Engineering Mechanics: Statics and Dynamics

R. C. Hibbeler

Chapter 2

Force Vectors - all with Video Answers

Educators

Chapter Questions

Problem 1

If $\theta=60^{\circ}$ and $F=450 \mathrm{N}$, determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive $x$ axis.

Donald Albin

Donald Albin

Numerade Educator

Problem 2

If the magnitude of the resultant force is to be $500 \mathrm{N}$ directed along the positive $y$ axis, determine the magnitude of force $\mathbf{F}$ and its direction $\theta$

Donald Albin

Numerade Educator

Problem 3

Determine the magnitude of the resultant force $\mathbf{F}_{R}=\mathbf{F}_{1}+\mathbf{F}_{2}$ and its direction, measured counterclockwise from the positive $x$ axis.

Supratim Pal

Numerade Educator

Problem 4

The vertical force $\mathbf{F}$ acts downward at $A$ on the twomembered frame. Determine the magnitudes of the two components of $\mathbf{F}$ directed along the axes of $A B$ and $A C$ $\operatorname{Set} F=500 \mathrm{N}$

Donald Albin

Numerade Educator

Problem 5

Solve Prob. $2-4$ with $F=350 \mathrm{lb}$

Donald Albin

Numerade Educator

Problem 6

Determine the magnitude of the resultant force $\mathbf{F}_{R}=\mathbf{F}_{1}+\mathbf{F}_{2}$ and its direction, measured clockwise from the positive $u$ axis.

Supratim Pal

Numerade Educator

Problem 7

Resolve the force $\mathbf{F}_{1}$ into components acting along the $u$ and $v$ axes and determine the magnitudes of the components.

Donald Albin

Numerade Educator

Problem 8

Resolve the force $\mathbf{F}_{2}$ into components acting along the $u$ and $v$ axes and determine the magnitudes of the components.

Donald Albin

Numerade Educator

Problem 9

If the resultant force acting on the support is to be $1200 \mathrm{lb},$ directed horizontally to the right, determine the force $\mathbf{F}$ in rope $A$ and the corresponding angle $\theta$

Donald Albin

Numerade Educator

Problem 10

Determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive $x$ axis.

Donald Albin

Numerade Educator

Problem 11

The plate is subjected to the two forces at $A$ and $B$ as shown. If $\theta=60^{\circ},$ determine the magnitude of the resultant of these two forces and its direction measured clockwise from the horizontal.

Donald Albin

Numerade Educator

Problem 12

Determine the angle $\theta$ for connecting member $A$ to the plate so that the resultant force of $\mathbf{F}_{A}$ and $\mathbf{F}_{B}$ is directed horizontally to the right. Also, what is the magnitude of the resultant force?

Donald Albin

Numerade Educator

Problem 13

The force acting on the gear tooth is $F=20 \mathrm{lb}$ Resolve this force into two components acting along the lines $a a$ and $b b$

Donald Albin

Numerade Educator

Problem 14

The component of force $\mathbf{F}$ acting along line aa is required to be 30 lb. Determine the magnitude of $\mathbf{F}$ and its component along line $b b$

Donald Albin

Numerade Educator

Problem 15

Force $\mathbf{F}$ acts on the frame such that its component acting along member $A B$ is 650 lb, directed from $B$ towards $A,$ and the component acting along member $B C$ is 500 Ib, directed from $B$ towards $C .$ Determine the magnitude of $\mathbf{F}$ and its direction $\theta .$ Set $\phi=60^{\circ}$

Donald Albin

Numerade Educator

Problem 16

Force $\mathbf{F}$ acts on the frame such that its component acting along member $A B$ is 650 lb, dirccted from $B$ towards $A .$ Determine the required angle $\phi\left(0^{\circ} \leq \phi \leq 45^{\circ}\right)$ and the component acting along member $B C .$ Set $F=850 \mathrm{lb}$ and $\theta=30^{\circ}$

Donald Albin

Numerade Educator

Problem 17

Determine the magnitude and direction of the resultant $\mathbf{F}_{R}=\mathbf{F}_{1}+\mathbf{F}_{2}+\mathbf{F}_{3}$ of the three forces by first finding the resultant $\mathbf{F}^{\prime}=\mathbf{F}_{1}+\mathbf{F}_{2}$ and then forming $\mathbf{F}_{R}=\mathbf{F}^{\prime}+\mathbf{F}_{3}$

Donald Albin

Numerade Educator

Problem 18

Determine the magnitude and direction of the resultant $\mathbf{F}_{R}=\mathbf{F}_{1}+\mathbf{F}_{2}+\mathbf{F}_{3}$ of the three forces by first finding the resultant $\mathbf{F}^{\prime}=\mathbf{F}_{2}+\mathbf{F}_{3}$ and then forming $\mathbf{F}_{R}=\mathbf{F}^{\prime}+\mathbf{F}_{1}$

Donald Albin

Numerade Educator

Problem 19

Determine the design angle $\theta\left(0^{\circ} \leq \theta \leq 90^{\circ}\right)$ for strut $A B$ so that the 400 -lb horizontal force has a component of 500 lb directed from $A$ towards $C .$ What is the component of force acting along member $A B ?$ Take $\phi=40^{\circ}$

Donald Albin

Numerade Educator

Problem 20

Determine the design angle $\phi\left(0^{\circ} \leq \phi \leq 90^{\circ}\right)$ between struts $A B$ and $A C$ so that the 400 -lb horizontal force has a component of 600 lb which acts up to the left, in the same direction as from $B$ towards $A$. Take $\theta=30^{\circ}$

Donald Albin

Numerade Educator

Problem 21

Determine the magnitude and direction of the resultant force, $\mathbf{F}_{R}$ measured counterclockwise from the positive $x$ axis. Solve the problem by first finding the resultant $\mathbf{F}^{\prime}=\mathbf{F}_{1}+\mathbf{F}_{2}$ and then forming $\mathbf{F}_{R}=\mathbf{F}^{\prime}+\mathbf{F}_{3}$

Donald Albin

Numerade Educator

Problem 22

Determine the magnitude and direction of the resultant force, measured counterclockwise from the positive $x$ axis. Solve $l$ by first finding the resultant $\mathbf{F}^{\prime}=\mathbf{F}_{2}+\mathbf{F}_{3}$ and then forming $\mathbf{F}_{R}=\mathbf{F}^{\prime}+\mathbf{F}_{1}$

Donald Albin

Numerade Educator

Problem 23

Two forces act on the screw eye. If $F_{1}=400 \mathrm{N}$ and $F_{2}=600 \mathrm{N},$ determine the angle $\theta\left(0^{\circ} \leq \theta \leq 180^{\circ}\right)$ between
them, so that the resultant force has a magnitude of $F_{R}=800 \mathrm{N}$

Donald Albin

Numerade Educator

Problem 24

Two forces $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ act on the screw cyc. If their lines of action are at an angle $\theta$ apart and the magnitude of each force is $F_{1}=\mathrm{F}_{2}=F,$ determine the magnitude of the resultant force $\mathbf{F}_{R}$ and the angle between $\mathbf{F}_{R}$ and $\mathbf{F}_{1}$

Donald Albin

Numerade Educator

Problem 25

If $F_{1}=30 \mathrm{lb}$ and $F_{2}=40 \mathrm{lb}$, determine the angles $\theta$ and $\phi$ so that the resultant force is directed along the positive $x$ axis and has a magnitude of $F_{R}=60 \mathrm{lb}$

Donald Albin

Numerade Educator

Problem 26

Determine the magnitude and direction $\theta$ of $\mathbf{F}_{A}$ so that the resultant force is directed along the positive $x$ axis and has a magnitude of $1250 \mathrm{N}$

Donald Albin

Numerade Educator

Problem 27

Determine the magnitude and dircction, mcasured counterclockwise from the positive $x$ axis, of the resultant force acting on the ring at $O,$ if $F_{A}=750 \mathrm{N}$ and $\theta=45^{\circ}$

Donald Albin

Numerade Educator

Problem 28

Determine the magnitude of force $\mathbf{F}$ so that the resultant $\mathbf{F}_{R}$ of the three forces is as small as possible. What is the minimum magnitude of $\mathbf{F}_{R} ?$

Donald Albin

Numerade Educator

Problem 29

If the resultant force of the two tugboats is $3 \mathrm{kN}$ directed along the positive $x$ axis, determine the required magnitude of force $\mathbf{F}_{B}$ and its direction $\theta$

Donald Albin

Numerade Educator

Problem 30

If $\mathbf{F}_{B}=3 \mathrm{kN}$ and $\theta=45^{\circ},$ determine the magnitude of the resultant force of the two tugboats and its direction measured clockwise form the positive $x$ axis.

Donald Albin

Numerade Educator

Problem 31

If the resultant force of the two tugboats is required to be directed towards the positive $x$ axis, and $\mathbf{F}_{B}$ is to be a minimum, determine the magnitude of $\mathbf{F}_{R}$ and $\mathbf{F}_{B}$ and the angle $\theta$

Supratim Pal

Numerade Educator

Problem 32

Determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive $x$ axis.

Donald Albin

Numerade Educator

Problem 33

Determine the magnitude of the resultant force and its direction, measured clockwise from the positive $x$ axis.

Donald Albin

Numerade Educator

Problem 34

Resolve $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ into their $x$ and $y$ components.

Donald Albin

Numerade Educator

Problem 35

Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive $x$ axis.

Donald Albin

Numerade Educator

Problem 36

Resolve each force acting on the gusset plate into its $x$ and $y$ components, and express each force as a Cartesian vector.

Donald Albin

Numerade Educator

Problem 37

Determine the magnitude of the resultant force acting on the plate and its dircction, measured counterclockwise from the positive $x$ axis.

Donald Albin

Numerade Educator

Problem 38

Express each of the three forces acting on the support in Cartesian vector form and determine the magnitude of the resultant force and its direction, measured clockwise from positive $x$ axis.

Donald Albin

Numerade Educator

Problem 39

Determine the $x$ and $y$ components of $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$

Donald Albin

Numerade Educator

Problem 40

Determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive $x$ axis.

Donald Albin

Numerade Educator

Problem 41

Determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive $x$ axis.

Donald Albin

Numerade Educator

Problem 42

Express $\mathbf{F}_{1}, \mathbf{F}_{2},$ and $\mathbf{F}_{3}$ as Cartesian vectors.

Donald Albin

Numerade Educator

Problem 43

Determine the magnitude of the resultant force and its dircction, measured counterclockwise from the positive $x$ axis

Donald Albin

Numerade Educator

Problem 44

Determine the magnitude of the resultant force and its direction, measured clockwise from the positive $x$ axis.

Donald Albin

Numerade Educator

Problem 45

Determine the magnitude and direction $\theta$ of the resultant force $\mathbf{F}_{R} .$ Express the result in terms of the magnitudes of the components $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ and the angle $\phi$

Donald Albin

Numerade Educator

Problem 46

Determine the magnitude and orientation $\theta$ of $\mathbf{F}_{B}$ so that the resultant force is directed along the positive $y$ axis and has a magnitude of $1500 \mathrm{N}$

Donald Albin

Numerade Educator

Problem 47

Determine the magnitude and orientation, measured counterclockwise from the positive $y$ axis, of the resultant force acting on the bracket, if $F_{B}=600 \mathrm{N}$ and $\theta=20^{\circ}$

Supratim Pal

Numerade Educator

Problem 48

Three forces act on the bracket. Determine the magnitude and dircction $\theta$ of $\mathbf{F}_{1}$ so that the resultant force is directed along the positive $x^{\prime}$ axis and has a magnitude of $800 \mathrm{N}$

Donald Albin

Numerade Educator

Problem 49

If $F_{1}=300 \mathrm{N}$ and $\theta=10^{\circ},$ determine the magnitude and dircction, measured counterclockwisc from the positive $x^{\prime}$ axis, of the resultant force acting on the bracket.

Donald Albin

Numerade Educator

Problem 50

Express $\mathbf{F}_{1}, \mathbf{F}_{2},$ and $\mathbf{F}_{3}$ as Cartesian vectors.

Donald Albin

Numerade Educator

Problem 51

Determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive $x$ axis.

Donald Albin

Numerade Educator

Problem 52

Determine the $x$ and $y$ componcnts of cach force acting on the gusset plate of a bridge truss. Show that the resultant force is zero.

Donald Albin

Numerade Educator

Problem 53

Express $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ as Cartesian vectors

Donald Albin

Numerade Educator

Problem 54

Determine the magnitude of the resultant force and its dircction measured counterclockwise from the positive $x$ axis.

Donald Albin

Numerade Educator

Problem 55

Determine the magnitude of force $\mathbf{F}$ so that the resultant force of the three forces is as small as possible. What is the magnitude of the resultant force?

Nick Johnson

Numerade Educator

Problem 56

If the magnitude of the resultant force acting on the bracket is to be $450 \mathrm{N}$ directed along the positive $u$ axis, determine the magnitude of $\mathbf{F}_{1}$ and its direction $\phi$

Donald Albin

Numerade Educator

Problem 57

If the resultant force acting on the bracket is required to be a minimum, determine the magnitudes of $\mathbf{F}_{1}$ and the resultant force. Set $\phi=30^{\circ}$

Supratim Pal

Numerade Educator

Problem 58

Three forces act on the bracket. Determine the magnitude and direction $\theta$ of $\mathbf{F}$ so that the resultant force is dirccted along the positive $x^{\prime}$ axis and has a magnitude of $8 \mathrm{kN}$

Donald Albin

Numerade Educator

Problem 59

If $F=5 \mathrm{kN}$ and $\theta=30^{\circ},$ determinc the magnitude of the resultant force and its direction, measured counterclockwise from the positive $x$ axis.

Donald Albin

Numerade Educator

Problem 60

The force $\mathbf{F}$ has a magnitude of 80 lb and acts within the octant shown. Determine the magnitudes of the $x, y, z$ components of $\mathbf{F}$

Donald Albin

Numerade Educator

Problem 61

The bolt is subjected to the force $\mathbf{F}$, which has components acting along the $x, y, z$ axes as shown. If the magnitude of $\mathbf{F}$ is $80 \mathrm{N},$ and $\alpha=60^{\circ}$ and $\gamma=45^{\circ},$ determinc the magnitudes of its components.

Donald Albin

Numerade Educator

Problem 62

Determine the magnitude and coordinate direction angles of the force $\mathbf{F}$ acting on the support. The component of $\mathbf{F}$ in the $x-y$ planc is $7 \mathrm{kN}$

Donald Albin

Numerade Educator

Problem 63

Determine the magnitude and coordinate direction angles of the resultant force and sketch this vector on the coordinate system.

Donald Albin

Numerade Educator

Problem 64

Specify the coordinate direction angles of $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ and express each force as a Cartesian vector.

Donald Albin

Numerade Educator

Problem 65

The screw eye is subjected to the two forces shown. Express each force in Cartesian vector form and then determine the resultant force. Find the magnitude and coordinate direction angles of the resultant force.

Donald Albin

Numerade Educator

Problem 66

Determine the coordinate direction angles of $\mathbf{F}_{1}$

Donald Albin

Numerade Educator

Problem 67

Determine the magnitude and coordinate direction angles of $\mathbf{F}_{3}$ so that the resultant of the three forces acts along the positive $y$ axis and has a magnitude of 600 lb.

Donald Albin

Numerade Educator

Problem 68

Determine the magnitude and coordinate dircction angles of $\mathbf{F}_{3}$ so that the resultant of the three forces is zero.

Donald Albin

Numerade Educator

Problem 69

Determine the magnitude and coordinate direction angles of the resultant force, and sketch this vector on the coordinate system.

Donald Albin

Numerade Educator

Problem 70

Determine the magnitude and coordinate direction angles of the resultant force, and skctch this vector on the coordinate system.

Donald Albin

Numerade Educator

Problem 71

Specify the magnitude and coordinate direction angles $\alpha_{1}, \beta_{1}, \gamma_{1}$ of $\mathbf{F}_{1}$ so that the resultant of the three forces acting on the bracket is $\mathbf{F}_{R}=\{-350 \mathbf{k}\}$ lb. Note that $\mathbf{F}_{3}$ lies in the $x-y$ plane.

Donald Albin

Numerade Educator

Problem 72

Two forces $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ act on the screw cyc. If the resultant force $\mathbf{F}_{R}$ has a magnitude of 150 lb and the coordinate direction angles shown, determine the magnitude of $\mathbf{F}_{2}$ and its coordinate dircction angles.

Donald Albin

Numerade Educator

Problem 73

Express each force in Cartesian vector form.

Donald Albin

Numerade Educator

Problem 74

Determine the magnitude and coordinate direction angles of the resultant force, and sketch this vector on the coordinate system.

Donald Albin

Numerade Educator

Problem 75

The spur gear is subjected to the two forces caused by contact with other gears. Express each force as a Cartesian vector.

Donald Albin

Numerade Educator

Problem 76

The spur gear is subjected to the two forces caused by contact with other gears. Determine the resultant of the two forces and express the result as a Cartesian vector.

Donald Albin

Numerade Educator

Problem 77

Determine the magnitude and coordinate direction angles of the resultant force, and sketch this vector on the coordinate system.

Donald Albin

Numerade Educator

Problem 78

The two forces $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ acting at $A$ have a resultant force of $\mathbf{F}_{R}=\{-100 \mathbf{k}\}$ lb. Determine the magnitude and coordinate direction angles of $\mathbf{F}_{2}$

Donald Albin

Numerade Educator

Problem 79

Determine the coordinate direction angles of the force $\mathbf{F}_{1}$ and indicate them on the figure.

Donald Albin

Numerade Educator

Problem 80

The bracket is subjected to the two forces shown. Express cach force in Cartesian vector form and then determine the resultant force $\mathbf{F}_{R} .$ Find the magnitude and coordinate direction angles of the resultant force.

Donald Albin

Numerade Educator

Problem 81

If the coordinate direction angles for $\mathbf{F}_{3}$ are $\alpha_{3}=120^{\circ}, \beta_{3}=60^{\circ}$ and $\gamma_{3}=45^{\circ},$ determine the magnitude
and coordinate direction angles of the resultant force acting on the cycbolt.

Donald Albin

Numerade Educator

Problem 82

If the coordinate direction angles for $\mathbf{F}_{3}$ are $\alpha_{3}=120^{\circ}, \quad \beta_{3}=45^{\circ}, \quad$ and $\quad \gamma_{3}=60^{\circ}, \quad$ determine the
magnitude and coordinate direction angles of the resultant force acting on the eyebolt.

Donald Albin

Numerade Educator

Problem 83

If the direction of the resultant force acting on the eyebolt is defined by the unit vector $\mathbf{u}_{F_{R}}=\cos 30^{\circ} \mathbf{j}+\sin 30^{\circ} \mathbf{k}$
determinc the coordinate dircction angles of $\mathbf{F}_{3}$ and the magnitude of $\mathbf{F}_{R}$

Donald Albin

Numerade Educator

Problem 84

The pole is subjected to the force $\mathbf{F}$, which has components acting along the $x, y, z$ axes as shown. If the magnitude of $\mathbf{F}$ is $3 \mathrm{kN}, \beta=30^{\circ},$ and $\gamma=75^{\circ},$ determinc the magnitudes of its three components.

Donald Albin

Numerade Educator

Problem 85

The pole is subjected to the force $\mathbf{F}$ which has components $F_{x}=1.5 \mathrm{kN}$ and $F_{z}=1.25 \mathrm{kN}$. If $\beta=75^{\circ}$
determine the magnitudes of $\mathbf{F}$ and $\mathbf{F}_{y}$

Donald Albin

Numerade Educator

Problem 86

Determine the length of the connecting rod $A B$ by first formulating a Cartesian position vector from $A$ to $B$ and then determining its magnitude.

Donald Albin

Numerade Educator

Problem 87

Express force $\mathbf{F}$ as a Cartesian vector; then determine its coordinate direction angles.

Donald Albin

Numerade Educator

Problem 88

Express cach of the forces in Cartesian vector form and determine the magnitude and coordinate direction angles of the resultant force.

Donald Albin

Numerade Educator

Problem 89

If $\mathbf{F}=\{350 \mathbf{i}-250 \mathbf{j}-450 \mathbf{k}\} \quad \mathbf{N}$ and cable $A B$ is $9 \mathrm{m}$ long, determine the $x, y, z$ coordinates of point $A$

Donald Albin

Numerade Educator

Problem 90

The 8 -m-long cable is anchored to the ground at $A$ If $x=4 \mathrm{m}$ and $y=2 \mathrm{m},$ determine the coordinate $z$ to the highest point of attachment along the column.

Donald Albin

Numerade Educator

Problem 91

The 8 -m-long cable is anchored to the ground at $A$. If $z=5 \mathrm{m},$ determine the location $+x,+y$ of point $A .$ Choose a value such that $x=y$

Donald Albin

Numerade Educator

Problem 92

Express each of the forces in Cartesian vector form and determine the magnitude and coordinate direction angles of the resultant force.

Donald Albin

Numerade Educator

Problem 93

If $F_{B}=560 \mathrm{N}$ and $F_{C}=700 \mathrm{N},$ determine the magnitude and coordinate direction angles of the resultant force acting on the flag pole.

Donald Albin

Numerade Educator

Problem 94

If $\quad F_{B}=700 \mathrm{N},$ and $F_{C}=560 \mathrm{N},$ determine the magnitude and coordinate direction angles of the resultant force acting on the flag pole.

Donald Albin

Numerade Educator

Problem 95

The plate is suspended using the three cables which exert the forces shown. Express each force as a Cartesian vector.

Donald Albin

Numerade Educator

Problem 96

The three supporting cables exert the forces shown on the sign. Represent each force as a Cartesian vector.

Donald Albin

Numerade Educator

Problem 97

Determine the magnitude and coordinate direction angles of the resultant force of the two forces acting on the sign at point $A$

Donald Albin

Numerade Educator

Problem 98

The force $\mathbf{F}$ has a magnitude of $80 \mathrm{lb}$ and acts at the midpoint $C$ of the thin rod. Express the force as a Cartesian vector.

Donald Albin

Numerade Educator

Problem 99

The load at $A$ creates a force of $60 \mathrm{lb}$ in wire $A B$ Express this force as a Cartesian vector acting on $A$ and directed toward $B$ as shown.

Donald Albin

Numerade Educator

Problem 100

Determine the magnitude and coordinate direction angles of the resultant force acting at point $A$ on the post.

Donald Albin

Numerade Educator

Problem 101

The two mooring cables exert forces on the stern of a ship as shown. Represent each force as as Cartesian vector and determinc the magnitude and coordinate dircction angles of the resultant.

Donald Albin

Numerade Educator

Problem 102

The engine of the lightweight plane is supported by struts that are connected to the space truss that makes up the structure of the plane. The anticipated loading in two of the struts is shown. Express each of those forces as Cartesian vector.

Donald Albin

Numerade Educator

Problem 103

Determine the magnitude and coordinate direction angles of the resultant force.

Donald Albin

Numerade Educator

Problem 104

If the force in each cable tied to the bin is $70 \mathrm{lb}$ determine the magnitude and coordinate dircction angles of the resultant force.

Donald Albin

Numerade Educator

Problem 105

If the resultant of the four forces is $\mathbf{F}_{R}=\{-360 \mathbf{k}\} 1 \mathrm{b}$ determine the tension developed in each cable. Due to symmetry, the tension in the four cables is the same.

Donald Albin

Numerade Educator

Problem 107

Express force $\mathbf{F}$ in Cartesian vector form if point $B$ is located $3 \mathrm{m}$ along the rod from end $C$.

Donald Albin

Numerade Educator

Problem 108

The chandelier is supported by three chains which are concurrent at point $O .$ If the force in each chain has a magnitude of 60 Ib, express each force as a Cartesian vector and determine the magnitude and coordinate direction angles of the resultant force.

Donald Albin

Numerade Educator

Problem 109

The chandelier is supported by three chains which are concurrent at point $O .$ If the resultant force at $O$ has a magnitude of $130 \mathrm{lb}$ and is directed along the negative
$z$ axis, determine the force in each chain.

Donald Albin

Numerade Educator

Problem 110

The window is held open by chain $A B .$ Determine the length of the chain, and express the 50 -lb force acting at $A$ along the chain as a Cartesian vector and determine its coordinate direction angles.

Donald Albin

Numerade Educator

Problem 111

The window is held open by cable $A B .$ Determine the length of the cable and express the 30 -N force acting at $A$ along the cable as a Cartesian vector.

Donald Albin

Numerade Educator

Problem 112

Given the three vectors $\mathbf{A}, \mathbf{B},$ and $\mathbf{D},$ show that $\mathbf{A} \cdot(\mathbf{B}+\mathbf{D})=(\mathbf{A} \cdot \mathbf{B})+(\mathbf{A} \cdot \mathbf{D})$

Donald Albin

Numerade Educator

Problem 113

Determine the magnitudes of the components of $F=600 \mathrm{N}$ acting along and perpendicular to segment $D E$ of the pipe assembly.

Donald Albin

Numerade Educator

Problem 113

Determine the magnitudes of the components of $F=600 \mathrm{N}$ acting along and perpendicular to segment $D E$ of the pipe assembly.

Donald Albin

Numerade Educator

Problem 114

Determine the angle $\theta$ between the two cables.

Donald Albin

Numerade Educator

Problem 115

Determine the magnitude of the projection of the force $\mathbf{F}_{1}$ along cable $A C$

Donald Albin

Numerade Educator

Problem 116

Determine the angle $\theta$ between the $y$ axis of the pole and the wire $A B.$

Donald Albin

Numerade Educator

Problem 117

Determine the magnitudes of the projected components of the force $\mathbf{F}=[60 \mathbf{i}+12 \mathbf{j}-40 \mathbf{k}] \mathrm{N}$ along the cables $A B$ and $A C$

Donald Albin

Numerade Educator

Problem 118

Determine the angle $\theta$ between cables $A B$ and $A C$

Donald Albin

Numerade Educator

Problem 119

A force of $\mathbf{F}=\{-40 \mathbf{k}\}$ lb acts at the end of the pipe. Determine the magnitudes of the components $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ which are directed along the pipe's axis and perpendicular to it.

Donald Albin

Numerade Educator

Problem 120

Two cables exert forces on the pipe. Determine the magnitude of the projected component of $\mathbf{F}_{1}$ along the line of action of $\mathbf{F}_{2}$

Donald Albin

Numerade Educator

Problem 121

Determine the angle $\theta$ between the two cables attached to the pipe.

Donald Albin

Numerade Educator

Problem 122

Determine the angle $\theta$ between the cables $A B$ and $A C$

Donald Albin

Numerade Educator

Problem 123

Determine the magnitude of the projected component of the force $\mathbf{F}=\{400 \mathbf{i}-200 \mathbf{j}+500 \mathbf{k}\} \mathrm{N}$ acting along the cable $B A$

Donald Albin

Numerade Educator

Problem 124

Determine the magnitude of the projected component of the force $\mathbf{F}=\{400 \mathbf{i}-200 \mathbf{j}+500 \mathbf{k}\} \mathrm{N}$ acting along the cable $C A$

Donald Albin

Numerade Educator

Problem 125

Determine the magnitude of the projection of force $F=600 \mathrm{N}$ along the $u$ axis.

Donald Albin

Numerade Educator

Problem 126

Determine the magnitude of the projected component of the 100 -lb force acting along the axis $B C$ of the pipe.

Donald Albin

Numerade Educator

Problem 127

Determine the angle $\theta$ between pipe segments $B A$ and $B C$

Donald Albin

Numerade Educator

Problem 128

Determine the angle $\theta$ between $B A$ and $B C$

Donald Albin

Numerade Educator

Problem 129

Determine the magnitude of the projected component of the 3 kN force acting along the axis $B C$ of the pipe.

Donald Albin

Numerade Educator

Problem 130

Determine the angles $\theta$ and $\phi$ made between the axes $O A$ of the flag pole and $A B$ and $A C,$ respectively, of each cable.

Donald Albin

Numerade Educator

Problem 131

Determine the magnitudes of the components of $\mathbf{F}$ acting along and perpendicular to segment $B C$ of the pipe assembly.

Donald Albin

Numerade Educator

Problem 132

Determine the magnitude of the projected component of $\mathbf{F}$ along $A C .$ Express this component as a Cartesian vector.

Donald Albin

Numerade Educator

Problem 133

Determine the angle $\theta$ between the pipe segments $B A$ and $B C.$

Donald Albin

Numerade Educator

Problem 134

If the force $F=100 \mathrm{N}$ lics in the planc $D B E C$ which is parallel to the $x-z$ plane, and makes an angle of $10^{\circ}$ with the extended line $D B$ as shown, determine the angle that $\mathbf{F}$ makes with the diagonal $A B$ of the crate.

Donald Albin

Numerade Educator

Problem 135

Determine the magnitudes of the components of the force $F=90$ lb acting parallel and perpendicular to diagonal $A B$ of the crate.

Donald Albin

Numerade Educator

Problem 136

Determine the magnitudes of the projected components of the force $F=300 \mathrm{N}$ acting along the $x$ and $y$ axes.

Donald Albin

Numerade Educator

Problem 137

Determine the magnitude of the projected component of the force $F=300 \mathrm{N}$ acting along line $O A$

Donald Albin

Numerade Educator

Problem 138

Determine the angle $\theta$ between the two cables

Donald Albin

Numerade Educator

Problem 139

Determine the projected component of the force $F=12$ lb acting in the direction of cable $A C$. Express the result as a Cartesian vector.

Donald Albin

Numerade Educator