Category Archives: Engineering Mathematics Blog
Chapter 9: Statics and Torque
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The Second Condition for Equilibrium
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
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Stability
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
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Applications of Statics, Including Problem-Solving Strategies
Problem 17
Problem 18
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Simple Machines
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
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Forces and Torques in Muscles and Joints
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
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Chapter 8: Linear Momentum and Collisions
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Linear Momentum and Force
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
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Impulse
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
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Conservation of Momentum
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
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Elastic Collisions in One Dimension
Problem 28
Problem 29
Problem 30
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Inelastic Collisions in One Dimension
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
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Collisions of Point Masses in Two Dimensions
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
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Introduction to Rocket Propulsion
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
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Chapter 7: Work, Energy, and Energy Resources
Work: The Scientific Definition
Kinetic Energy and the Work-Energy Theorem
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Gravitational Potential Energy
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Conservative Forces and Potential Energy
Problem 22
Problem 23
Nonconservative Forces
Problem 24
Problem 25
Conservation of Energy
Problem 26
Problem 27
Problem 28
Problem 29
Power
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Work, Energy, and Power in Humans
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
World Energy Use
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Chapter 6: Uniform Circular Motion and Gravitation
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Rotation Angle and Angular Velocity
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Centripetal Acceleration
Problem 22
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Centripetal Force
Problem 31
Problem 32
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Newton’s Universal Law of Gravitation
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
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Satellites and Kepler’s Laws: An Argument for Simplicity
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
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Chapter 5: Further Applications of Newton’s Laws: Friction, Drag, and Elasticity
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Friction
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
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Drag Forces
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
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Elasticity: Stress and Strain
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
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Chapter 4: Dynamics: Force and Newton’s Laws of Motion
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Newton’s Second Law of Motion: Concept of a System
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
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Newton’s Third Law of Motion: Symmetry in Forces
Problem 15
Problem 16
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Normal, Tension, and Other Example of Forces
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
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Problem Solving Strategies
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
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Further Applications of Newton’s Laws of Motion
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
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Further Applications of Newton’s Laws of Motion
Problem 52
Problem 53
Problem 54
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Chapter 3: Two-Dimensional Kinematics
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Vector Addition and Subtraction: Graphical Methods
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Vector Addition and Subtraction: Analytical Methods
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Projectile Motion
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Addition of Velocities
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
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Chapter 2: Force Vectors
Vector Addition of Forces
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Addition of a System of Coplanar Forces
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Cartesian Vectors | Addition of Cartesian Vectors
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Force Vector Directed Along a Line
Problem 86
Problem 87
Problem 88
Problem 89
Problem 90
Problem 91
Problem 92
Problem 93
Problem 94
Problem 95
Problem 96
Problem 97
Problem 98
Problem 99
Problem 100
Problem 101
Problem 102
Problem 103
Problem 104
Problem 105
Dot Product
Problem 106
Problem 107
Problem 108
Problem 109
Problem 110
Problem 111
Problem 112
Problem 113
Problem 114
Problem 115
Problem 116
Problem 117
Problem 118
Problem 119
Problem 120
Problem 121
Problem 122
Problem 123
Problem 124
Problem 125
Problem 126
Problem 127
Problem 128
Problem 129
Problem 130
Problem 131
Problem 132
Problem 133
Problem 134
Problem 135
Problem 136
Problem 137
Problem 138
Problem 139
Hibbeler Statics 14E P1.1 — Converting mass to weight in newtons
What is the weight in newtons of an object that has a mass of (a) 8 kg, (b) 0.04 kg, and (c) 760 Mg?
Statics of Rigid Bodies 14th Edition by RC Hibbeler, Problem 1-1
Solution:
Part A: To convert the given mass in kilogram to newton force, we simply need to multiply by the acceleration due to gravity of 9.81 m/s2. We need to take into account that 1\:\text{kg m/s}^2\:=1\:\text{N} .
\begin {aligned}
8\:\text{kg} & =8\:\text{kg}\times 9.81\:\text{m/s}^2 \\
&=78.48\:\text{N}
\end {aligned}Part B: Using the same principle from Part A, we have
\begin {aligned}
0.04\:\text{kg}&=0.04\:\text{kg}\times 9.81\:\text{m/s}^2\\
&=0.3924\:\text{N}
\end {aligned}Part C: So, we are given 760 Mg (megagram). We know that 1 Mg is equivalent to 1000 kg. Therefore, 760 Mg is equal to 760,000 kg. Therefore, we have
\begin {aligned}
760\:000\:\text{kg}&=760\:000\:\text{kg}\times 9.81\:\text{m/s}^2\\
&=7\:455\:600\:\text{N}
\end{aligned}
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