Question 1

Vectors   and   are shown. What is the magnitude of a vector   if   ?

Accepted Answer

A)  46 
B)  10 
C)  30 
D)  78 
E)  90 
A)  46 
B)  10 
C)  30 
D)  78 
E)  90 A

Question 2

Anthony has added the vectors listed below and gotten the result   . What errors has he made?

Accepted Answer

A)  He lost the minus sign in vector
  . 
B)  He read the
  in
  as
  . 
C)  He lost the minus sign in vector
  . 
D)  All of the above are correct. 
E)  Only (a) and (b) above are correct. 
A)  He lost the minus sign in vector
  . 
B)  He read the
  in
  as
  . 
C)  He lost the minus sign in vector
  . 
D)  All of the above are correct. 
E)  Only (a) and (b) above are correct. E

Question 3

The rectangular coordinates of a point are (5.00, y) and the polar coordinates of this point are (r, 67.4°). What is the value of the polar coordinate r in this case?

Accepted Answer

A)  1.92 
B)  4.62 
C)  12.0 
D)  13.0 
E)  More information is needed. 
A)  1.92 
B)  4.62 
C)  12.0 
D)  13.0 
E)  More information is needed. D

Question 4

If vector   is added to vector   , the result is   . If   is subtracted from   , the result is   . What is the magnitude of   ?

Accepted Answer

A)  5.1 
B)  4.1 
C)  5.4 
D)  5.8 
E)  8.2 
A)  5.1 
B)  4.1 
C)  5.4 
D)  5.8 
E)  8.2

Question 5

A vector   is added to   . The resultant vector is in the positive x direction and has a magnitude equal to   . What is the magnitude of   ?

Accepted Answer

A)  11 
B)  5.1 
C)  7.1 
D)  8.3 
E)  12.2 
A)  11 
B)  5.1 
C)  7.1 
D)  8.3 
E)  12.2

Question 6

Instructions: On occasion, the notation   = [A, θ] will be a shorthand notation for   .
-The displacement of the tip of the 10 cm long minute hand of a clock between 12:15 A.M. and 12:45 P.M. is:

Accepted Answer

A)  10 cm, 90° 
B)  10 cm, 180° 
C)  10 cm, 4 500° 
D)  20 cm, 180° 
E)  20 cm, 540° 
A)  10 cm, 90° 
B)  10 cm, 180° 
C)  10 cm, 4 500° 
D)  20 cm, 180° 
E)  20 cm, 540°

Question 7

The diagram below shows 3 vectors which sum to zero, all of equal length. Which statement below is true?

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E) 
  
A) 
  
B) 
  
C) 
  
D) 
  
E)

Question 8

Instructions: On occasion, the notation   = [A, θ] will be a shorthand notation for   .
-Dana says any vector   can be represented as the sum of two vectors:   . Ardis says any vector   can be represented as the difference of two vectors:   . Which one, if either, is correct?

Accepted Answer

A)  They are both wrong: every vector is unique. 
B)  Dana is correct: Any vector can be represented as a sum of components and not as a difference. 
C)  Ardis is correct: Any vector can be represented as a difference of vector components and not as a sum. 
D)  They are both correct: A difference of vectors is a sum
  . 
E)  They are both wrong: Vectors can be moved as long as they keep the same magnitude and direction. 
A)  They are both wrong: every vector is unique. 
B)  Dana is correct: Any vector can be represented as a sum of components and not as a difference. 
C)  Ardis is correct: Any vector can be represented as a difference of vector components and not as a sum. 
D)  They are both correct: A difference of vectors is a sum
  . 
E)  They are both wrong: Vectors can be moved as long as they keep the same magnitude and direction.

Question 9

Instructions: On occasion, the notation   = [A, θ] will be a shorthand notation for   .
Exhibit 3-3
The vectors   ,   , and   are shown below.   Use this exhibit to answer the following question(s).
-Refer to Exhibit 3-3. Which diagram below correctly represents   ?

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E) 
  
A) 
  
B) 
  
C) 
  
D) 
  
E)

Question 10

If two collinear vectors   and   are added, the resultant has a magnitude equal to 4.0. If   is subtracted from   , the resultant has a magnitude equal to 8.0. What is the magnitude of   ?

Accepted Answer

A)  2.0 
B)  3.0 
C)  4.0 
D)  5.0 
E)  6.0 
A)  2.0 
B)  3.0 
C)  4.0 
D)  5.0 
E)  6.0

Question 11

Given that   and   , what is   ?

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E) 
  
A) 
  
B) 
  
C) 
  
D) 
  
E)

Question 12

The vector   has components +5 and +7 along the x and y axes respectively. Along a set of axes rotated 90 degrees counterclockwise relative to the original axes, the vector's components are

Accepted Answer

A)  −7; −5. 
B)  7; −5. 
C)  −7; 5. 
D)  7; 5. 
E)  7; 0. 
A)  −7; −5. 
B)  7; −5. 
C)  −7; 5. 
D)  7; 5. 
E)  7; 0.

Question 13

Given that   and   , what is   ?

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E) 
  
A) 
  
B) 
  
C) 
  
D) 
  
E)

Question 14

Given the statement that   , what can we conclude?

Accepted Answer

A) 
  and
  . 
B) 
  . 
C) 
  and
  . 
D)  Any one of the answers above is correct. 
E)  Only (a) and (b) may be correct. 
A) 
  and
  . 
B) 
  . 
C) 
  and
  . 
D)  Any one of the answers above is correct. 
E)  Only (a) and (b) may be correct.

Question 15

Instructions: On occasion, the notation   = [A, θ] will be a shorthand notation for   .
Exhibit 3-1
The three forces shown act on a particle.   Use this exhibit to answer the following question(s).
-Refer to Exhibit 3-1. What is the direction of the resultant of these three forces?

Accepted Answer

A)  35° 
B)  45° 
C)  65° 
D)  55° 
E)  85° 
A)  35° 
B)  45° 
C)  65° 
D)  55° 
E)  85°

Question 16

Instructions: On occasion, the notation   = [A, θ] will be a shorthand notation for   .
Exhibit 3-2
A child starts at one corner of a cubical jungle gym in a playground and climbs up to the diagonally opposite corner. The original corner is the coordinate origin, and the x, y and z axes are oriented along the jungle gym edges. The length of each side is 2 m.   Use this exhibit to answer the following question(s).
-Refer to Exhibit 3-2. The child's displacement is:

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E) 
  
A) 
  
B) 
  
C) 
  
D) 
  
E)

Question 17

The vector   has components +5 and +7 along the x and y axes respectively. If the vector is now rotated 90 degrees counterclockwise relative to the original axes, the vector's components are now

Accepted Answer

A)  −7; −5. 
B)  7; −5. 
C)  −7; 5. 
D)  7; 5. 
E)  7; 0. 
A)  −7; −5. 
B)  7; −5. 
C)  −7; 5. 
D)  7; 5. 
E)  7; 0.

Question 18

Which statement is true about the unit vectors   ,   and   ?

Accepted Answer

A)  Their directions are defined by a left-handed coordinate system. 
B)  The angle between any two is 90 degrees. 
C)  Each has a length of 1 m. 
D)  If
  is directed east and
  is directed south,
  points up out of the surface. 
E)  All of the above. 
A)  Their directions are defined by a left-handed coordinate system. 
B)  The angle between any two is 90 degrees. 
C)  Each has a length of 1 m. 
D)  If
  is directed east and
  is directed south,
  points up out of the surface. 
E)  All of the above.

Question 19

Vectors   and   have equal magnitudes. Which statement is always true?

Accepted Answer

A) 
  . 
B) 
  . 
C) 
  is perpendicular to
  . 
D) 
  is perpendicular to
  . 
E)  The magnitude of
  equals the magnitude of
  . 
A) 
  . 
B) 
  . 
C) 
  is perpendicular to
  . 
D) 
  is perpendicular to
  . 
E)  The magnitude of
  equals the magnitude of
  .

Question 20

Instructions: On occasion, the notation   = [A, θ] will be a shorthand notation for   .
-If vector   is added to vector   , the result is a third vector that is perpendicular to   and has a magnitude equal to 3   . What is the ratio of the magnitude of   to that of   ?

Accepted Answer

A)  1.8 
B)  2.2 
C)  3.2 
D)  1.3 
E)  1.6 
A)  1.8 
B)  2.2 
C)  3.2 
D)  1.3 
E)  1.6

Exam 3: Vectors

Vectors and are shown. What is the magnitude of a vector if ?

Anthony has added the vectors listed below and gotten the result . What errors has he made?

The rectangular coordinates of a point are (5.00, y) and the polar coordinates of this point are (r, 67.4°). What is the value of the polar coordinate r in this case?

If vector is added to vector , the result is . If is subtracted from , the result is . What is the magnitude of ?

A vector is added to . The resultant vector is in the positive x direction and has a magnitude equal to . What is the magnitude of ?

Instructions: On occasion, the notation = [A, θ] will be a shorthand notation for . -The displacement of the tip of the 10 cm long minute hand of a clock between 12:15 A.M. and 12:45 P.M. is:

The diagram below shows 3 vectors which sum to zero, all of equal length. Which statement below is true?

Instructions: On occasion, the notation = [A, θ] will be a shorthand notation for . -Dana says any vector can be represented as the sum of two vectors: . Ardis says any vector can be represented as the difference of two vectors: . Which one, if either, is correct?

Instructions: On occasion, the notation = [A, θ] will be a shorthand notation for . Exhibit 3-3 The vectors , , and are shown below. Use this exhibit to answer the following question(s). -Refer to Exhibit 3-3. Which diagram below correctly represents ?

If two collinear vectors and are added, the resultant has a magnitude equal to 4.0. If is subtracted from , the resultant has a magnitude equal to 8.0. What is the magnitude of ?

Given that and , what is ?

The vector has components +5 and +7 along the x and y axes respectively. Along a set of axes rotated 90 degrees counterclockwise relative to the original axes, the vector's components are

Given that and , what is ?

Given the statement that , what can we conclude?

Instructions: On occasion, the notation = [A, θ] will be a shorthand notation for . Exhibit 3-1 The three forces shown act on a particle. Use this exhibit to answer the following question(s). -Refer to Exhibit 3-1. What is the direction of the resultant of these three forces?

The vector has components +5 and +7 along the x and y axes respectively. If the vector is now rotated 90 degrees counterclockwise relative to the original axes, the vector's components are now

Which statement is true about the unit vectors , and ?

Vectors and have equal magnitudes. Which statement is always true?

Instructions: On occasion, the notation = [A, θ] will be a shorthand notation for . -If vector is added to vector , the result is a third vector that is perpendicular to and has a magnitude equal to 3 . What is the ratio of the magnitude of to that of ?

Physics and Measurement

Motion in One Dimension

Motion in Two Dimensions

The Laws of Motion

Circular Motion and Other Applications of Newtons Laws

Energy of a System

Conservation of Energy

Linear Momentum and Collisions

Rotation of a Rigid Object About a Fixed Axis

Angular Momentum

Static Equilibrium and Elasticity

Universal Gravitation

Fluid Mechanics

Oscillatory Motion

Wave Motion

Superposition and Standing Waves

Temperature

The First Law of Thermodynamics

The Kinetic Theory of Gases

Heat Engines, Entropy, and the Second Law of Thermodynamics

Electric Fields

Gausss Law

Electric Potential

Capacitance and Dielectrics

Current and Resistance

Direct-Current Circuits

Magnetic Fields

Sources of the Magnetic Field

Faradays Law

Inductance

Alternating-Current Circuits

Electromagnetic Waves

The Nature of Light and the Principles of Ray Optics

Image Formation

Wave Optics

Diffraction Patterns and Polarization

Relativity

Introduction to Quantum Physics

Quantum Mechanics

Atomic Physics

Molecules and Solids

Nuclear Structure

Particle Physics and Cosmology

Filters