Physics for Scientists & Engineers with Modern Physics (Volume 1) 5e (Global Edition) By Douglas C. Giancoli (Test Bank All Chapters, 100% Original Verified, A+ Grade) (36-44 Chapters Are Missing) Answers At The End Of Each Chapter Chapter 1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Estimation: Estimate the number of times the earth will rotate on its axis during a
human's lifetime. A) 3 × 107
B) 3 × 104
C) 3 × 106
D) 3 × 108
E) 3 × 105
2) Estimation: Approximately how many pennies would you have to stack to reach an
average 8-foot ceiling? A) 2 × 104 B) 2 × 103
C) 2 × 105
D) 2 × 106
1)
2)
E) 2 × 102
3) Scientific notation: 0.00325 × 10-8 cm can also be expressed in mm as
3)
A) 3.25 × 10-12 mm. B) 3.25 × 10-11 mm. C) 3.25 × 10-8 mm. D) 3.25 × 10-10 mm. E) 3.25 × 10-9 mm. 4) Significant figures: Add 3685 g and 66.8 kg and express your answer in milligrams
(mg). A) 7.05 × 104 mg C) 7.05 × 107 mg
B) 7.05 × 106 mg D) 7.05 × 105 mg
5) Estimation: The mass of a typical adult woman is closest to A) 150 kg.
B) 35 kg.
C) 20 kg.
5) D) 75 kg.
6) Metric system: Scientists use the metric system chiefly because it is more accurate than
the English system. A) True
6)
B) False
7) Significant figures: What is the product of 11.24 and 1.95 written with the correct
number of significant figures? A) 22 B) 21.9
C) 21.92
D) 21.918
B) 100 cm.
C) 500 cm.
1
7)
E) 21.9180
8) Estimation: The height of the ceiling in a typical home, apartment, or dorm room is
closest to A) 400 cm.
4)
D) 200 cm.
8)
9) Estimation: Approximately how many times does an average human heart beat in a
lifetime? A) 3 × 109
B) 3 × 108
C) 3 × 1011
D) 3 × 107
E) 3 × 1010
10) Conversion of units: If a woman weighs 125 lb, her mass expressed in kilograms is x kg,
where x is A) less than 125.
10)
B) greater than 125.
11) Significant figures: What is the sum of 1.53 + 2.786 + 3.3 written with the correct
number of significant figures? A) 8 B) 7.6
9)
C) 7.62
D) 7.616
E) 7.6160
12) Conversion of units: A plot of land contains 5.8 acres. How many square meters does it
contain? [1 acre = 43,560 ft2] A) 7.1 × 103 m2 B) 2.3 × 104 m2
C) 7.0 × 104 m2
12)
D) 5.0 × 104 m2
13) Conversion of units: If a flower is 6.5 cm wide, its width expressed in millimeters is x
mm, where x is A) less than 6.5.
11)
13)
B) greater than 6.5.
14) Significant figures: What is the result of 1.58 ÷ 3.793 written with the correct number of
14)
significant figures? A) 4.17 × 10-1 B) 4.2 × 10-1 C) 4.1656 × 10-1 D) 4.166 × 10-1 E) 4 × 10-1 15) Significant figures: What is 34 + (3) × (1.2465) written with the correct number of
significant figures? A) 38 B) 4 × 101
C) 37.7395
D) 37.7
E) 37.74
16) Conversion of units: If an operatic aria lasts for 5.75 min, its length expressed in seconds
is x s, where x is A) greater than 5.75.
15)
16)
B) less than 5.75.
17) Conversion of units: A weight lifter can bench press 171 kg. How many milligrams (mg)
is this? A) 1.71 × 108 mg C) 1.71 × 107 mg
B) 1.71 × 109 mg D) 1.71 × 106 mg
2
17)
18) Conversion of units: A certain CD-ROM disk can store approximately 6.0 × 102
18)
megabytes of information, where 106 bytes = 1 megabyte. If an average word requires 9.0 bytes of storage, how many words can be stored on one disk? A) 6.7 × 107 words B) 2.0 × 109 words C) 2.1 × 107 words
D) 5.4 × 109 words
19) Metric system: The current definition of the standard kilogram of mass is based on
19)
A) the mass of the earth. B) the mass of a cesium-133 atom. C) the mass of the sun. D) the mass a particular object kept in France.
in = 20) Conversion of units: The following exact conversion equivalents are given: 1 m = 100 cm, 120) 2.54 cm, and 1 ft = 12 in. If a computer screen has an area of 1.27 ft2, this area is closest to A) 0.118 m2. B) 0.284 m2. C) 0.00284 m2. D) 0.0465 m2. E) 4.65 m2. 21) Significant figures: The length and width of a rectangle are 1.125 m and 0.606 m,
21)
respectively. Multiplying, your calculator gives the product as 0.68175. Rounding properly to the correct number of significant figures, the area should be written as A) 0.6818 m2. B) 0.7 m2. C) 0.68 m2. D) 0.682 m2. E) 0.68175 m2. 22) Significant figures: What is the value of (8.104)2, written with the correct number of
significant figures? A) 206.3 B) 200
C) 206.323
D) 206
E) 206.324
23) Metric system: The current definition of the standard second of time is based on A) the duration of one year. B) the frequency of radiation emitted by cesium atoms. C) the oscillation of a particular pendulum kept in France. D) the earth's rotation rate.
3
22)
23)
24) Scientific notation: Write out the number 7.35 × 10-5 in full with a decimal point and
24)
correct number of zeros. A) 0.00000735 B) 0.0000735 C) 0.000735 D) 0.00735 E) 0.0735 25) Dimensional analysis: The period of a pendulum is the time it takes the pendulum to
25)
swing back and forth once. If the only dimensional quantities that the period depends on are the acceleration of gravity, g, and the length of the pendulum, , what combination of g and must the period be proportional to? (Acceleration has SI units of m s-2.). /g A) g B) g C) D) g E) g 2 26) Conversion of units: How many nanoseconds does it take for a computer to perform one
26)
calculation if it performs 6.7 × 107 calculations per second? A) 67 ns
B) 65 ns
C) 15 ns
D) 11 ns
27) Conversion of units: A person on a diet loses 1.6 kg in a week. How many
micrograms/second ( g/s) are lost? A) 6.4 × 104 g/s C) 1.6 × 105
B) 44
g/s
D) 2.6 × 103
g/s
27)
g/s
28) Significant figures: The number 0.003010 has
28)
A) 2 significant figures.
B) 6 significant figures.
C) 7 significant figures.
D) 4 significant figures.
29) Significant figures: What is 56 + (32.00)/(1.2465 + 3.45) written with the correct number
29)
of significant figures? A) 63 B) 62.81 C) 62.812 D) 62.8123846 E) 62.8 30) Conversion of units: The wavelength of a certain laser is 0.35 micrometers, where
1 micrometer = 1 × 10-6 m. Express this wavelength in nanometers. A) 3.5 × 103 nm B) 3.5 × 104 nm C) 3.5 × 101 nm
4
D) 3.5 × 102 nm
30)
31) Metric system: The current definition of the standard meter of length is based on
31)
A) the length of a particular object kept in France. B) the distance between the earth's equator and north pole. C) the distance between the earth and the sun. D) the distance traveled by light in a vacuum. 32) Dimensional analysis: The speed of a wave pulse on a string depends on the tension, F,
32)
in the string and the mass per unit length, , of the string. Tension has SI units of kg m s-2 and the mass per unit length has SI units of kg m-1. What combination of F and must the speed of the wave be proportional to? F /F A) F/ B) F / u C) / F D) E) 33) Conversion of units: If a tree is 15 m tall, its height expressed in feet is x ft, where x is A) greater than 15.
33)
B) less than 15.
34) Conversion of units: Convert a speed of 4.50 km/h to units of ft/min. (1.00 m = 3.28 ft)
34)
A) 246 ft/min B) 82.3 ft/min C) 0.246 ft/min D) 886 ft/min E) 165 ft/min 35) Significant figures: What is the difference between 103.5 and 102.24 written with the
correct number of significant figures? A) 1 B) 1.3 C) 1.26
D) 1.260
35)
E) 1.2600
36) Conversion of units: The exhaust fan on a typical kitchen stove pulls 600 CFM (cubic
36)
feet per minute) through the filter. Given that 1.00 in. = 2.54 cm, how many cubic meters per second does this fan pull? A) 0.328 m3/sec B) 32.8 m3/sec C) 0.283 m3/sec D) 3.05 m3/sec 37) Estimation: Approximately how many times does an average human heart beat in a year? A) 4 × 107
B) 4 × 106
C) 4 × 109
D) 4 × 108
E) 4 × 105
38) Scientific notation: Convert 1.2 × 10-3 to decimal notation. A) 1.200
B) 0.1200
C) 0.0120
D) 0.0012
38) E) 0.00012
39) Significant figures: Express (4.3 × 106)-1/2 in scientific notation. A) 2.1 × 10-5
B) 4.8 × 10-4
C) 2.1 × 103
5
37)
39) D) 2.1 × 104
40) Conversion of units: In addition to 1 m = 39.37 in., the following exact conversion
40)
equivalents are given: 1 mile = 5280 ft , 1 ft = 12 in , 1 hour = 60 min, and 1 min = 60 s. If a particle has a velocity of 8.4 miles per hour, its velocity, in m/s, is closest to A) 3.0 m/s. B) 3.4 m/s. C) 3.8 m/s. D) 4.1 m/s. E) 4.5 m/s. 41) Significant figures: What is the sum of 1123 and 10.3 written with the correct number of
41)
significant figures? A) 1.13 × 103 B) 1133.3000 C) 1133 D) 1.1 × 103 E) 1133.3 42) Conversion of units: The shortest wavelength of visible light is approximately 400 nm.
42)
Express this wavelength in centimeters. A) 4 × 10-5 cm B) 400 × 10-11 cm C) 4 × 10-9 cm D) 4 × 10-11 cm E) 4 × 10-7 cm 43) Estimation: A marathon is 26 mi and 385 yd long. Estimate how many strides would be
43)
required to run a marathon. Assume a reasonable value for the average number of feet/stride. A) 4.5 × 103 strides B) 4.5 × 106 strides C) 4.5 × 104 strides D) 4.5 × 105 strides 44) Dimensional analysis: The position x, in meters, of an object is given by the equation x =
44)
A + Bt + Ct2, where t represents time in seconds. What are the SI units of A, B, and C? A) m/s, m/s2, m/s3 B) m, s, s2 C) m, m/s, m/s2 D) m, m, m E) m, s, s 45) Significant figures: If, in a parallel universe,
has the value 3.14149, express
universe to four significant figures. A) 3.141 B) 3.1414
C) 3.142
in that
D) 3.1415
46) Estimation: Estimate the number of pennies that would fit in a box one foot long by one
foot wide by one foot tall. A) 5 × 105 B) 5 × 103
C) 5 × 104
6
45)
D) 5 × 102
E) 5 × 106
46)
47) Significant figures: What is 0.2052/3, expressed to the proper number of significant
figures? A) 0.35
B) 0.3477
C) 0.3
47)
D) 0.348
48) Significant figures: When determining the number of significant figures in a number,
48)
zeroes to the left of the decimal point are never counted. A) True B) False 49) Scientific notation: 0.0001776 can also be expressed as
49)
A) 1.776 × 10-3. B) 1.776 × 10-4. C) 17.72 × 104. D) 1772 × 105. E) 177.2 × 107.
50) Significant figures: What is A) 0.911
0.674 to the proper number of significant figures? 0.74
B) 0.9
C) 0.91
50)
D) 0.9108
51) Significant figures: When adding two numbers, the number of significant figures in the
sum is equal to the number of significant figures in the least accurate of the numbers being added. A) True B) False SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 52) Conversion of units: Albert uses as his unit of length (for walking to visit his
neighbors or plowing his fields) the albert (A), the distance Albert can throw a small rock. One albert is 92 meters. How many square alberts is equal to one acre? (1 acre = 43,560 ft2 = 4050 m2)
7
52)
51)
Answer Key Testname: CHAPTER 1 1) B 2) B 3) D 4) C 5) D 6) B 7) B 8) D 9) A 10) A 11) B 12) B 13) B 14) A 15) A 16) A 17) A 18) A 19) D 20) A 21) D 22) A 23) B 24) B 25) C 26) C 27) D 28) D 29) A 30) D 31) D 32) A 33) A 34) A 35) B 36) C 37) A 38) D 39) B 40) C 41) C 42) A 43) C 44) D 45) A 46) C 47) D 48) B 49) B 50) C 8
Answer Key Testname: CHAPTER 1 51) B 52) 1.29 A2
9
Chapter 2 Exam Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Components: If the eastward component of vector A is equal to the westward component
1)
of vector B and their northward components are equal. Which one of the following statements about these two vectors is correct? A) Vector A is parallel to vector B . B) The magnitude of vector A is twice the magnitude of vector B . C) Vectors A and B point in opposite directions. D) The magnitude of vector A is equal to the magnitude of vector B . E) Vector A is perpendicular to vector B . 2) Addition and subtraction: A rabbit trying to escape a fox runs north for 8.0 m, darts
2)
northwest for 1.0 m, then drops 1.0 m down a hole into its burrow. What is the magnitude of the net displacement of the rabbit? A) 66 m B) 10 m C) 8.8 m D) 8.1 m ^
^
3) Scalar (dot) product: The angle between vector A = 2.00i + 3.00j and vector B is 45.0°.
The scalar product of vectors A and B is 3.00. If the x component of vector B is positive, what is vector B . ^
^
^
^
^
^
A) 2.96i + -0.973j B) 3.42i + 0.684j C) 1.15i + 0.231j ^
^
D) 0.871i + 0.419j ^
^
E) 4.76i + 0.952j
1
3)
4) Scalar (dot) product: For the vectors shown in the figure, assume numbers are accurate to
4)
two significant figures. The scalar product A × C is closest to
A) -16.
B) -45.
C) 16.
D) zero.
E) 45.
5) Addition and subtraction: If A > B, under what condition is | A - B | = A - B?
5)
A) The statement is never true. B) Vectors A and B re in perpendicular directions. C) Vectors A and B are in the same direction. D) Vectors A and B are in opposite directions. E) The statement is always true. 6) Components: Which of the following is an accurate statement?
6)
A) It is possible to add a scalar quantity to a vector. B) The magnitude of a vector can be zero even though one of its components is not
zero. C) Rotating a vector about an axis passing through the tip of the vector does not change the vector. D) The magnitude of a vector is independent of the coordinate system used. E) Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero. 7) Vector (cross) product: What is the magnitude of the cross product of a vector of
magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north? A) 4.00 B) 6.93 C) 8.00 D) -6.93 E) -4.00
2
7)
8) Unit vectors: Vectors A and B are shown in the figure. What is |-5.00 A + 4.00 B |
A) 1028 B) 31.8 C) 34.0 ^
^
^
^
D) -2.00 i - 32.0 j E) -32.0 i - 2.00 j
3
8)
9) Addition and subtraction: Vectors A and B are shown in the figure. Vector C is given
9)
by C = B - A . The magnitude of vector A is 16.0 units, and the magnitude of vector B is 7.00 units. What is the magnitude of vector C ?
A) 9.53
B) 17.5
C) 9.00
D) 16.2
E) 15.5
10) Components: The components of vector B are B x = -3.5 and By = -9.7, and the
10)
components of vector C are Cx = -6 and C y = +8.1. What is the angle (less than 180 degrees) between vectors B and C ? A) 17° B) 163° ^
C) 106°
D) 124°
^
E) 56°
^
11) Unit vectors: Vector A = -3.00 i + 3.00 j and vector B = 3.00 i + 4.00 j . What is vector
11)
C = A + B? ^
^
A) -3.00 i + 7.00 j ^
^
^
^
^
^
^
^
B) -3.00 i -3.00 j
C) 0.00 i + 3.00 j D) 0.00 i + 7.00 j E) 7.00 i + 7.00 j
12) Vector (cross) product: If two vectors are perpendicular to each other, their cross product
must be zero. A) True
B) False
4
12)
13) Addition and subtraction: Under what condition is | A - B | = A + B?
13)
A) Vectors A and B are in opposite directions. B) Vectors A and B are in perpendicular directions. C) The magnitude of vector B is zero. D) Vectors A and B are in the same direction. E) The statement is never true. 14) Components: An airplane undergoes the following displacements: First, it flies 66 km in
14)
a direction 30° east of north. Next, it flies 49 km due south. Finally, it flies 100 km 30° north of west. Using vector components, determine how far the airplane ends up from its starting point. A) 78 km B) 76 km C) 79 km D) 81 km E) 82 km 15) Components: The components of vector A are A x = + 3.90 and Ay = -4.00. What is the
angle measured counterclockwise from the +x-axis to vector A ? A) 136° B) 314° C) 224° D) 46.0°
E) 134°
16) Scalar (dot) product: The value of the dot product of two vectors depends on the
particular coordinate system being used. A) True
15)
16)
B) False
17) Components: A helicopter is flying horizontally with a speed of 444 m/s over a hill that
17)
slopes upward with a 2% grade (that is, the "rise" is 2% of the "run"). What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill? A) 444 m/s B) 8.9 m/s C) 435 m/s D) 220 m/s 18) Vector (cross) product: If A and B are nonzero vectors for which A B = 0, it must
18)
follow that A) A × B = 0.
B) | A × B | = 1.
C) | A × B | = AB.
D) A is parallel to B .
19) Vector (cross) product: If two vectors point in opposite directions, their cross product
must be zero. A) True
B) False
5
19)
20) Components: As shown in the figure, three force vectors act on an object. The
20)
magnitudes of the forces as shown in the figure are F1 = 80.0 N, F2 = 60.0 N, and F3 = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by
A) 180 N at an angle 60.0° with respect to +x-axis. B) 35.5 N at an angle 34.3° with respect to +x-axis. C) 40.0 N at an angle 60.0° with respect to +x-axis. D) 60.0 N at an angle 90.0° with respect to +x-axis. E) 20.0 N at an angle 34.3° with respect to +x-axis. ^
^
^
21) Unit vectors: What is the magnitude of A + B + C , where A = 1.00 i + 4.00 j - 1.00 k, ^
^
^
^
B = 3.00 i - 1.00 j - 4.00 k and C = -1.00 i + 1.00 j ? A) 8.12 B) 7.07 C) 6.78
D) 10.76 ^
E) 2.00 ^
^
22) Scalar (dot) product: What is the angle between the vector A = +3i - 2j - 3k and the
+y-axis? A) 115°
B) 65°
21)
^
C) 90°
D) 25°
E) 155°
23) Components: The magnitude of a vector can never be less than the magnitude of one of
its components. A) True
B) False
6
22)
23)
^
^
^
^
24) Vector (cross) product: If C = -4i - 2j - 3k, what is C × j ? ^
^
^
^
^
^
^
^
^
^
24)
A) +3i + 4k ^
B) +3i + 2 j - 4k C) +3i - 4k D) -3i + 4k ^
E) -3i - 2 j + 4k 25) Scalar (dot) product: A rectangular box is positioned with its vertices at the following points:25)
A = (0,0,0) C = (2,4,0) E = (0,0,3) G = (2,4,3) B = (2,0,0) D = (0,4,0) F = (2,0,3) H = (0,4,3) If the coordinates all have three significant figures, the angle between the line segments AG and AH is closest to: A) 36.9°. B) 26.6°. C) 45.0°. D) 21.8°. E) 22.5°. 26) Addition and subtraction: Vectors A and B are shown in the figure. Vector C is given
by C = B - A . The magnitude of vector A is 16.0 units, and the magnitude of vector B is 7.00 units. What is the angle of vector C , measured counterclockwise from the +x-axis?
A) 73.1°
B) 22.4°
C) 292°
7
D) 16.9°
E) 287°
26)
^
^
^
^
27) Scalar (dot) product: Determine the scalar product of A = 6.0 i + 4.0j - 2.0k and B = 5.0i ^
27)
^
- 6.0j - 3.0k. A) 12 ^
^
^
^
^
^
B) 30 i - 24j + 6k C) 30 i + 24j + 6k D) 60 E) undefined 28) Components: Vector A has a magnitude 5.00 and points in a direction 40.0° clockwise
28)
from the negative y axis. What are the x and y components of vector A . A) Ax = 4.29 and A y = 2.16 B) Ax = 3.83 and A y = 3.21 C) Ax = 3.83 and A y = -3.21 D) Ax = -3.21 and A y = -3.83 E) Ax = -3.21 and A y = 3.83 29) Scalar (dot) product: If the dot product of two nonzero vectors is zero, the vectors must
be perpendicular to each other. A) True
29)
B) False
30) Addition and subtraction: You walk 55 m to the north, then turn 60° to your right and
30)
walk another 45 m. How far are you from where you originally started? A) 94 m B) 46 m C) 87 m D) 50 m 31) Components: Three forces are exerted on an object placed on a tilted floor. Forces are
vectors. The three forces are directed as shown in the figure. If the forces have magnitudes F 1 = 1.0 N, F 2 = 8.0 N and F 3 = 7.0 N, where N is the standard unit of force, what is the component of the net force F net = F 1 + F 2 + F 3 parallel to the floor?
A) 7.8 N
B) 5.1 N
C) 6.0 N 8
D) 2.5 N
31)
32) Components: The components of vector A are A x = +2.2 and Ay = -6.9 , and the
32)
components of vector B are given are B x = -6.1 and By = -2.2. What is the magnitude of the vector B - A ? A) 0.76
B) 9.5
C) 6.1
D) 91
E) 9.9
33) Components: If the magnitude of vector A is less than the magnitude of vector B , then
33)
the x component of A is less than the x component of B . A) True B) False ^
^
^
^
^
^
34) Vector (cross) product: If B = -2i - 6j + 2k and C = -2i -2j - 3k, which of the following
numbers is closest to the magnitude of C × B ? A) 17 B) 25 C) 13 ^
^
D) 9
34)
E) 21 ^
^
35) Unit vectors: Vector A = -1.00 i + -2.00 j and vector B = 3.00 i + 4.00 j What are the
35)
magnitude and direction of vector C = 3.00 A + 2.00 B ? A) 3.61 in a direction -56.3° counterclockwise from the positive x-axis B) 3.61 in a direction 56.3° counterclockwise from the positive x-axis C) 5.00 in a direction 56.3° counterclockwise from the positive x axis D) 6.72 in a direction 34.4° counterclockwise from the positive x-axis E) 3.61 in a direction 33.7° counterclockwise from the positive x-axis ^
36) Scalar (dot) product: Determine the angle between the directions of vector A = 3.00i + ^
^
1.00j and vector B = -3.00i + 3.00j. A) 26.6° B) 30.0°
C) 117°
D) 45.2° ^
E) 88.1° ^
^
37) Vector (cross) product: What is the vector product of A = 2.00 i + 3.00 j + 1.00k and B ^
^
^
= 1.00 i - 3.00 j - 2.00k? ^
^
^
^
^
^
A) -9.00 i - 3.00 j - 3.00k B) 2.00 i - 9.00 j - 2.00k ^
^
^
^
^
^
^
^
^
36)
^
C) -5.00 i + 2.00 j - 6.00k D) -4.00 i + 3.00 j - 1.00k E) -3.00 i + 5.00 j - 9.00k
9
37)
38) Components: A teacher sends her students on a treasure hunt. She gives the following
38)
instructions: 1. Walk 300 m north 2. Walk 400 m northwest 3. Walk 700 m east-southeast and the treasure is buried there. As all the other students walk off following the instructions, Jane physics student quickly adds the displacements and walks in a straight line to find the treasure. How far and in what direction does Jane need to walk? A) 284 m in a direction 28.2° west of north B) 481 m in a direction 40.9° north of east C) 399 m in a direction 52.5° north of east D) 187 m in a direction 67.3° north of east E) The treasure position cannot be reached in one straight walk. ^
^
^
^
^
^
39) Unit vectors: If A = +4 i - 2 j - 3 k and C = -4 i -2 j - 3 k, which of the following
numbers is closest to the magnitude of A - C ? A) 11 B) 9 C) 8
D) 10 ^
39)
E) 7 ^
40) Scalar (dot) product: The scalar product of vector A = 3.00i + 2.00j and vector B is
40)
10.0. Which of the following vectors could be vector B ? ^
^
^
^
A) 2.00i + 2.00j B) 5.00i + 4.00j ^
C) 12.0i
^
^
^
^
D) 2.00i + 4.00j E) 4.00i + 6.00j
41) Addition and subtraction: You walk 53 m to the north, then turn 60° to your right and
41)
walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east. A) 50° N of E B) 63° N of E C) 69° N of E D) 57° N of E 42) Unit vectors: If all the components of a vector are equal to 1, then that vector is a unit
vector. A) True
42)
B) False
43) Addition and subtraction: If A - B = 0, then the vectors A and B have equal magnitudes
and are directed in the opposite directions from each other. A) True B) False
10
43)
44) Vector (cross) product: For the vectors shown in the figure, find the magnitude and
44)
direction of the vector product A × C that the quantities shown are accurate to two significant figures.
A) 45, directed out of the plane B) 45, directed into the plane C) 16, directed out of the plane D) 16, directed into the plane E) 45, directed on the plane 45) Components: An apple falls from an apple tree growing on a 20° slope. The apple hits
45)
the ground with an impact velocity of 16.2 m/s straight downward. What is the component of the apple's impact velocity parallel to the surface of the slope? A) 12 m/s B) 8.7 m/s C) 15 m/s D) 5.5 m/s 46) Vector (cross) product: For the vectors shown in the figure, find the magnitude and
46)
direction of B × A , assuming that the quantities shown are accurate to two significant figures.
A) 31, directed into the plane B) 26, directed into the plane C) 31, directed on the plane D) 26, directed out of the plane E) 31, directed out of the plane
11
^
^
^
^
47) Unit vectors: Vector A = 1.00 i + -2.00 j and vector B = 3.00 i + 4.00 j What are the
47)
magnitude and direction of vector C = A + B ? A) 4.47 in a direction 26.6° counterclockwise from the positive x axis B) 6.00 in a direction 63.4° counterclockwise from the positive x axis C) 4.47 in a direction 6.34° counterclockwise from the positive x axis D) 7.21 in a direction 33.7° counterclockwise from the positive x axis E) 7.21 in a direction 56.3° counterclockwise from the positive x axis 48) Scalar (dot) product: If two nonzero vectors point in the same direction, their dot product
must be zero. A) True
B) False
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 49) Components: Vector A has a magnitude of 5.5 cm and points along the x-axis.
49)
Vector B has a magnitude of 7.5 cm and points at +30° above the negative x-axis. (a) Determine the x and y components of Vector A . (b) Determine the x and y components of Vector B . (c) Determine x and y components of the sum of these two vectors. (d) Determine the magnitude and direction of the sum of these two vectors. 50) Components: Vector A has a magnitude of 75.0 cm and points at 30° above the
50)
positive x-axis. Vector C has a magnitude of 25.0 cm and points along the negative x-axis. Vector C has a magnitude of 40.0 cm and points at 45° below the negative x-axis. (a) Determine the x and y components of Vector A . (b) Determine the x and y components of Vector B . (c) Determine the x and y components of Vector C . (d) Determine x and y components of the sum of these three vectors. (e) Determine the magnitude and direction of the sum of these three vectors. 51) Scalar (dot) product: Two boys searching for buried treasure are standing
51)
underneath the same tree. One boy walks 18 m east and then 18 m north. The other boy walks 16 m west and then 11 m north. Find the scalar product of their net displacements from the tree. 52) Vector (cross) product: If the magnitude of the cross product of two vectors is
one-half the dot product of the same vectors, what is the angle between the two vectors? 12
52)
48)
^ ^
^
^
^
^
53) Scalar (dot) product: If A = 3 i - j + 4k and B = x i + j - 5k, find x so B will be
53)
perpendicular to A . 54) Components: In the figure, the magnitude of vector A is 18.0 units, and the
54)
magnitude of vector B is 12.0 units. What vector C must be added to the vectors A and B so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector C by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.
55) Addition and subtraction: For the vectors shown in the figure, express vector S in
terms of vectors M and N .
13
55)
Answer Key Testname: CHAPTER 2 1) D 2) C 3) C 4) A 5) C 6) D 7) B 8) B 9) D 10) D 11) D 12) B 13) A 14) C 15) B 16) B 17) B 18) C 19) A 20) B 21) B 22) A 23) A 24) C 25) D 26) E 27) A 28) D 29) A 30) C 31) D 32) B 33) B 34) B 35) E 36) C 37) E 38) B 39) C 40) A 41) B 42) B 43) B 44) A 45) D 46) B 47) A 48) B
14
Answer Key Testname: CHAPTER 2
49) (a) A x = 5.5 cm, A y = 0
(b) B x = -6.5 cm, B y = 3.8 cm (c) R x = -1.0 cm, Ry = 3.8 cm (d) 3.9 cm at 75° above -x-axis 50) (a) A x = 65 cm, A y = 38 cm (b) B x = -25 cm, B y = 0 (c) C x = -28 cm, C y = -28 cm (d) R x = 12 cm, Ry = 9.2 cm (e) 15 cm at 38° above +x-axis 51) -90 m2 52) 26.6° 53) 7 54) 15.5, 209° 55) S = M - N
15
Chapter 3 Exam Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Basic kinematics variables: When can we be certain that the average velocity of an object
1)
is always equal to its instantaneous velocity? A) always B) never C) only when the acceleration is constant D) only when the velocity is constant E) only when the acceleration is changing at a constant rate 2) Basic kinematics variables using calculus: The velocity of an object as a function of time
2)
is given by v(t) = 2.00 m/s + (3.00 m/s) t - (1.0 m/s2) t2. Determine the instantaneous acceleration of the object at time t = 4.00 s. A) -5.00 m/s2 B) -1.00 m/s2 C) -2.00 m/s2 D) 1.00 m/s2 E) 0.00 m/s2 3) Basic kinematics variables: If the graph of the position as a function of time for an object
3)
is a horizontal line, that object cannot be accelerating. A) True B) False 4) Basic kinematics variables using calculus: The position of an object as a function of time
4)
is given by x = bt2 - ct, where b = 2.0 m/s2 and c = 6.7 m/s, and x and t are in SI units. What is the instantaneous velocity of the object when t = 2.2? A) 2.1 m/s B) 2.7 m/s C) 1.7 m/s D) 2.3 m/s 5) Free fall: Two identical objects A and B fall from rest from different heights to the
ground and feel no appreciable air resistance. If object B takes TWICE as long as object A to reach the ground, what is the ratio of the heights from which A and B fell? A) hA /hB = 1/8 B) hA /hB = 1/ 2 C) hA /hB = 1/4 D) hA /hB = 1/2
1
5)
6) Basic kinematics variables: An object is moving in a straight line along the x-axis. A plot
of its velocity in the x direction as a function of time is shown in the figure. Which graph represents its acceleration in the x direction as a function of time?
A)
2
6)
B)
C)
3
D)
E)
4
7) Basic kinematics variables: A racing car accelerates uniformly from rest along a straight track. 7)
This track has markers spaced at equal distances along it from the start, as shown in the figure. The car reaches a speed of 140 km/h as it passes marker 2. Where on the track was the car when it was traveling at 70 km/h?
A) Before marker 1 B) Between marker 1 and marker 2 C) At marker 1 8) Free fall: Two identical stones are dropped from rest and feel no air resistance as they
8)
fall. Stone A is dropped from height h, and stone B is dropped from height 2h. If stone A takes time t to reach the ground, stone B will take time A) 2t. B) t/ 2 C) t/2. D) 4t. E) t 2. 9) Basic kinematics variables using calculus: The acceleration of an object as a function of
9)
time is given by a(t) = (3.00 m/s3)t, where t is in seconds. If the object has a velocity 1.00 m/s at time what is the displacement of the object between time t = 2.00 s and time t = 4.00 s? A) 36.0 m
B) 30.0 m
C) 33.0 m
D) 27.0 m
10) Constant acceleration: A runner maintains constant acceleration after starting from rest
10)
as she runs a distance of 60.0 m. The runner's speed at the end of the 60.0 m is 9.00 m/s. How much time did it take the runner to complete the 60.0 m distance? A) 13.3 s B) 9.80 s C) 10.2 s D) 6.67 s E) 15.0 s 11) Free fall: A test rocket is fired straight up from rest with a net acceleration of 20.0 m/s2.
11)
After 4.00 seconds the motor turns off, but the rocket continues to coast upward with no appreciable air resistance. What maximum elevation does the rocket reach? A) 487 m B) 408 m C) 160 m D) 327 m E) 320 m 12) Free fall: A toy rocket is launched vertically from ground level (y = 0.00 m), at time t =
0.00 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 72 m and acquired a velocity of 30 m/s. The rocket continues to rise in unpowered flight, reaches maximum height, and falls back to the ground with negligible air resistance. The speed of the rocket upon impact on the ground is closest to A) 39 m/s B) 59 m/s C) 44 m/s D) 48 m/s E) 54 m/s 5
12)
13) Basic kinematics variables: The figure shows the position of an object (moving along a straight 13)
line) as a function of time. Assume two significant figures in each number. Which of the following statements about this object is true over the interval shown?
A) The acceleration of the object is in the same direction as its velocity. B) The object is accelerating to the left. C) The object is accelerating to the right. D) The average speed of the object is 1.0 m/s. 14) Free fall: On the earth, when an astronaut throws a 0.250-kg stone vertically upward, it
14)
returns to his hand a time T later. On planet X he finds that, under the same circumstances, the stone returns to his hand in 2T. In both cases, he throws the stone with the same initial velocity and it feels negligible air resistance. The acceleration due to gravity on planet X (in terms of g) is A) g/ 2. B) 2g. C) g/2. D) g/4. E) g 2. 15) Constant acceleration: A car is 200 m from a stop sign and traveling toward the sign at
15)
40.0 m/s. At this time, the driver suddenly realizes that she must stop the car. If it takes 0.200 s for the driver to apply the brakes, what must be the magnitude of the constant acceleration of the car after the brakes are applied so that the car will come to rest at the stop sign? A) 3.42 m/s2 B) 4.17 m/s2 C) 2.89 m/s2 D) 2.08 m/s2 E) 3.89 m/s2 16) Basic kinematics variables: Suppose that a car traveling to the west (the -x direction)
begins to slow down as it approaches a traffic light. Which statement concerning its acceleration in the x direction is correct? A) Its acceleration is positive but its velocity is negative. B) Both its acceleration and its velocity are negative. C) Its acceleration is negative but its velocity is positive. D) Both its acceleration and its velocity are positive.
6
16)
17) Basic kinematics variables: An object is moving with constant non-zero acceleration
17)
along the +x-axis. A graph of the velocity in the x direction as a function of time for this object is A) a parabolic curve. B) a vertical straight line. C) a straight line making an angle with the time axis. D) a horizontal straight line. 18) Basic kinematics variables: An object starts its motion with a constant velocity of 2.0
m/s toward the east. After 3.0 s, the object stops for 1.0 s. The object then moves toward the west a distance of 2.0 m in 3.0 s. The object continues traveling in the same direction, but increases its speed by 1.0 m/s for the next 2.0 s. Which graph below could represent the motion of this object? A)
B)
7
18)
C)
D)
8
19) Basic kinematics variables: The figure represents the velocity of a particle as it travels
19)
along the x-axis. At what value (or values) of t is the instantaneous acceleration equal to zero?
A) t = 0
B) t = 1 s
C) t = 0.5 s and t = 2 s
20) Basic kinematics variables: If the fastest you can safely drive is 65 mi/h, what is the
20)
longest time you can stop for dinner if you must travel 541 mi in 9.6 h total? A) 1.0 h B) 1.3 h C) 1.4 h D) You can't stop at all. 21) Constant acceleration: A car starts from rest and accelerates with a constant acceleration
21)
of 1.00 m/s2 for 3.00 s. The car continues for 5.00 s at constant velocity. How far has the car traveled from its starting point? A) 4.50 m B) 19.5 m C) 9.00 m D) 24.0 m E) 15.0 m 22) Constant acceleration: A car accelerates from 10.0 m/s to 30.0 m/s at a rate of 3.00 m/s2.
How far does the car travel while accelerating? A) 399 m B) 133 m C) 226 m
D) 80.0 m
23) Basic kinematics variables: If the acceleration of an object is negative, the object must be
slowing down. A) True
B) False
9
22)
23)
24) Basic kinematics variables using calculus: The position of an object is given by
24)
x = at3 - bt2 + ct, where a = 4.1 m/s3, b = 2.2 m/s2, c = 1.7 m/s, and x and t are in SI units. What is the instantaneous acceleration of the object when t = 0.7 s? A) -13 m/s2 B) 4.6 m/s2 C) 2.9 m/s2 D) 13 m/s2 25) Basic kinematics variables: The figure shows the graph of the position x as a function of
time for an object moving in the straight line (the x-axis). Which of the following graphs best describes the velocity along the x-axis as a function of time for this object?
A)
B)
10
25)
C)
D)
E)
26) Basic kinematics variables using calculus: The acceleration of an object as a function of
26)
time is given by a(t) = (3.00 m/s3)t, where t is in seconds. If the object is at rest at time t = 0.00 s, what is the velocity of the object at time t = 6.00 s? A) 108 m/s B) 54.0 m/s C) 18.0 m/s D) 0.00 m/s E) 15.0 m/s 27) Basic kinematics variables: If an object is accelerating toward a point, then it must be
getting closer and closer to that point. A) True
B) False
11
27)
28) Basic kinematics variables: The motions of a car and a truck along a straight road are
28)
represented by the velocity-time graphs in the figure. The two vehicles are initially alongside each other at time t = 0. At time T, what is true about these two vehicles since time t = 0?
A) The car will have traveled further than the truck. B) The truck will have traveled further than the car. C) The car will be traveling faster than the truck. D) The truck and the car will have traveled the same distance. 29) Free fall: Which one of the following graphs could possibly represent the vertical
position as a function of time for an object in free fall? A)
12
29)
B)
C)
13
D)
E)
14
30) Basic kinematics variables: The figure shows the velocity of a particle as it travels along
30)
the x-axis. What is the direction of the acceleration at t = 0.5 s?
A) in the -x direction B) in the +x direction C) The acceleration is zero. 31) Constant acceleration: An airplane that is flying level needs to accelerate from a speed of
31)
2.00 × 102 m/s to a speed of 2.40 × 102 m/s while it flies a distance of 1.20 km. What must be the acceleration of the plane? A) 2.45 m/s2 B) 7.33 m/s2 C) 1.34 m/s2 D) 4.44 m/s2 E) 5.78 m/s2 32) Free fall: A ball is projected upward at time t = 0.00 s, from a point on a roof 70 m above
the ground and experiences negligible air resistance. The ball rises, then falls and strikes the ground. The initial velocity of the ball is 28.5 m/s. Consider all quantities as positive in the upward direction. The velocity of the ball when it is 39 m above the ground is closest to A) -30 m/s. B) -38 m/s. C) -23 m/s. D) -45 m/s. E) -15 m/s.
15
32)
33) Free fall: A ball is projected upward at time t = 0.0 s, from a point on a roof 90 m above
33)
the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is 36.2 m/s if air resistance is negligible. The time when the ball strikes the ground is closest to A) 9.0 s B) 8.7 s C) 9.4 s D) 9.7 s E) 10 s 34) Constant acceleration: A dragster starts from rest and travels 1/4 mi in 6.70 s with
34)
constant acceleration. What is its velocity when it crosses the finish line? A) 135 mi/h B) 188 mi/h C) 296 mi/h D) 269 mi/h 35) Free fall: Two objects are dropped from a bridge, an interval of 1.0 s apart, and
35)
experience no appreciable air resistance. As time progresses, the DIFFERENCE in their speeds A) decreases. B) increases. C) decreases at first, but then stays constant. D) remains constant. E) increases at first, but then stays constant. 36) Basic kinematics variables: Suppose that an object is moving with constant nonzero
36)
acceleration. Which of the following is an accurate statement concerning its motion? A) In equal times it moves equal distances. B) In equal times its speed changes by equal amounts. C) A graph of its velocity as a function of time is a horizontal line. D) In equal times its velocity changes by equal amounts. E) A graph of its position as a function of time has a constant slope. 37) Free fall: At the same moment from the top of a building 3.0 × 102 m tall, one rock is
37)
dropped and one is thrown downward with an initial velocity of 10 m/s. Both of them experience negligible air resistance. How much EARLIER does the thrown rock strike the ground? A) 0.67 s B) 0.95 s C) 0.86 s D) They land at exactly the same time. 38) Constant acceleration: A ball rolls across a floor with an acceleration of 0.100 m/s2 in a
direction opposite to its velocity. The ball has a velocity of 4.00 m/s after rolling a distance 6.00 m across the floor. What was the initial speed of the ball? A) 4.15 m/s B) 5.21 m/s C) 5.85 m/s D) 3.85 m/s E) 4.60 m/s
16
38)
39) Free fall: Two objects are thrown from the top of a tall building and experience no
39)
appreciable air resistance. One is thrown up, and the other is thrown down, both with the same initial speed. What are their speeds when they hit the street? A) The one thrown up is traveling faster. B) They are traveling at the same speed. C) The one thrown down is traveling faster. 40) Constant acceleration: A speeding car is traveling at a constant 30.0 m/s when it passes a
40)
stationary police car. If the police car delays for 1.00 s before starting, what must be the magnitude of the constant acceleration of the police car to catch the speeding car after the police car travels a distance of 300 m? A) 3.70 m/s2 B) 6.00 m/s2 C) 7.41 m/s2 D) 1.45 m/s2 E) 3.00 m/s2 41) Constant acceleration: An object starts from rest at time t = 0.00 s and moves in the +x
direction with constant acceleration. The object travels 12.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object? A) 4.00 m/s2 B) 24.0 m/s2 C) -12.0 m/s2 D) 8.00 m/s2 E) -4.00 m/s2
17
41)
graph 42) Basic kinematics variables: The motion of a particle is described in the velocity versus time 42) shown in the figure. We can say that its speed
A) decreases and then increases.
B) increases.
C) increases and then decreases.
D) decreases.
43) Basic kinematics variables using calculus: The velocity of an object is given by the
43)
expression v(t) = 3.00 m/s + (4.00 m/s3)t2, where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time t = 0.000 s. A) 1.33 m B) 1.00 m + (3.00 m/s)t + (1.33 m/s3)t3 C) (3.00 m/s)t + (1.33 m/s3)t3 D) (4.00 m/s)t + 1.00 m E) (4.00 m/s)t 44) Free fall: To determine the height of a flagpole, Abby throws a ball straight up and times
44)
it. She sees that the ball goes by the top of the pole after 0.50 s and then reaches the top of the pole again after a total elapsed time of 4.1 s. How high is the pole above the point where the ball was launched? (You can ignore air resistance.) A) 10 m B) 26 m C) 16 m D) 18 m E) 13 m 45) Free fall: A package is dropped from a helicopter moving upward at 15 m/s. If it takes
16.0 s before the package strikes the ground, how high above the ground was the package when it was released if air resistance is negligible? A) 1200 m B) 1500 m C) 1000 m D) 810 m
18
45)
46) Free fall: A rock is dropped from the top of a vertical cliff and takes 3.00 s to reach the
46)
ground below the cliff. A second rock is thrown vertically from the cliff, and it takes this rock 2.00 s to reach the ground below the cliff from the time it is released. With what velocity was the second rock thrown, assuming no air resistance? A) 4.76 m/s downward B) 12.3 m/s downward C) 4.76 m/s upward D) 12.3 m/s upward E) 5.51 m/s downward 47) Free fall: A ball is thrown directly upward and experiences no air resistance. Which one
of the following statements about its motion is correct? A) The acceleration of the ball is downward while it is traveling up and upward while it is traveling down. B) The acceleration is downward during the entire time the ball is in the air. C) The acceleration of the ball is upward while it is traveling up and downward while it is traveling down. D) The acceleration of the ball is downward while it is traveling up and downward while it is traveling down but is zero at the highest point when the ball stops. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
a 48) Basic kinematics variables: As part of an exercise program, a woman walks south at 48) speed of 2.00 m/s for 60.0 minutes. She then turns around and walks north a distance 3000 m in 25.0 minutes (a) What is the woman's average velocity during her entire motion? A) 0.824 m/s south B) 1.93 m/s south C) 2.00 m/s south D) 1.79 m/s south E) 800 m/s south (b) What is the woman's average speed during her entire motion? A) 0.824 m/s B) 1.93 m/s C) 2.00 m/s D) 1.79 m/s E) 800 m/s 49) Constant acceleration: A soccer ball is released from rest at the top of a grassy
incline. After 8.6 seconds, the ball travels 87 meters and 1.0 s after this, the ball reaches the bottom of the incline. (a) What was the magnitude of the ball's acceleration, assume it to be constant? (b) How long was the incline?
19
49)
47)
50) Free fall: A rocket takes off vertically from the launchpad with no initial velocity
50)
but a constant upward acceleration of 2.25 m/s2. At 15.4 s after blastoff, the engines fail completely so the only force on the rocket from then on is the pull of gravity. (a) What is the maximum height the rocket will reach above the launchpad? (b) How fast is the rocket moving at the instant before it crashes onto the launchpad? (c) How long after engine failure does it take for the rocket to crash onto the launchpad? 51) Basic kinematics variables using calculus: The position of an object as a function
51)
of time is given by x(t) = at3 - bt2 + ct - d, where a = 3.6 m/s3, b = 4.0 m/s2, c = 60 m/s and d = 7.0 m. (a) Find the instantaneous acceleration at t =2.4 s. (b) Find the average acceleration over the first 2.4 seconds. time 52) Basic kinematics variables: The figure shows a graph of the velocity as a function of 52) for a basketball player traveling up and down the court in a straight-line path. For the 10 s shown on the graph, find (a) the net displacement of the player. (b) the total distance run by the player.
20
53) Basic kinematics variables: The figure shows the position of an object as a
53)
function of time, with all numbers accurate to two significant figures. Between time t = 0.0 s and time t = 9.0 s (a) what is the average speed of the object? (b) what is the average velocity of the object?
a 54) Basic kinematics variables: The graph in the figure shows the position of an object as54) function of time. The letters H-L represent particular moments of time. At which moments shown (H, I, etc.) is the speed of the object (a) the greatest? (b) the smallest?
21
55) Free fall: A foul ball is hit straight up into the air with a speed of 30.0 m/s.
55)
(a) Calculate the time required for the ball to rise to its maximum height. (b) Calculate the maximum height reached by the ball. (c) Determine the time at which the ball pass a point 25.0 m above the point of contact between the bat and ball. (d) Explain why there are two answers to part (c). 56) Basic kinematics variables: The figure represents the position of a particle as it
56)
travels along the x-axis. Between t = 2 s and t = 4 s, what is (a) the average speed of the particle and (b) the average velocity of the particle?
57) Basic kinematics variables: Arthur and Betty start walking toward each other
57)
when they are 100 m apart. Arthur has a speed of 3.0 m/s and Betty has a speed of 2.0 m/s. Their dog, Spot, starts by Arthur's side at the same time and runs back and forth between them at 5.0 m/s. By the time Arthur and Betty meet, what distance has Spot run? 58) Basic kinematics variables: A cat runs along a straight line (the x-axis) from
point A to point B to point C, as shown in the figure. The distance between points A and C is 5.00 m, the distance between points B and C is 10.0 m, and the positive direction of the x-axis points to the right. The time to run from A to B is 20.0 s, and the time from B to C is 8.00 s. As the cat runs along the x-axis between points A and C (a) what is the magnitude of its average velocity? (b) what is its average speed?
22
58)