Question 1

Which expression is false concerning the vectors shown in the sketch?

Accepted Answer

A)    =   +   
B)    +   = -   
C)    +   +   = 0 
D) C 2 + B 2 = C 2 
A)    =   +   
B)    +   = -   
C)    +   +   = 0 
D) C 2 + B 2 = C 2

Question 2

A bug crawls 2.25 m along the base of a wall. Upon reaching a corner, the bug's direction of travel changes from south to west. The bug then crawls 3.15 m before stopping. What is the magnitude of the bug's displacement?

Accepted Answer

A) 5.40 m 
B) 2.72 m 
C) 3.87 m 
D) 4.11 m 
E) 3.29 m 
A) 5.40 m 
B) 2.72 m 
C) 3.87 m 
D) 4.11 m 
E) 3.29 m

Question 3

What is the minimum number of vectors with unequal magnitudes whose vector sum can be zero?

Accepted Answer

A) two 
B) three 
C) four 
D) five 
E) six 
A) two 
B) three 
C) four 
D) five 
E) six

Question 4

A force,   , of magnitude 2.0 N and directed due east is exerted on an object. A second force exerted on the object is   = 2.0 N, due north. What is the magnitude and direction of a third force,   , which must be exerted on the object so that the resultant force is zero?

Accepted Answer

A) 1.4 N, 45° north of east 
B) 1.4 N, 45° south of west 
C) 2.8 N, 45° north of east 
D) 2.8 N, 45° south of west 
E) 4.0 N, 45° east of north 
A) 1.4 N, 45° north of east 
B) 1.4 N, 45° south of west 
C) 2.8 N, 45° north of east 
D) 2.8 N, 45° south of west 
E) 4.0 N, 45° east of north

Question 5

An escaped convict runs 1.70 km due east of the prison. He then runs due north to a friend's house. If the magnitude of the convict's total displacement vector is 2.50 km, what is the direction of his total displacement vector with respect to due east?

Accepted Answer

A) 43° south of east 
B) 47° north of east 
C) 56° north of east 
D) 34° south of east 
E) 34° north of east 
A) 43° south of east 
B) 47° north of east 
C) 56° north of east 
D) 34° south of east 
E) 34° north of east

Question 6

Which one of the following choices is equivalent to 8.0 m2?

Accepted Answer

A) 8.0 × 10-4 cm2 
B) 8.0 × 102 cm2 
C) 8.0 × 10-2 cm2 
D) 8.0 × 104 cm2 
E) 8.0 × 103 cm2 
A) 8.0 × 10-4 cm2 
B) 8.0 × 102 cm2 
C) 8.0 × 10-2 cm2 
D) 8.0 × 104 cm2 
E) 8.0 × 103 cm2

Question 7

What is the minimum number of vectors with equal magnitudes whose vector sum can be zero?

Accepted Answer

A) two 
B) three 
C) four 
D) five 
E) six 
A) two 
B) three 
C) four 
D) five 
E) six

Question 8

Complete the following statement: The ratio   is equal to

Accepted Answer

A) 102. 
B) 103. 
C) 106. 
D) 10-3. 
E) 10-6. 
A) 102. 
B) 103. 
C) 106. 
D) 10-3. 
E) 10-6.

Question 9

In a diving competition, a woman dives from a platform that is ten meters above the surface of the water. What is the height, expressed in feet, of the platform?

Accepted Answer

A) 13 feet 
B) 18 feet 
C) 24 feet 
D) 33 feet 
E) 47 feet 
A) 13 feet 
B) 18 feet 
C) 24 feet 
D) 33 feet 
E) 47 feet

Question 10

A pole is held vertically by attaching wires at a height of 13.4 m above the ground. The other end of each wire is anchored in the ground at a distance of 9.54 m from the base of the pole. The pole makes a right angle with the ground. What is the length of each wire?

Accepted Answer

A) 14.1 m 
B) 19.7 m 
C) 11.5 m 
D) 16.4 m 
E) 22.8 m 
A) 14.1 m 
B) 19.7 m 
C) 11.5 m 
D) 16.4 m 
E) 22.8 m

Question 11

Use the component method of vector addition to find the components of the resultant of the four displacements shown in the figure. The magnitudes of the displacements are: A = 2.25 cm, B = 6.35 cm, C = 5.47 cm, and D = 4.19 cm.   x component y component

Accepted Answer

A) 2.19 cm -6.92 cm 
B) 3.71 cm -1.09 cm 
C) 5.45 cm -2.82 cm 
D) 1.09 cm -3.71 cm 
E) 6.93 cm -2.19 cm 
A) 2.19 cm -6.92 cm 
B) 3.71 cm -1.09 cm 
C) 5.45 cm -2.82 cm 
D) 1.09 cm -3.71 cm 
E) 6.93 cm -2.19 cm

Question 12

Which one of the following statements concerning vectors and scalars is false?

Accepted Answer

A) In calculations, the vector components of a vector may be used in place of the vector itself. 
B) It is possible to use vector components that are not perpendicular. 
C) A scalar component may be either positive or negative. 
D) A vector that is zero may have components other than zero. 
E) Two vectors are equal only if they have the same magnitude and direction. 
A) In calculations, the vector components of a vector may be used in place of the vector itself. 
B) It is possible to use vector components that are not perpendicular. 
C) A scalar component may be either positive or negative. 
D) A vector that is zero may have components other than zero. 
E) Two vectors are equal only if they have the same magnitude and direction.

Question 13

Two displacement vectors of magnitudes 21 cm and 79 cm are added. Which one of the following is the only possible choice for the magnitude of the resultant?

Accepted Answer

A) 0 cm 
B) 28 cm 
C) 37 cm 
D) 82 cm 
E) 114 cm 
A) 0 cm 
B) 28 cm 
C) 37 cm 
D) 82 cm 
E) 114 cm

Question 14

Two vectors, = and  , are added together to form the vector  =  +   .
The relationship between the magnitudes of these vectors is given by:
CS1U1B1xS1U1B0  = 0, CS1U1B1yS1U1B0  = A sin 60° + B sin 30°
AS1U1B1xS1U1B0 and Ay point in the positive x and y directions, respectively.
-How does the magnitude of   compare with that of   ?

Accepted Answer

A) A = B 
B) A = 1.7B 
C) A = 0.4B 
D) A = 0.5B 
E) A = 0.7B 
A) A = B 
B) A = 1.7B 
C) A = 0.4B 
D) A = 0.5B 
E) A = 0.7B

Question 15

A student adds two displacement vectors with magnitudes of 6.0 m and 8.0 m, respectively. Which one of the following could not be a possible choice for the resultant?

Accepted Answer

A) 2.3 m 
B) 6.6 m 
C) 10.0 m 
D) 12.8 m 
E) 14.8 m 
A) 2.3 m 
B) 6.6 m 
C) 10.0 m 
D) 12.8 m 
E) 14.8 m

Question 16

The surface of a lake has an area of 15.5 km2. What is the area of the lake in m2?

Accepted Answer

A) 1.55 × 104 m2 
B) 1.55 × 105 m2 
C) 1.55 × 106 m2 
D) 1.55 × 107 m2 
E) 1.55 × 108 m2 
A) 1.55 × 104 m2 
B) 1.55 × 105 m2 
C) 1.55 × 106 m2 
D) 1.55 × 107 m2 
E) 1.55 × 108 m2

Question 17

A vector   has a magnitude of 40.0 units and points 35.0° above the positive x axis. A second vector   has a magnitude of 65.0 units and points in the negative x direction. Use the component method of vector addition to find the magnitude and direction, relative to the positive x axis, of the resultant   =   +   .

Accepted Answer

A) 53.3 units, 141.8° relative to the +x axis 
B) 53.3 units, 52.1° relative to the +x axis 
C) 39.6 units, 125.4° relative to the +x axis 
D) 39.6 units, 54.6° relative to the +x axis 
E) 46.2 units, 136.0° relative to the +x axis 
A) 53.3 units, 141.8° relative to the +x axis 
B) 53.3 units, 52.1° relative to the +x axis 
C) 39.6 units, 125.4° relative to the +x axis 
D) 39.6 units, 54.6° relative to the +x axis 
E) 46.2 units, 136.0° relative to the +x axis

Question 18

A certain physical quantity, R, is calculated using the formula: R = 4a2(b - c) where a, b, and c are distances. What is the SI unit for R?

Accepted Answer

A) cm 
B) cm2 
C) m 
D) m2 
E) m3 
A) cm 
B) cm2 
C) m 
D) m2 
E) m3

Question 19

Which one of the following statements is true concerning scalar quantities?

Accepted Answer

A) Scalar quantities must be represented by base units. 
B) Scalar quantities have both magnitude and direction. 
C) Scalar quantities can be added to vector quantities using rules of trigonometry. 
D) Scalar quantities can be added to other scalar quantities using rules of trigonometry. 
E) Scalar quantities can be added to other scalar quantities using rules of ordinary addition. 
A) Scalar quantities must be represented by base units. 
B) Scalar quantities have both magnitude and direction. 
C) Scalar quantities can be added to vector quantities using rules of trigonometry. 
D) Scalar quantities can be added to other scalar quantities using rules of trigonometry. 
E) Scalar quantities can be added to other scalar quantities using rules of ordinary addition.

Question 20

Complete the following statement: Today, the standard unit of mass is defined in terms of

Accepted Answer

A) a specified volume of water at 4 °C. 
B) a standard platinum-iridium cylinder. 
C) a specified number of cesium atoms. 
D) a standard platinum bar. 
E) the speed of light. 
A) a specified volume of water at 4 °C. 
B) a standard platinum-iridium cylinder. 
C) a specified number of cesium atoms. 
D) a standard platinum bar. 
E) the speed of light.

Exam 1: Introduction and Mathematical Concepts

Which expression is false concerning the vectors shown in the sketch?

A bug crawls 2.25 m along the base of a wall. Upon reaching a corner, the bug's direction of travel changes from south to west. The bug then crawls 3.15 m before stopping. What is the magnitude of the bug's displacement?

What is the minimum number of vectors with unequal magnitudes whose vector sum can be zero?

A force, , of magnitude 2.0 N and directed due east is exerted on an object. A second force exerted on the object is = 2.0 N, due north. What is the magnitude and direction of a third force, , which must be exerted on the object so that the resultant force is zero?

An escaped convict runs 1.70 km due east of the prison. He then runs due north to a friend's house. If the magnitude of the convict's total displacement vector is 2.50 km, what is the direction of his total displacement vector with respect to due east?

Which one of the following choices is equivalent to 8.0 m2?

What is the minimum number of vectors with equal magnitudes whose vector sum can be zero?

Complete the following statement: The ratio is equal to

In a diving competition, a woman dives from a platform that is ten meters above the surface of the water. What is the height, expressed in feet, of the platform?

A pole is held vertically by attaching wires at a height of 13.4 m above the ground. The other end of each wire is anchored in the ground at a distance of 9.54 m from the base of the pole. The pole makes a right angle with the ground. What is the length of each wire?

Use the component method of vector addition to find the components of the resultant of the four displacements shown in the figure. The magnitudes of the displacements are: A = 2.25 cm, B = 6.35 cm, C = 5.47 cm, and D = 4.19 cm. x component y component

Which one of the following statements concerning vectors and scalars is false?

Two displacement vectors of magnitudes 21 cm and 79 cm are added. Which one of the following is the only possible choice for the magnitude of the resultant?

A student adds two displacement vectors with magnitudes of 6.0 m and 8.0 m, respectively. Which one of the following could not be a possible choice for the resultant?

The surface of a lake has an area of 15.5 km2. What is the area of the lake in m2?

A certain physical quantity, R, is calculated using the formula: R = 4a2(b - c) where a, b, and c are distances. What is the SI unit for R?

Which one of the following statements is true concerning scalar quantities?

Complete the following statement: Today, the standard unit of mass is defined in terms of

Kinematics in One Dimension

Kinematics in Two Dimensions

Forces and Newtons Laws of Motion

Dynamics of Uniform Circular Motion

Work and Energy

Impulse and Momentum

Rotational Kinematics

Rotational Dynamics

Simple Harmonic Motion and Elasticity

Fluids

Temperature and Heat

The Transfer of Heat

The Ideal Gas Law and Kinetic Theory

Thermodynamics

Waves and Sound

The Principle of Linear Superposition and Interference Phenomena

Electric Forces and Electric Fields

Electric Potential Energy and the Electric Potential

Electric Circuits

Magnetic Forces and Magnetic Fields

Electromagnetic Induction

Alternating Current Circuits

Electromagnetic Waves

The Refl Ection of Light: Mirrors

The Refraction of Light: Lenses and Optical Instruments

Interference and the Wave Nature of Light

Special Relativity

Particles and Waves

The Nature of the Atom

Nuclear Physics and Radioactivity

Ionizing Radiation, Nuclear Energy, and Elementary Particles

Filters

Which one of the following choices is equivalent to 8.0 m²?

The surface of a lake has an area of 15.5 km². What is the area of the lake in m²?

A certain physical quantity, R, is calculated using the formula: R = 4a²(b - c) where a, b, and c are distances. What is the SI unit for R?