2.5 D) 4.0

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Passage XVII

75. Which of the following diagrams best represents the magnetic field created by the current?

An electromagnetic railgun is a device that can fire projectiles by using electromagnetic energy instead of chemical energy. A schematic of a typical railgun is shown below.

A)

B)

The operation of the railgun is simple. Current flows from the current source into the top rail, through a movable, conducting armature into the bottom rail, then back to the current source. The current in the 2 rails produces a magnetic field directly proportional to the amount of current. This field produces a force on the charges moving through the movable armature. The force pushes the armature and the projectile along the rails.

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D)

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The force is proportional to the square of the current running through the railgun. For a given current, the force and the magnetic field will be constant along the entire length of the railgun. The detectors placed outside the railgun give off a signal when the projectile passes them. This information can be used to determine the exit speed and kinetic energy of the projectile. Projectile mass, rail current, and exit speed are listed below. Projectile Mass (kg) 0.01 0.01 0.02 0.04

C)

Rail current (A) 10.0 15.0 10.0 10.0

Exit Speed (km/s) 2.0 3.0 1.4 1.0

76. Starting from a resting position at the right end of the railgun, the armature applies a constant force of 3.0 N to a projectile with a mass of 0.06 kg. How long will it take for the projectile to move 1.0 m? A) 0.02 sec B) 0.04 sec C) 0.20 sec D) 0.40 sec

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77. If a projectile leaves a railgun near the surface of Earth with a speed of 2.0 km/s horizontally, how far will it fall in 0.01 sec? A) 4.9 × 10–4 m

78. If a projectile with a mass of 0.1 kg accelerates from a resting position to a speed of 10 m/s in 2 sec, what is the average power supplied by the railgun to the projectile?

B) 4.9 × 10–2 m

A) 0.5 W

C) 9.8 × 10–2 m

B) 2.5 W

D) 2.0 × 101 m

C) 5.0 W D) 10.0 W

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These questions are not based on a descriptive passage and are independent of each other.

81. A square-wave voltage signal is sent into a resistor-capacitor circuit as shown.

79. In a healthy person standing at rest, a comparison of arterial blood pressure measured in the arm with that measured in the leg shows that the pressure in the leg is: A) lower, because the blood flow rate is less. B) lower, because viscous flow resistance causes pressure loss. C) the same, because viscous pressure loss precisely compensates the hydrostatic pressure increase. D) greater, because the column of blood between the arm and the leg has a hydrostatic pressure.

Which plot gives the typical voltage response between points A and B? A)

80. The intensity level of Sound B is 20 dB greater than the intensity level of Sound A. How many times greater is the intensity level of Sound B than the intensity level of Sound A? A) 2 B) 10 C) 20 D) 100

e t u b i r t s i D t o B)

C)

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D)

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82. A force F is used to raise a 4-kg mass M from the ground to a height of 5 m.

What is the work done by the force F? (Note: sin 60o = 0.87; cos 60o = 0.50. Ignore friction and the weights of the pulleys.) A) 50 J B) 100 J C) 174 J D) 200 J

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Passage XVIII Mercury, the innermost planet, moves in an elliptical orbit. The point in the orbit where Mercury is closest to the Sun is called the perihelion point. In the midnineteenth century, scientists observed that the perihelion point advances, or precesses, around the Sun at a rate of about 500 arcsec/century. The perihelion points, PA and PB, for two successive orbits, A and B, respectively, of Mercury are shown in Figure 1. (Note: The figure is not drawn to scale.)

involved the existence of a planet, called Vulcan, with an orbit closer to the Sun than Mercury's. Other planets were proposed to exist in orbits between those of Mercury and Venus. Neither Vulcan nor these other planets have been shown to exist.

83. A radar signal is transmitted to Mercury from Earth. The signal is reflected and returns to Earth with a frequency that is 1.3 × 106 cycles/sec higher than that of the transmitted signal. The frequency change is best explained by which of the following? A) Mercury was moving toward Earth at the time of the experiment. B) Mercury was moving away from Earth at the time of the experiment. C) Mercury was moving neither toward nor away from Earth at the time of the experiment.

e t u b i r t s i D t o D) Mercury is not rotating.

84. Some scientists have proposed that Ω will be affected if the diameter of the Sun at its equator is larger than that measured between the Sun's poles. This equatorial bulge would most likely be caused by the:

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Figure 1 Perihelion precession of Mercury's orbit

Recently, radar signals were used to find the rate of precession, Ω, of the perihelion point. Signals with a frequency of 7.8 x 109 cycles/sec were transmitted from Earth to Mercury, where they were reflected back to Earth. Based on the time required for the signals to make the round-trip, scientists verified that Ω ≈ 500 arcsec/century.

Scientists in the nineteenth century attempted to explain the precession on the basis of Newton's theory of gravitation. Taking into account the gravitational effects of the planets known to be in the solar system, Newton's theory gave a value of Ω that was smaller than the observed value by an amount Ωs ≈ 43 arcsec/century. To account for Ωs, other hypotheses were proposed that still employed the Newtonian theory of gravitation. One of the earliest hypotheses

A) Sun's rotation.

B) high-pressure gases in the Sun's core.

C) temperatures at the Sun's core being higher than those on the surface. D) hydrogen in the Sun's atmosphere.

85. Based on the information in the passage, how many centuries will be required for Mercury's perihelion to precess 360o? A) (360/60) × (60 × 500) B) 360 × (60/60) × 500 C) 360 × 60 × (60/500) D) 360 × 60 × 60 × 500

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86. Assume that the major axis (the length) and the eccentricity (the ratio of the length to the width) of Mercury's orbital ellipse are both constant over time. As Mercury's perihelion precesses, the figure traced by the perihelion point is a:

87. At one point in its orbit, Venus is about 5 × 1010 m from Earth. If the motions of Venus and Earth are NOT included, a radar signal will make the round-trip between the 2 planets in approximately how much time?

A) circle.

A) 50 sec

B) hyperbola.

B) 300 sec

C) parabola.

C) 500 sec

D) sphere.

D) 3,600 sec

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Passage XIX The head of a comet in orbit around the sun consists of a solid nucleus, typically of radius 10–100 km, surrounded by a tenuous cloud of dust particles and gas. This cloud, or “coma,” conceals the interior of the nucleus so that its size and nature can only be inferred. There are two models of cometary nuclei: (1) a rubble pile, a loose agglomeration of rocks and gravel, or (2) a dirty snowball, bits of rock held in a matrix of frozen H2O, CH4, and NH3, called ices. Calculations based on Newton’s law of gravity do not predict cometary orbits precisely. There are unanticipated slight deviations in their orbits. These deviations imply that nongravitational forces are also involved. The dirty-snowball model nicely explains these effects: Sunlight warms the surface of the nucleus, causing the various frozen solids to sublimate, i.e., go directly from the solid phase to the vapor phase without passing through the liquid phase. As the gases leave, they exert perturbing forces on the cometary nucleus–much as an attached rocket engine would.

A) The law of inertia (Newton’s 1st law) B) The law relating force, mass, and acceleration (Newton’s 2nd law) C) The law relating action and reaction (Newton’s 3rd law) D) The law of gravitation (Newton’s inverse-square law) 89. A dirty-snowball cometary nucleus would be expected to disintegrate less readily in the atmosphere of Jupiter than a rubble-pile nucleus of the same mass would because: A) a rubble-pile nucleus has only gravitational forces to hold it together. B) a rubble-pile nucleus would be incapable of inelastic collisions.

e t u b i r t s i D t o

The rubble-pile model does not explain the orbital deviations; therefore it has generally been abandoned. However, when Comet Shoemaker-Levy 9 struck Jupiter in July 1994, the theory was revived. The cometary fragments exploded considerably higher in the atmosphere of the planet than predicted by the dirty-snowball model, suggesting that the nucleus of the comet was not very cohesive.

N Do

88. The perturbing force resulting from sublimation in the dirty-snowball model is accounted for directly by which of Newton’s laws?

Comets become visible to the unaided eye when, under the influence of radiation and the steady outstreaming of ionized hydrogen from the sun (the solar wind), the coma forms and extends into a vast, long tail of gas and dust. However, nearly all of the mass of the comet remains concentrated in the nucleus.

C) a dirty-snowball nucleus initially would have a lower temperature.

D) a dirty-snowball nucleus would be incapable of inelastic collisions.

90. In the dirty-snowball model, does the perturbing force on the comet due to sublimation act in any preferred direction? A) No, because the nucleus tends to have a roughly spherical surface

B) No, because the sun radiates with equal intensity in all directions C) Yes, more or less outward from the sun because of shadowing effects D) Yes, more or less toward the sun because of the temperature gradient

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91. Because comets shine predominantly by reflected sunlight, what one sees when viewing a comet is: A ) the coma gas. B) the coma dust. C) the tail gas. D) the ices.

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Figure 2

Passage XX Students in a physics class measure the tension T in a pendulum string, Figure 1.

Time dependence of the string tension of a swinging pendulum

In the small angle approximation (sin ≈) the tension in units of the weight of the bob is given by T/mg = o2cos2 t + cos(osin  t) where o is the amplitude of the swing and  is the angular frequency, in rad/s, of the pendulum. Use g = 10 m/s2 when needed. A strain gauge is used as the force sensor at point P. This device is based on the fact that the resistance of metals and semiconductors varies with the external pressure or force exerted on them. A change in the resistance of a strain gauge can be measured accurately by using a Wheatstone bridge, Figure 3, in which the voltage V changes when RSG changes.

Figure 1

Pendulum variables and forces

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The tension arises from two sources: the component of the weight of the bob mg in the direction of the string and the centrifugal force FC, which is the reaction force to the centripetal force on the bob causing it to move along a circular arc of radius L. A force sensor at the pivot point P gives a voltage output proportional to the tension as a function of time, Figure 2.

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Figure 3

Wheatstone bridge

92. If all the resistors in Figure 3 are 200 Ω, what is the current from the battery when V0 = 12 V? A) 30 mA B) 60 mA C) 120 mA D) 240 mA

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93. What mechanism supplies the tension in the string at the molecular level?

95. What is the expression for the angular frequency  of a pendulum?

A) Magnetic forces

A) 2πmg/L

B) Electron transfer

B) (L/g)1/2

C) Gravitational forces

C) 2π(g/L)1/2

D) Stretching bond lengths

D) (g/L)1/2

94. What is the magnitude of the restoring force on the pendulum bob at angle ? A) mg B) mgsin C) mgcos D) mgtan

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Passage XXI

96. 55. How will W change if the initial speed of the box at Point A is increased by a factor of 2?

A factory that operates on 2 levels needs a quick method of transporting boxes from the upper level to the lower level. A ramp designed to accomplish this is shown on a 2-dimensional coordinate system in Figure 1. Point O is the origin of the coordinate system, i is the unit vector in the x direction, and j is the unit vector in the y direction. The ramp is designed at a 45° angle.

A) W will decrease by 50%. B) W will not change. C) W will increase by 50%. D) W will increase by 100%. 97. Which of the following expressions is equal to a, the acceleration vector of the box as it moves from Point B to Point C? (Note: The coefficient of friction between the box and the surface between Point B and Point C is equal to μkh) A) (–g + μkh)i B) C) μkhgi D) –μkhgi

Figure 1

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A box with a mass of M is given an initial speed of vA down the ramp from Point A. It reaches Point B with a speed of vB and kinetic energy equal to Mgd, where d is the height of the ramp and g is the acceleration due to gravity. After reaching Point B, the box travels on a flat surface and stops at Point C, a distance of L from Point B. The speed (v) of the box as a function of time (t) is shown in Figure 2, where t = 0 at Point A, t = tB at Point B, and t = tC at Point C. (Note: The work done by friction on the box as it travels down the ramp is equal to W.)

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98. What physical quantity is represented by the area of quadrilateral OABC in Figure 2? A) Average speed of the box

B) Average acceleration of the box C) Distance traveled by the box D) Work done on the box

99. How will W change if the angle of the ramp to the horizontal is increased?

A) W will decrease, because the normal force to the surface of the ramp will decrease. B) W will not change, because the coefficient of friction between the box and the ramp will not change. C) W will not change, because the gravitational force is always constant and the length of the ramp is not changed. D) W will increase, because the height from which the box falls increases.

Figure 2

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Passage XXII Some students built an electric motor from these items: a large U-shaped magnet, a 250-cm long wire with a square cross section (1 mm per side), a set of contact plates, a battery with an EMF of VB, a switch S, and some leads. The wire was wound into a rectangular loop of 10 turns (r = 5 cm, L = 2 cm, Rloop = 2.5 Ω) and attached to a shaft mounted between the north (N) and south (S) poles of the magnet as shown in Figure 1; the wire’s ends were extended along the shaft to reach the contact plates.

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e t u b i r t s i D t o Figure 1 Electric Motor Apparatus

The shaft was mounted on bearings (not shown), allowing it to spin around its long axis. When the battery was directly connected to the loop (not the contact plates), the loop oscillated around a fixed angular position. With the current flowing as in Figure 1a, the students realized the forces FB (Figure 2) turned the loop.

Figure 2 Forces on the loop as seen from Figure 1b’s perspective

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The forces FB act perpendicular to B and to the current direction I with a magnitude FB = ILB sin Φ, with Φ (not shown) as the angle between the current direction and B. When wired to VB, the contact plates reversed the current’s direction after each half-rotation of the shaft, turning the loop continuously. Some experimental data using this electric motor appear in Table 1. Table 1 Loop’s Maximum Angular Speed vs Battery Voltage VB(V)

Maximum Angular Speed (rad/s) 1800 3600 5400

1.5 3.0 4.5

A 1.0-cm-diameter disk was then attached to the shaft’s end, and a cord was wrapped around the disk and connected to a mass M so that the motor could be used to lift M. During one trial with VB = 4.5 V and M = 0.20 kg, M was raised 20 cm in 5.0 s.

100. Given that the friction between the bearings and axle will slightly increase, which of the following changes would most likely be true of the motion of the loop and shaft if a solid disk of metal were attached to the end of the shaft? The loop and shaft with an attached disk would accelerate more:

101. Suppose the mass M described in the passage is lifted from rest at a constant acceleration a. The tension in the cord would then be closest to which of the following?

A) slowly and reach a lower maximum angular speed.

C) Mg + Ma

B) slowly but reach a higher maximum angular speed.

D) Mg – Ma

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C) quickly but reach a lower maximum angular speed.

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D) quickly and reach a higher maximum angular speed.

A) Mg B) Ma

102. If the loop wire were replaced with a similar wire having a square cross section measuring 2.0 mm per side, the resulting loop resistance would be closest to: A) 5.0 Ω B) 2.5 Ω C) 1.3 Ω D) 0.63 Ω

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Passage XXIII The study of the flight of projectiles has many practical applications. The main forces acting on a projectile are air resistance and gravity. The path of a projectile is often approximated by ignoring the effects of air resistance. Gravity is then the only force acting on the projectile. When air resistance is included in the analysis, another force, FR, is introduced. FR is proportional to the square of the velocity, v. The direction of the air resistance is exactly opposite the direction of motion. The equation for air resistance is FR = pv2, where p is a proportionality constant that depends on such factors as the density of the air and the shape of the projectile. Air resistance was studied by launching a 0.5 kg projectile from a level surface. The projectile was launched with a speed of 30 m/s at a 40° angle to the surface. (Note: Assume air resistance is present unless otherwise specified. Acceleration due to gravity is g = 9.8 m/s2; sin40° = 0.64; cos40° = 0.77)

104. Which of the following graphs best illustrates the relationship between the total speed of the projectile (v) and its horizontal distance from the launch point (x). (Note: Assume that the effects of air resistance are negligible and that the left axis represents the location of the launch point.) A)

B)

e t u b i r t s i D t o C)

103. If a 0.5 kg projectile is launched straight up and is given initial kinetic energy of 250 J, what will be the maximum height that the projectile will rise? (Note: Assume that the effects of air resistance are negligible.)

N Do A) 26 m B) 51 m

C) 102 m

D)

D) 204 m

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105. What is the approximate total kinetic energy of the projectile at the highest point in its path? (Note: Assume that the effects of air resistance are negligible.)

106. What is the magnitude of the horizontal component of air resistance on the projectile at any point during flight? (Note: v× = horizontal speed.)

A) 92 J

A) (pv2)cos 40°

B) 133 J

B)

C) 184 J C) (pv×2)sin 40°

D) 225 J

D) pv×2

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These questions are not based on a descriptive passage and are independent of each other. 107. Electric power for transmission over long distances is “stepped up” to a very high voltage in order: A) to produce currents of higher density. B) to produce higher currents in the transmission wires. C) to make less insulation necessary. D) to cut down the heat loss in the transmission wires.

108. A 0.5-kg uniform meter stick is suspended by a single string at the 30-cm mark. A 0.2-kg mass hangs at the 80 cm mark. What mass hung at the 10-cm mark will produce equilibrium? A) 0.3 kg B) 0.5 kg C) 0.7 kg D) 1.0 kg 109. An unknown solid weighs 31.6 N. When submerged in water, its apparent weight is 19.8 N. What is the specific gravity of the unknown sample? A) 2.96 B) 2.68 C) 2.02 D) 1.68

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Post-test Confidence Self-Assessment Congratulations! You have completed a test of The Official MCAT® Self-Assessment Package. Now that you have completed the test, reconsider your confidence rating of your knowledge of the content in this test. Has your confidence level changed after answering the questions? Why might this be? Both your initial and revised confidence ranking for each content category will be displayed in the analytic summary.

®

MCAT is a program of the Association of American Medical Colleges

Test/Content Categories

A=1-Not Confident at all

1. Physics Overall 2. Atomic and Nuclear Structure

N Do 3. Electrostatics and Electromagnetism

B=2Somewhat Confident

C=3Moderately Confident

D=4-Very Confident

E=5Extremely Confident

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4. Electronic Circuit Elements 5. Equilibrium and Momentum 6. Fluids and Solids 7. Force and Motion, Gravitation

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8. Light and Geometrical Optics 9. Sound 10. Translational Motion 11. Waves and Periodic Motion 12. Work and Energy

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Pre-test Confidence SelfAssessment 1 (A) (B) (C) (D) (E) 2 (A) (B) (C) (D) (E) 3 (A) (B) (C) (D) (E) 4 (A) (B) (C) (D) (E) 5 (A) (B) (C) (D) (E) 6 (A) (B) (C) (D) (E) 7 (A) (B) (C) (D) (E) 8 (A) (B) (C) (D) (E) 9 (A) (B) (C) (D) (E) 10 (A) (B) (C) (D) (E) 11 (A) (B) (C) (D) (E) 12 (A) (B) (C) (D) (E) Physics Questions 1 (A) (B) (C) 2 (A) (B) (C) 3 (A) (B) (C) 4 (A) (B) (C) 5 (A) (B) (C) 6 (A) (B) (C) 7 (A) (B) (C) 8 (A) (B) (C) 9 (A) (B) (C) 10 (A) (B) (C) 11 (A) (B) (C) 12 (A) (B) (C) 13 (A) (B) (C) 14 (A) (B) (C) 15 (A) (B) (C) 16 (A) (B) (C) 17 (A) (B) (C) 18 (A) (B) (C) 19 (A) (B) (C) 20 (A) (B) (C) 21 (A) (B) (C) 22 (A) (B) (C) 23 (A) (B) (C) 24 (A) (B) (C) 25 (A) (B) (C) 26 (A) (B) (C) 27 (A) (B) (C) 28 (A) (B) (C)

(D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D)

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29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 58 59 60 61 62 63 64 66 65 66 67 68 69 70 71 72

(A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A)

(B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B)

(C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C)

(D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D)

73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109

(A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A) (A)

(B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B) (B)

(C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C) (C)

(D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D) (D)

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Post-test Confidence SelfAssessment 1 (A) (B) (C) (D) (E) 2 (A) (B) (C) (D) (E) 3 (A) (B) (C) (D) (E) 4 (A) (B) (C) (D) (E)

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5 (A) (B) (C) (D) (E) 6 (A) (B) (C) (D) (E) 7 (A) (B) (C) (D) (E)

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8 (A) (B) (C) (D) (E) 9 (A) (B) (C) (D) (E) 10 (A) (B) (C) (D) (E)

11 (A) (B) (C) (D) (E) 12 (A) (B) (C) (D) (E)

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