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Engineering Mechanics: Statics

Anthony M. Bedford, Wallace Fowler

Chapter 4

Systems of Forces and Moments - all with Video Answers

Educators

Chapter Questions

05:19

Problem 1

In Active Example 4.1, the $40-\mathrm{kN}$ force points $30^{\circ}$ above the horizontal. Suppose that the force points $30^{\circ}$ below the horizontal instead. Draw a sketch of the beam with the new orientation of the force. What is the moment of the force about point $A$ ?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
13:38

Problem 2

The mass $m_1=20 \mathrm{~kg}$. The magnitude of the total moment about $B$ due to the forces exerted on bar $A B$ by the weights of the two suspended masses is $170 \mathrm{~N}-\mathrm{m}$. What is the magnitude of the total moment due to the forces about point $A$ ?
(FIGURE CAN'T COPY)

Paul A.
Paul A.
California State Polytechnic University, Pomona
04:58

Problem 3

The wheels of the overhead crane exert downward forces on the horizontal $\mathrm{I}$-beam at $B$ and $C$. If the force at $B$ is $40 \mathrm{kip}$ and the force at $C$ is $44 \mathrm{kip}$, determine the sum of the moments of the forces on the beam about (a) point $A$, (b) point $D$.
(FIGURE CAN'T COPY)

Ryan Pollard
Ryan Pollard
Numerade Educator
01:03

Problem 5

What force $F$ applied to the pliers is required to exert a $4 \mathrm{~N}-\mathrm{m}$ moment about the center of the bolt at $P$ ?
(FIGURE CAN'T COPY)

Stephen Zaffke
Stephen Zaffke
Numerade Educator
02:30

Problem 5

Two forces of equal magnitude $F$ are applied to the wrench as shown. If a $50 \mathrm{~N}-\mathrm{m}$ moment is required to loosen the nut, what is the necessary value of $F$ ?
(FIGURE CAN'T COPY)

Surendra Kumar
Surendra Kumar
Numerade Educator

Problem 6

The force $F=8 \mathrm{kN}$. What is the moment of the force about point $P$ ?
(FIGURE CAN'T COPY)

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Problem 7

If the magnitude of the moment due to the force $F$ about $Q$ is $30 \mathrm{kN}-\mathrm{m}$, what is $F$ ?
(FIGURE CAN'T COPY)

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:50

Problem 8

The support at the left end of the beam will fail if the moment about $A$ of the $15-\mathrm{kN}$ force $F$ exceeds $18 \mathrm{kN}-\mathrm{m}$. Based on this criterion, what is the largest allowable length of the beam?
(FIGURE CAN'T COPY)

Rashmi Sinha
Rashmi Sinha
Numerade Educator
16:23

Problem 9

The length of the bar $A P$ is $650 \mathrm{~mm}$. The radius of the pulley is $120 \mathrm{~mm}$. Equal forces $T=50 \mathrm{~N}$ are applied to the ends of the cable. What is the sum of the moments of the forces (a) about $A$; (b) about $P$ ?
(FIGURE CAN'T COPY)

Benjamin Junkroski
Benjamin Junkroski
Numerade Educator
06:47

Problem 10

The force $F=12 \mathrm{kN}$. A structural engineer determines that the magnitude of the moment due to $F$ about $P$ should not exceed $5 \mathrm{kN}-\mathrm{m}$. What is the acceptable range of the angle $\alpha$ ? Assume that $0 \leq \alpha \leq 90^{\circ}$.
(FIGURE CAN'T COPY)

Susan Hallstrom
Susan Hallstrom
Numerade Educator
12:34

Problem 11

The length of bar $A B$ is $350 \mathrm{~mm}$. The moments exerted about points $B$ and $C$ by the vertical force $F$ are $M_B=-1.75 \mathrm{kN}-\mathrm{m}$ and $M_C=-4.20 \mathrm{kN}-\mathrm{m}$. Determine the force $F$ and the length of bar $A C$.
(FIGURE CAN'T COPY)

Vidhi Bhatt
Vidhi Bhatt
Numerade Educator
03:55

Problem 12

In Example 4.2, suppose that the $2-\mathrm{kN}$ force points upward instead of downward. Draw a sketch of the machine part showing the orientations of the forces. What is the sum of the moments of the forces about the origin $O$ ?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
06:10

Problem 13

Two equal and opposite forces act on the beam. Determine the sum of the moments of the two forces (a) about point $P$, (b) about point $Q$; (c) about the point with coordinates $x=7 \mathrm{~m}, y=5 \mathrm{~m}$.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
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Problem 14

The moment exerted about point $E$ by the weight is $299 \mathrm{in}-\mathrm{lb}$. What moment does the weight exert about point $S$ ?
(FIGURE CAN'T COPY)

Susan Hallstrom
Susan Hallstrom
Numerade Educator
12:34

Problem 15

The magnitudes of the forces exerted on the pillar at $D$ by the cables $A, B$, and $C$ are equal: $F_A=F_B=F_C$. The magnitude of the total moment about $E$ due to the forces exerted by the three cables at $D$ is $1350 \mathrm{kN}-\mathrm{m}$. What is $F_A$ ?
(FIGURE CAN'T COPY)

Vidhi Bhatt
Vidhi Bhatt
Numerade Educator

Problem 16

Three forces act on the piping. Determine the sum of the moments of the three forces about point $P$.
(FIGURE CAN'T COPY)

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12:02

Problem 17

The forces $F_1=30 \mathrm{~N}, F_2=80 \mathrm{~N}$, and $F_3=40 \mathrm{~N}$. What is the sum of the moments of the forces about point $A$ ?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
03:36

Problem 18

The force $F_1=30 \mathrm{~N}$. The vector sum of the three forces is zero. What is the sum of the moments of the forces about point $A$ ?
(FIGURE CAN'T COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
12:02

Problem 19

The forces $F_A=30 \mathrm{lb}, F_B=40 \mathrm{lb}, F_C=20 \mathrm{lb}$, and $F_D=30 \mathrm{lb}$. What is the sum of the moments of the forces about the origin of the coordinate system?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
08:52

Problem 20

The force $F_A=30 \mathrm{lb}$. The vector sum of the forces on the beam is zero, and the sum of the moments of the forces about the origin of the coordinate system is zero. (a) Determine the forces $F_B, F_C$, and $F_D$. (b) Determine the sum of the moments of the forces about the right end of the beam.
(FIGURE CAN'T COPY)

Kebur Fantahun
Kebur Fantahun
Numerade Educator

Problem 21

Three forces act on the car. The sum of the forces is zero and the sum of the moments of the forces about point $P$ is zero.
(a) Determine the forces $A$ and $B$.
(b) Determine the sum of the moments of the forces about point $Q$.
(FIGURE CAN'T COPY)

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03:31

Problem 22

Five forces act on the piping. The vector sum of the forces is zero and the sum of the moments of the forces about point $P$ is zero.
(a) Determine the forces $A, B$, and $C$.
(b) Determine the sum of the moments of the forces about point $Q$.
(FIGURE CAN'T COPY)

Stephen Zaffke
Stephen Zaffke
Numerade Educator
20:32

Problem 23

In Example 4.3, suppose that the attachment point $B$ is moved upward and the cable is lengthened so that the vertical distance from $C$ to $B$ is $9 \mathrm{ft}$. (The positions of points $C$ and $A$ are unchanged.) Draw a sketch of the system with the cable in its new position. What is the tension in the cable?

Manan Sheel
Manan Sheel
Numerade Educator
02:49

Problem 24

The tension in the cable is the same on both sides of the pulley. The sum of the moments about point $A$ due to the $800-\mathrm{lb}$ force and the forces exerted on the bar by the cable at $B$ and $C$ is zero. What is the tension in the cable?
(FIGURE CAN'T COPY)

Monica Miller
Monica Miller
Numerade Educator
06:45

Problem 24

The $160-\mathrm{N}$ weights of the arms $A B$ and $B C$ of the robotic manipulator act at their midpoints. Determine the sum of the moments of the three weights about $A$.
(FIGURE CAN'T COPY)

Jonathan Ibarra
Jonathan Ibarra
Numerade Educator
05:31

Problem 26

The space shuttle's attitude thrusters exert two forces of magnitude $F=7.70 \mathrm{kN}$. What moment do the thrusters exert about the center of mass $G$ ?
(FIGURE CAN'T COPY)

Vipender Yadav
Vipender Yadav
Numerade Educator
04:34

Problem 27

The force $F$ exerts a $200 \mathrm{ft}$-lb counterclockwise moment about $A$ and a $100 \mathrm{ft}-\mathrm{lb}$ clockwise moment about $B$. What are $F$ and $\theta$ ?
(FIGURE CAN'T COPY)

Surendra Kumar
Surendra Kumar
Numerade Educator
06:25

Problem 28

Five forces act on a link in the gear-shifting mechanism of a lawn mower. The vector sum of the five forces on the bar is zero. The sum of their moments about the point where the forces $A_x$ and $A_y$ act is zero.
(a) Determine the forces $A_x, A_y$, and $B$.
(b) Determine the sum of the moments of the forces about the point where the force $B$ acts.
(FIGURE CAN'T COPY)

Guilherme Barros
Guilherme Barros
Numerade Educator
03:19

Problem 29

Five forces act on a model truss built by a civil engineering student as part of a design project. The dimensions are $b=300 \mathrm{~mm}$ and $h=400 \mathrm{~mm}$ and $F=100 \mathrm{~N}$. The sum of the moments of the forces about the point where $A_x$ and $A_y$ act is zero. If the weight of the truss is negligible, what is the force $B$ ?
(FIGURE CAN'T COPY)

Sachin Rao
Sachin Rao
Numerade Educator

Problem 30

The dimensions are $b=3 \mathrm{ft}$ and $h=4 \mathrm{ft}$ and $F=300 \mathrm{lb}$. The vector sum of the forces acting on the truss is zero, and the sum of the moments of the forces about the point where $A_x$ and $A_y$ act is zero.
(a) Determine the forces $A_x, A_y$, and $B$.
(b) Determine the sum of the moments of the forces about the point where the force $B$ acts.
(FIGURE CAN'T COPY)

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07:26

Problem 31

The mass $m=70 \mathrm{~kg}$. What is the moment about $A$ due to the force exerted on the beam at $B$ by the cable?
(FIGURE CAN'T COPY)

Jonathan Ibarra
Jonathan Ibarra
Numerade Educator
15:06

Problem 32

The weights $W_1$ and $W_2$ are suspended by the cable system shown. The weight $W_1=12 \mathrm{lb}$. The cable $B C$ is horizontal. Determine the moment about point $P$ due to the force exerted on the vertical post at $D$ by the cable $C D$.
(FIGURE CAN'T COPY)

Benjamin Junkroski
Benjamin Junkroski
Numerade Educator
05:37

Problem 33

The bar $A B$ exerts a force at $B$ that helps support the vertical retaining wall. The force is parallel to the bar. The civil engineer wants the bar to exert a $38 \mathrm{kN}$-m moment about $O$. What is the magnitude of the force the bar must exert?
(FIGURE CAN'T COPY)

Guilherme Barros
Guilherme Barros
Numerade Educator
04:37

Problem 34

A contestant in a fly-casting contest snags his line in some grass. If the tension in the line is $5 \mathrm{lb}$, what moment does the force exerted on the rod by the line exert about point $H$, where he holds the rod?
(FIGURE CAN'T COPY)

Vipender Yadav
Vipender Yadav
Numerade Educator
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Problem 35

The cables $A B$ and $A C$ help support the tower. The tension in cable $A B$ is $5 \mathrm{kN}$. The points $A, B, C$, and $O$ are contained in the same vertical plane. (a) What is the moment about $O$ due to the force exerted on the tower by cable $A B$ ? (b) If the sum of the moments about $O$ due to the forces exerted on the tower by the two cables is zero, what is the tension in cable $A C$ ?
(FIGURE CAN'T COPY)

Rashmi Sinha
Rashmi Sinha
Numerade Educator
06:22

Problem 36

The cable from $B$ to $A$ (the sailboat's forestay) exerts a $230-\mathrm{N}$ force at $B$. The cable from $B$ to $C$ (the backstay) exerts a $660-\mathrm{N}$ force at $B$. The bottom of the sailboat's mast is located at $x=4 \mathrm{~m}, y=0$. What is the sum of the moments about the bottom of the mast due to the forces exerted at $B$ by the forestay and backstay?
(FIGURE CAN'T COPY)

Pawan Yadav
Pawan Yadav
Numerade Educator
05:19

Problem 37

The cable $A B$ exerts a $290-\mathrm{kN}$ force on the crane's boom at $B$. The cable $A C$ exerts a $148-\mathrm{kN}$ force on the boom at $C$. Determine the sum of the moments about $P$ due to the forces the cables $A B$ and $A C$ exert on the boom.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
09:25

Problem 38

The mass of the crane's boom is $9000 \mathrm{~kg}$. Its weight acts at $G$. The sum of the moments about $P$ due to the boom's weight, the force exerted at $B$ by the cable $A B$, and the force exerted at $C$ by the cable $A C$ is zero. Assume that the tensions in cables $A B$ and $A C$ are equal. Determine the tension in the cables.
(FIGURE CAN'T COPY)

Jonathan Ibarra
Jonathan Ibarra
Numerade Educator
02:41

Problem 39

The mass of the luggage carrier and the suitcase combined is $12 \mathrm{~kg}$. Their weight acts at $A$. The sum of the moments about the origin of the coordinate system due to the weight acting at $A$ and the vertical force $F$ applied to the handle of the luggage carrier is zero. Determine the force $F$ (a) if $\alpha=30^{\circ}$;
(b) if $\alpha=50^{\circ}$.
(FIGURE CAN'T COPY)

Prabhu Ramji
Prabhu Ramji
Numerade Educator
31:04

Problem 40

The hydraulic cylinder $B C$ exerts a $300-\mathrm{kN}$ force on the boom of the crane at $C$. The force is parallel to the cylinder. What is the moment of the force about $A$ ?
(FIGURE CAN'T COPY)

Donald Albin
Donald Albin
Numerade Educator
01:04

Problem 41

The hydraulic piston $A B$ exerts a $400-\mathrm{lb}$ force on the ladder at $B$ in the direction parallel to the piston. The sum of the moments about $C$ due to the force exerted on the ladder by the piston and the weight $W$ of the ladder is zero. What is the weight of the ladder?
(FIGURE CAN'T COPY)

Dominador Tan
Dominador Tan
Numerade Educator
06:24

Problem 42

The hydraulic cylinder exerts an $8-\mathrm{kN}$ force at $B$ that is parallel to the cylinder and points from $C$ toward $B$. Determine the moments of the force about points $A$ and $D$.
(FIGURE CAN'T COPY)

Donald Albin
Donald Albin
Numerade Educator

Problem 43

The structure shown in the diagram is one of two identical structures that support the scoop of the excavator. The bar $B C$ exerts a $700-\mathrm{N}$ force at $C$ that points from $C$ toward $B$. What is the moment of this force about $K$ ?
(FIGURE CAN'T COPY)

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06:24

Problem 44

The bar $B C$ exerts a force at $C$ that points from $C$ toward $B$. The hydraulic cylinder $D H$ exerts a $1550-\mathrm{N}$ force at $D$ that points from $D$ toward $H$. The sum of the moments of these two forces about $K$ is zero. What is the magnitude of the force that bar $B C$ exerts at $C$ ?
(FIGURE CAN'T COPY)

Donald Albin
Donald Albin
Numerade Educator
00:53

Problem 45

In Active Example 4.4, what is the moment of $\mathbf{F}$ about the origin of the coordinate system?

Hast Aggarwal
Hast Aggarwal
Numerade Educator
05:42

Problem 46

Use Eq. (4.2) to determine the moment of the $80-\mathrm{N}$ force about the origin $O$ letting $\mathbf{r}$ be the vector (a) from $O$ to $A$; (b) from $O$ to $B$.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
06:07

Problem 47

A bioengineer studying an injury sustained in throwing the javelin estimates that the magnitude of the maximum force exerted was $|\mathbf{F}|=360 \mathrm{~N}$ and the perpendicular distance from $O$ to the line of action of $\mathbf{F}$ was $550 \mathrm{~mm}$. The vector $\mathbf{F}$ and point $O$ are contained in the $x-y$ plane. Express the moment of $\mathbf{F}$ about the shoulder joint at $O$ as a vector.
(FIGURE CAN'T COPY)

Gordon Ayadju
Gordon Ayadju
Numerade Educator
12:02

Problem 48

Use Eq. (4.2) to determine the moment of the $100-\mathrm{kN}$ force (a) about $A$; (b) about $B$.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator

Problem 49

The cable $A B$ exerts a $200-\mathrm{N}$ force on the support at $A$ that points from $A$ toward $B$. Use Eq. (4.2) to determine the moment of this force about point $P$, (a) letting $\mathbf{r}$ be the vector from $P$ to $A$; (b) letting $\mathbf{r}$ be the vector from $P$ to $B$.
(FIGURE CAN'T COPY)

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07:42

Problem 50

The line of action of $\mathbf{F}$ is contained in the $x-y$ plane. The moment of $F$ about $O$ is $140 \mathrm{k}(\mathrm{N}-\mathrm{m}$ ), and the moment of $\mathbf{F}$ about $A$ is $280 \mathrm{k}(\mathrm{N}-\mathrm{m})$. What are the components of $\mathbf{F}$ ?
(FIGURE CAN'T COPY)

Donald Albin
Donald Albin
Numerade Educator

Problem 51

Use Eq. (4.2) to determine the sum of the moments of the three forces (a) about $A$; (b) about $B$.
(FIGURE CAN'T COPY)

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01:04

Problem 52

Three forces are applied to the plate. Use Eq (4.2) to determine the sum of the moments of the three forces about the origin $O$.
(FIGURE CAN'T COPY)

Dominador Tan
Dominador Tan
Numerade Educator

Problem 53

Three forces act on the plate. Use Eq. (4.2) to determine the sum of the moments of the three forces about point $P$.
(FIGURE CAN'T COPY)

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06:06

Problem 54

(a) Determine the magnitude of the moment of the $150-\mathrm{N}$ force about $A$ by calculating the perpendicular distance from $A$ to the line of action of the force.
(b) Use Eq (4.2) to determine the magnitude of the moment of the $150-\mathrm{N}$ force about $A$
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
05:38

Problem 55

(a) Determine the magnitude of the moment of the $600-\mathrm{N}$ force about $A$ by calculating the perpendicular distance from $A$ to the line of action of the force.
(b) Use Eq. (4.2) to determine the magnitude of the moment of the $600-\mathrm{N}$ force about $A$.
(FIGURE CAN'T COPY)

Ahmed Kamel
Ahmed Kamel
Numerade Educator
01:43

Problem 56

What is the magnitude of the moment of $\mathbf{F}$ about point $B$ ?
(FIGURE CAN'T COPY)

Nick Johnson
Nick Johnson
Numerade Educator
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Problem 57

In Example 4.5, suppose that the attachment point $C$ is moved to the location $(8,2,0) \mathrm{m}$ and the tension in cable $A C$ changes to $25 \mathrm{kN}$. What is the sum of the moments about $O$ due to the forces exerted on the attachment point $A$ by the two cables?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
05:04

Problem 58

The rope exerts a force of magnitude $|\mathbf{F}|=200 \mathrm{lb}$ on the top of the pole at $B$. Determine the magnitude of the moment of $\mathbf{F}$ about $A$.
(FIGURE CAN'T COPY)

AS
Anderson Speed
Numerade Educator

Problem 59

The force $\mathbf{F}=30 \mathbf{i}+20 \mathbf{j}-10 \mathbf{k}(\mathrm{N})$.
(a) Determine the magnitude of the moment of $\mathbf{F}$ about $A$.
(b) Suppose that you can change the direction of $\mathbf{F}$ while keeping its magnitude constant, and you want to choose a direction that maximizes the moment of $\mathbf{F}$ about $A$. What is the magnitude of the resulting maximum moment?
(FIGURE CAN'T COPY)

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06:07

Problem 60

The direction cosines of the force $\mathbf{F}$ are $\cos \theta_x=0.818$, $\cos \theta_y=0.182$, and $\cos \theta_z=-0.545$. The support of the beam at $O$ will fail if the magnitude of the moment of $\mathbf{F}$ about $O$ exceeds $100 \mathrm{kN}-\mathrm{m}$. Determine the magnitude of the largest force $\mathbf{F}$ that can safely be applied to the beam.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:39

Problem 61

The force $\mathbf{F}$ exerted on the grip of the exercise machine points in the direction of the unit vector $\mathbf{e}=\frac{2}{3} \mathbf{i}-\frac{2}{3} \mathbf{j}+\frac{1}{3} \mathbf{k}$ and its magnitude is $120 \mathrm{~N}$. Determine the magnitude of the moment of $\mathbf{F}$ about the origin $O$.
(FIGURE CAN'T COPY)

Ryan Pollard
Ryan Pollard
Numerade Educator
06:07

Problem 62

The force $\mathbf{F}$ points in the direction of the unit vector $\mathbf{e}=\frac{2}{3} \mathbf{i}-\frac{2}{3} \mathbf{j}+\frac{1}{3} \mathbf{k}$. The support at $O$ will safely support a moment of $560 \mathrm{~N}-\mathrm{m}$ magnitude. (a) Based on this criterion, what is the largest safe magnitude of $\mathbf{F}$ ? (b) If the force $\mathbf{F}$ may be exerted in any direction, what is its largest safe magnitude?
(FIGURE CAN'T COPY)

Gordon Ayadju
Gordon Ayadju
Numerade Educator
02:25

Problem 63

A civil engineer in Boulder, Colorado, estimates that under the severest expected Chinook winds, the total force on the highway sign will be $\mathbf{F}=2.8 \mathbf{i}-1.8 \mathbf{j}(\mathrm{kN})$. Let $\mathbf{M}_O$ be the moment due to $\mathbf{F}$ about the base $O$ of the cylindrical column supporting the sign. The $y$ component of $\mathbf{M}_O$ is called the torsion exerted on the cylindrical column at the base, and the component of $\mathbf{M}_O$ parallel to the $x-z$ plane is called the bending moment. Determine the magnitudes of the torsion and bending moment.
(FIGURE CAN'T COPY)

Averell Hause
Averell Hause
Carnegie Mellon University
01:04

Problem 64

The weights of the arms $O A$ and $A B$ of the robotic manipulator act at their midpoints. The direction cosines of the centerline of arm $O A$ are $\cos \theta_x=0.500, \cos \theta_y=0.866$, and $\cos \theta_z=0$, and the direction cosines of the centerline of arm $A B$ are $\cos \theta_x=0.707, \cos \theta_y=0.619$, and $\cos \theta_z=-0.342$. What is the sum of the moments about $O$ due to the two forces?
(FIGURE CAN'T COPY)

Dominador Tan
Dominador Tan
Numerade Educator
14:10

Problem 65

The tension in cable $A B$ is $100 \mathrm{lb}$. If you want the magnitude of the moment due to the forces exerted on the tree by the two ropes about the base $O$ of the tree to be $1500 \mathrm{ft}-\mathrm{lb}$, what is the necessary tension in rope $A C$ ?
(FIGURE CAN'T COPY)

JM
Joseph Martinez
Numerade Educator
02:36

Problem 66

A force $\mathbf{F}$ acts at the top end $A$ of the pole. Its magnitude is $|\mathbf{F}|=6 \mathrm{kN}$ and its $x$ component is $F_x=4 \mathrm{kN}$. The coordinates of point $A$ are shown. Determine the components of $\mathbf{F}$ so that the magnitude of the moment due to $\mathbf{F}$ about the base $P$ of the pole is as large as possible.
(FIGURE CAN'T COPY)

Jonah Han
Jonah Han
Numerade Educator
06:30

Problem 67

The force $\mathbf{F}=5 \mathrm{i}(\mathrm{kN})$ acts on the ring $A$ where the cables $A B, A C$, and $A D$ are joined. What is the sum of the moments about point $D$ due to the force $\mathbf{F}$ and the three forces exerted on the ring by the cables?
(FIGURE CAN'T COPY)

Jonathan Ibarra
Jonathan Ibarra
Numerade Educator
06:19

Problem 68

In Problem 4.67, determine the moment about point $D$ due to the force exerted on the ring $A$ by the cable $A B$.
(FIGURE CAN'T COPY)

Jonathan Ibarra
Jonathan Ibarra
Numerade Educator
05:19

Problem 69

The tower is $70 \mathrm{~m}$ tall. The tensions in cables $A B, A C$, and $A D$ are $4 \mathrm{kN}, 2 \mathrm{kN}$, and $2 \mathrm{kN}$, respectively. Determine the sum of the moments about the origin $O$ due to the forces exerted by the cables at point $A$.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:44

Problem 70

Suppose that the tension in cable $A B$ is $4 \mathrm{kN}$, and you want to adjust the tensions in cables $A C$ and $A D$ so that the sum of the moments about the origin $O$ due to the forces exerted by the cables at point $A$ is zero. Determine the tensions.
(FIGURE CAN'T COPY)

Eric Mockensturm
Eric Mockensturm
Numerade Educator
05:42

Problem 71

The tension in cable $A B$ is $150 \mathrm{~N}$. The tension in cable $A C$ is $100 \mathrm{~N}$. Determine the sum of the moments about $D$ due to the forces exerted on the wall by the cables.
(FIGURE CAN'T COPY)

Henry York
Henry York
Numerade Educator
01:16

Problem 72

The total force exerted by the two cables in the direction perpendicular to the wall is $2 \mathrm{kN}$. The magnitude of the sum of the moments about $D$ due to the forces exerted on the wall by the cables is $18 \mathrm{kN}-\mathrm{m}$. What are the tensions in the cables?
(FIGURE CAN'T COPY)

Dominador Tan
Dominador Tan
Numerade Educator
05:37

Problem 73

The tension in the cable $B D$ is $1 \mathrm{kN}$. As a result, cable $B D$ exerts a $1-\mathrm{kN}$ force on the "ball" at $B$ that points from $B$ toward $D$. Determine the moment of this force about point $A$.
(FIGURE CAN'T COPY)

Guilherme Barros
Guilherme Barros
Numerade Educator
06:20

Problem 74

Suppose that the mass of the suspended object $E$ is $100 \mathrm{~kg}$ and the mass of the bar $A B$ is $20 \mathrm{~kg}$. Assume that the weight of the bar acts at its midpoint. If the sum of the moments about point $A$ due to the weight of the bar and the forces exerted on the "ball" at $B$ by the three cables $B C, B D$, and $B E$ is zero, determine the tensions in the cables $B C$ and $B D$.
(FIGURE CAN'T COPY)

Christopher Dzorkpata
Christopher Dzorkpata
Numerade Educator

Problem 75

The $200-\mathrm{kg}$ slider at $A$ is held in place on the smooth vertical bar by the cable $A B$. Determine the moment about the bottom of the bar (point $C$ with coordinates $x=2 \mathrm{~m}, y=z=0$ ) due to the force exerted on the slider by the cable.
(FIGURE CAN'T COPY)

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Problem 76

To evaluate the adequacy of the design of the vertical steel post, you must determine the moment about the bottom of the post due to the force exerted on the post at $B$ by the cable $A B$. A calibrated strain gauge mounted on cable $A C$ indicates that the tension in cable $A C$ is $22 \mathrm{kN}$. What is the moment?
(FIGURE CAN'T COPY)

Rashmi Sinha
Rashmi Sinha
Numerade Educator
06:07

Problem 77

The force $\mathbf{F}=20 \mathbf{i}+40 \mathbf{j}-10 \mathbf{k}(\mathrm{N})$. Use both of the procedures described in Example 4.7 to determine the moment due to $\mathbf{F}$ about the $z$ axis.
(FIGURE CAN'T COPY)

Gordon Ayadju
Gordon Ayadju
Numerade Educator
06:28

Problem 78

Use Eqs. (4.5) and (4.6) to determine the moment of the $20-\mathrm{N}$ force about (a) the $x$ axis, (b) the $y$ axis, (c) the $z$ axis. (First see if you can write down the results without using the equations.)
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator

Problem 79

Three forces parallel to the $y$ axis act on the rectangular plate. Use Eqs. (4.5) and (4.6) to determine the sum of the moments of the forces about the $x$ axis.
(FIGURE CAN'T COPY)

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Problem 80

The three forces are parallel to the $y$ axis. Determine the sum of the moments of the forces (a) about the $y$ axis; (b) about the $z$ axis.
(FIGURE CAN'T COPY)

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02:27

Problem 81

The person exerts a force $\mathbf{F}=0.2 \mathbf{i}-0.4 \mathbf{j}+1.2 \mathbf{k}(\mathrm{lb})$ on the gate at $C$. Point $C$ lies in the $x-y$ plane. What moment does the person exert about the gate's hinge axis, which is coincident with the $y$ axis?
(FIGURE CAN'T COPY)

Dominador Tan
Dominador Tan
Numerade Educator

Problem 82

Four forces act on the plate. Their components are
$$
\begin{aligned}
& \mathbf{F}_A=-2 \mathbf{i}+4 \mathbf{j}+2 \mathbf{k}(\mathrm{kN}) \\
& \mathbf{F}_B=3 \mathbf{j}-3 \mathbf{k}(\mathrm{kN}) \\
& \mathbf{F}_C=2 \mathbf{j}+3 \mathbf{k}(\mathrm{kN}) \\
& \mathbf{F}_D=2 \mathbf{i}+6 \mathbf{j}+4 \mathbf{k}(\mathrm{kN}) .
\end{aligned}
$$
Determine the sum of the moments of the forces (a) about the $x$ axis; (b) about the $z$ axis.
(FIGURE CAN'T COPY)

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06:28

Problem 83

The force $\mathbf{F}=30 \mathbf{i}+20 \mathbf{j}-10 \mathbf{k}$ (lb).
(a) What is the moment of $\mathbf{F}$ about the $y$ axis?
(b) Suppose that you keep the magnitude of $\mathbf{F}$ fixed, but you change its direction so as to make the moment of $\mathbf{F}$ about the $y$ axis as large as possible. What is the magnitude of the resulting moment?
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:01

Problem 84

The moment of the force $\mathbf{F}$ about the $x$ axis is $-80 \mathbf{i}(\mathrm{ft}-\mathrm{lb})$, the moment about the $y$ axis is zero, and the moment about the $z$ axis is $160 \mathrm{k}$ (ft-lb). If $F_y=80 \mathrm{lb}$, what are $F_x$ and $F_z$ ?
(FIGURE CAN'T COPY)

Donald Albin
Donald Albin
Numerade Educator
02:29

Problem 85

The robotic manipulator is stationary. The weights of the arms $A B$ and $B C$ act at their midpoints. The direction cosines of the centerline of arm $A B$ are $\cos \theta_x=0.500, \cos \theta_y=0.866$, $\cos \theta_z=0$, and the direction cosines of the centerline of arm $B C$ are $\cos \theta_x=0.707, \cos \theta_y=0.619, \cos \theta_z=-0.342$. What total moment is exerted about the $z$ axis by the weights of the arms?
(FIGURE CAN'T COPY)

Manish Jain
Manish Jain
Numerade Educator
01:00

Problem 86

In Problem 4.85, what total moment is exerted about the $x$ axis by the weights of the arms?
(FIGURE CAN'T COPY)

Dominador Tan
Dominador Tan
Numerade Educator
03:55

Problem 87

In Active Example 4.6, suppose that the force changes to $\mathbf{F}=-2 \mathbf{i}+3 \mathbf{j}+6 \mathbf{k}(\mathrm{kN})$. Determine the magnitude of the moment of the force about the axis of the bar $B C$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
12:02

Problem 88

Determine the moment of the $20-\mathrm{N}$ force about the line $A B$. Use Eqs. (4.5) and (4.6), letting the unit vector $\mathbf{e}$ point (a) from $A$ toward $B$, (b) from $B$ toward $A$.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
03:55

Problem 89

The force $\mathbf{F}=-10 \mathbf{i}+5 \mathbf{j}-5 \mathbf{k}$ (kip). Determine the moment of $\mathbf{F}$ about the line $A B$. Draw a sketch to indicate the direction of the moment.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
06:07

Problem 90

The force $\mathbf{F}=10 \mathbf{i}+12 \mathbf{j}-6 \mathbf{k}(\mathrm{N})$. What is the moment of $\mathbf{F}$ about the line $A O$ ? Draw a sketch to indicate the direction of the moment.
(FIGURE CAN'T COPY)

Gordon Ayadju
Gordon Ayadju
Numerade Educator
05:19

Problem 91

The tension in the cable $A B$ is $1 \mathrm{kN}$. Determine the moment about the $x$ axis due to the force exerted on the hatch by the cable at point $B$. Draw a sketch to indicate the direction of the moment.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
11:33

Problem 92

Determine the moment of the force applied at $D$ about the straight line through the hinges $A$ and $B$.
(FIGURE CAN'T COPY)

Narayan Hari
Narayan Hari
Numerade Educator
03:08

Problem 93

The tension in the cable $C E$ is $160 \mathrm{lb}$. Determine the moment of the force exerted by the cable on the hatch at $C$ about the straight line through the hinges $A$ and $B$.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
05:39

Problem 94

The coordinates of $A$ are $(-2.4,0,-0.6) \mathrm{m}$, and the coordinates of $B$ are $(-2.2,0.7,-1.2) \mathrm{m}$. The force exerted at $B$ by the sailboat's main sheet $A B$ is $130 \mathrm{~N}$. Determine the moment of the force about the centerline of the mast (the $y$ axis). Draw a sketch to indicate the direction of the moment.
(FIGURE CAN'T COPY)

Guilherme Barros
Guilherme Barros
Numerade Educator
05:19

Problem 95

The tension in cable $A B$ is $200 \mathrm{lb}$. Determine the moments about each of the coordinate axes due to the force exerted on point $B$ by the cable. Draw sketches to indicate the direction of the moments.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:33

Problem 96

The total force exerted on the blades of the turbine by the steam nozzle is $\mathbf{F}=20 \mathbf{i}-120 \mathbf{j}+100 \mathbf{k}(\mathrm{N})$, and it effectively acts at the point $(100,80,300) \mathrm{mm}$. What moment is exerted about the axis of the turbine (the $x$ axis)?
(FIGURE CAN'T COPY)

Donald Albin
Donald Albin
Numerade Educator
01:11

Problem 97

The pneumatic support $A B$ holds a trunk lid in place. It exerts a $35-\mathrm{N}$ force on the fixture at $B$ that points in the direction from $A$ toward $B$. Determine the magnitude of the moment of the force about the hinge axis of the lid, which is the $z$ axis.
(FIGURE CAN'T COPY)

Prashant Bana
Prashant Bana
Numerade Educator
05:37

Problem 98

The tension in cable $A B$ is $80 \mathrm{lb}$. What is the moment about the line $C D$ due to the force exerted by the cable on the wall at $B$ ?
(FIGURE CAN'T COPY)

Guilherme Barros
Guilherme Barros
Numerade Educator
05:49

Problem 99

The magnitude of the force $\mathbf{F}$ is $0.2 \mathrm{~N}$ and its direction cosines are $\cos \theta_x=0.727, \cos \theta_y=-0.364$, and $\cos \theta_z=0.582$. Determine the magnitude of the moment of $\mathbf{F}$ about the axis $A B$ of the spool.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:21

Problem 100

A motorist applies the two forces shown to loosen a lug nut. The direction cosines of $\mathbf{F}$ are $\cos \theta_x=\frac{4}{13}, \cos \theta_y=\frac{12}{13}$, and $\cos \theta_z=\frac{3}{13}$. If the magnitude of the moment about the $x$ axis must be $32 \mathrm{ft}$ - $\mathrm{lb}$ to loosen the nut, what is the magnitude of the forces the motorist must apply? (See Example 4.8.)
(FIGURE CAN'T COPY)

Ren Jie Tuieng
Ren Jie Tuieng
Numerade Educator
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Problem 101

The tension in cable $A B$ is $2 \mathrm{kN}$. What is the magnitude of the moment about the shaft $C D$ due to the force exerted by the cable at $A$ ? Draw a sketch to indicate the direction of the moment about the shaft.
(FIGURE CAN'T COPY)

Rashmi Sinha
Rashmi Sinha
Numerade Educator
02:28

Problem 102

The axis of the car's wheel passes through the origin of the coordinate system and its direction cosines are $\cos \theta_x=0.940$, $\cos \theta_y=0, \cos \theta_z=0.342$. The force exerted on the tire by the road effectively acts at the point $x=0, y=-0.36 \mathrm{~m}, z=0$ and has components $\mathbf{F}=-720 \mathbf{i}+3660 \mathbf{j}+1240 \mathbf{k}(\mathrm{N})$. What is the moment of $\mathbf{F}$ about the wheel's axis?
(FIGURE CAN'T COPY)

Jayashree Behera
Jayashree Behera
Numerade Educator
02:32

Problem 103

The direction cosines of the centerline $O A$ are $\cos \theta_x=$ $0.500, \cos \theta_y=0.866$, and $\cos \theta_z=0$, and the direction cosines of the line $A G$ are $\cos \theta_x=0.707, \cos \theta_y=0.619$, and $\cos \theta_z=$ -0.342 . What is the moment about $O A$ due to the $250-\mathrm{N}$ weight? Draw a sketch to indicate the direction of the moment about the shaft.
(FIGURE CAN'T COPY)

Manish Jain
Manish Jain
Numerade Educator
05:49

Problem 104

The radius of the steering wheel is $200 \mathrm{~mm}$. The distance from $O$ to $C$ is $1 \mathrm{~m}$. The center $C$ of the steering wheel lies in the $x-y$ plane. The driver exerts a force $\mathbf{F}=10 \mathbf{i}+10 \mathbf{j}-5 \mathbf{k}(\mathrm{N})$ on the wheel at $A$. If the angle $\alpha=0$, what is the magnitude of the moment about the shaft $O C$ ? Draw a sketch to indicate the direction of the moment about the shaft.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
14:10

Problem 105

The magnitude of the force $\mathbf{F}$ is $10 \mathrm{~N}$. Suppose that you want to choose the direction of the force $\mathbf{F}$ so that the magnitude of its moment about the line $L$ is a maximum. Determine the components of $\mathbf{F}$ and the magnitude of its moment about $L$ (There are two solutions for $\mathbf{F}$.)
(FIGURE CAN'T COPY)

Donald Albin
Donald Albin
Numerade Educator

Problem 106

The weight $W$ causes a tension of $100 \mathrm{lb}$ in cable $C D$. If $d=2 \mathrm{ft}$, what is the moment about the $z$ axis due to the force exerted by the cable $C D$ at point $C$ ?
(FIGURE CAN'T COPY)

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55:22

Problem 107

The $y$ axis points upward. The weight of the $4-\mathrm{kg}$ rectangular plate acts at the midpoint $G$ of the plate. The sum of the moments about the straight line through the supports $A$ and $B$ due to the weight of the plate and the force exerted on the plate by the cable $C D$ is zero. What is the tension in the cable?
(FIGURE CAN'T COPY)

AG
Allison Gleason
Numerade Educator

Problem 108

In Active Example 4.9, suppose that the point of application of the force $\mathbf{F}$ is moved from $(8,3,0) \mathrm{m}$ to $(8,8,0) \mathrm{m}$. Draw a sketch showing the new position of the force. From your sketch, will the moment due to the couple be clockwise or counterclockwise? Calculate the moment due to the couple. Represent the moment by its magnitude and a circular arrow indicating its direction.

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02:08

Problem 109

The forces are contained in the $x-y$ plane.
(a) Determine the moment of the couple and represent it as shown in Fig. 4.18c.
(b) What is the sum of the moments of the two forces about the point $(10,-40,20) \mathrm{ft}$ ?
(FIGURE CAN'T COPY)

Ahmed Kamel
Ahmed Kamel
Numerade Educator

Problem 110

The moment of the couple is $600 \mathrm{k}(\mathrm{N}-\mathrm{m})$. What is the angle $\alpha$ ?
(FIGURE CAN'T COPY)

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06:07

Problem 111

Point $P$ is contained in the $x-y$ plane, $|\mathbf{F}|=100 \mathrm{~N}$, and the moment of the couple is $-500 \mathrm{k}(\mathrm{N}-\mathrm{m})$. What are the coordinates of $P$ ?
(FIGURE CAN'T COPY)

Gordon Ayadju
Gordon Ayadju
Numerade Educator
06:23

Problem 112

Three forces of equal magnitude are applied parallel to the sides of an equilateral triangle. (a) Show that the sum of the moments of the forces is the same about any point. (b) Determine the magnitude of the sum of the moments.
(FIGURE CAN'T COPY)

Tarandeep Singh
Tarandeep Singh
Numerade Educator

Problem 113

In Example 4.10, suppose that the $200 \mathrm{ft}-\mathrm{lb}$ couple is counterclockwise instead of clockwise. Draw a sketch of the beam showing the forces and couple acting on it. What are the forces $A$ and $B$ ?

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03:01

Problem 114

The moments of two couples are shown. What is the sum of the moments about point $P$ ?
(FIGURE CAN'T COPY)

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator

Problem 115

Determine the sum of the moments exerted on the plate by the two couples.
(FIGURE CAN'T COPY)

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12:02

Problem 116

Determine the sum of the moments exerted about $A$ by the couple and the two forces.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
12:02

Problem 117

Determine the sum of the moments exerted about $A$ by the couple and the two forces.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
12:02

Problem 118

The sum of the moments about point $A$ due to the forces and couples acting on the bar is zero.
(a) What is the magnitude of the couple $C$ ?
(b) Determine the sum of the moments about point $B$ due to the forces and couples acting on the bar.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
05:09

Problem 119

In Example 4.11, suppose that instead of acting in the positive $z$ axis direction, the upper $20-\mathrm{N}$ force acts in the positive $x$ axis direction. Instead of acting in the negative $z$ axis direction, let the lower $20-\mathrm{N}$ force act in the negative $x$ axis direction. Draw a sketch of the pipe showing the forces acting on it. Determine the sum of the moments exerted on the pipe by the two couples.

Surjit Tewari
Surjit Tewari
Numerade Educator
12:02

Problem 120

(a) What is the moment of the couple?
(b) Determine the perpendicular distance between the lines of action of the two forces.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator

Problem 121

Determine the sum of the moments exerted on the plate by the three couples.
(FIGURE CAN'T COPY)

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02:08

Problem 122

What is the magnitude of the sum of the moments exerted on the T-shaped structure by the two couples?
(FIGURE CAN'T COPY)

Ahmed Kamel
Ahmed Kamel
Numerade Educator
04:03

Problem 123

The tension in cables $A B$ and $C D$ is $500 \mathrm{~N}$.
(a) Show that the two forces exerted by the cables on the rectangular hatch at $B$ and $C$ form a couple.
(b) What is the moment exerted on the plate by the cables?
(FIGURE CAN'T COPY)

Ryan Pollard
Ryan Pollard
Numerade Educator
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Problem 124

The cables $A B$ and $C D$ exert a couple on the vertical pipe. The tension in each cable is $8 \mathrm{kN}$. Determine the magnitude of the moment the cables exert on the pipe.
(FIGURE CAN'T COPY)

Rashmi Sinha
Rashmi Sinha
Numerade Educator

Problem 125

The bar is loaded by the forces
$$
\begin{aligned}
& \mathbf{F}_B=2 \mathbf{i}+6 \mathbf{j}+3 \mathbf{k}(\mathrm{kN}), \\
& \mathbf{F}_C=\mathbf{i}-2 \mathbf{j}+2 \mathbf{k}(\mathrm{kN}),
\end{aligned}
$$
and the couple
$$
\mathbf{M}_C=2 \mathbf{i}+\mathbf{j}-2 \mathbf{k}(\mathrm{kN}-\mathrm{m}) .
$$
Determine the sum of the moments of the two forces and the couple about $A$.
(FIGURE CAN'T COPY)

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08:57

Problem 126

The forces
$$
\begin{aligned}
& \mathbf{F}_B=2 \mathbf{i}+6 \mathbf{j}+3 \mathbf{k}(\mathrm{kN}), \\
& \mathbf{F}_C=\mathbf{i}-2 \mathbf{j}+2 \mathbf{k}(\mathrm{kN}),
\end{aligned}
$$
and the couple
$$
\mathbf{M}_C=\mathbf{M}_{C y} \mathbf{j}+\mathbf{M}_{C Z} \mathbf{k}(\mathrm{kN}-\mathrm{m}) .
$$
Determine the values of $\mathbf{M}_{C y}$ and $\mathbf{M}_{C Z}$ so that the sum of the moments of the two forces and the couple about $A$ is zero.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
09:46

Problem 127

Two wrenches are used to tighten an elbow fitting. The force $\mathbf{F}=10 \mathbf{k}$ ( $\mathrm{lb})$ on the right wrench is applied at $(6,-5,-3)$ in, and the force $-\mathbf{F}$ on the left wrench is applied at $(4,-5,3)$ in.
(a) Determine the moment about the $x$ axis due to the force exerted on the right wrench.
(b) Determine the moment of the couple formed by the forces exerted on the two wrenches.
(c) Based on the results of (a) and (b), explain why two wrenches are used.
(FIGURE CAN'T COPY)

Vidhi Bhatt
Vidhi Bhatt
Numerade Educator
09:26

Problem 128

Two systems of forces act on the beam. Are they equivalent?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
09:26

Problem 129

Two systems of forces and moments act on the beam. Are they equivalent?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
09:26

Problem 130

Four systems of forces and moments act on an $8-\mathrm{m}$ beam. Which systems are equivalent?

Sanu Kumar
Sanu Kumar
Numerade Educator

Problem 131

The four systems can be made equivalent by adding a couple to one of the systems. Which system is it, and what couple must be added?
(FIGURE CAN'T COPY)

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Problem 132

System 1 is a force $\mathbf{F}$ acting at a point $O$. System 2 is the force $\mathbf{F}$ acting at a different point $O^{\prime}$ along the same line of action. Explain why these systems are equivalent.
(FIGURE CAN'T COPY)

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Problem 133

The vector sum of the forces exerted on the log by the cables is the same in the two cases. Show that the systems of forces exerted on the $\log$ are equivalent.
(FIGURE CAN'T COPY)

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Problem 134

Systems 1 and 2 each consist of a couple. If they are equivalent, what is $F$ ?
(FIGURE CAN'T COPY)

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08:57

Problem 135

Two equivalent systems of forces and moments act on the $\mathrm{L}$-shaped bar. Determine the forces $F_A$ and $F_B$ and the couple $M$.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
09:26

Problem 136

Two equivalent systems of forces and moments act on the plate. Determine the force $F$ and the couple $M$.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator

Problem 137

In Example 4.13, suppose that the $30-\mathrm{kN}$ vertical force in system 1 is replaced by a $230-\mathrm{kN}$ vertical force. Draw a sketch of the new system 1. If you represent system 1 by a single force $\mathbf{F}$ as in system 3, at what position $D$ on the $x$ axis must the force be placed?

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05:25

Problem 138

Three forces and a couple are applied to a beam (system 1).
(a) If you represent system 1 by a force applied at $A$ and a couple (system 2), what are $\mathbf{F}$ and $M$ ?
(b) If you represent system 1 by the force $\mathbf{F}$ (system 3), what is the distance $D$ ?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
05:10

Problem 139

Represent the two forces and couple acting on the beam by a force $\mathbf{F}$. Determine $\mathbf{F}$ and determine where its line of action intersects the $x$ axis.
(FIGURE CAN'T COPY)

Gordon Ayadju
Gordon Ayadju
Numerade Educator

Problem 140

The bracket is subjected to three forces and a couple. If you represent this system by a force $\mathbf{F}$, what is $\mathbf{F}$ and where does its line of action intersect the $x$ axis?
(FIGURE CAN'T COPY)

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08:01

Problem 141

The vector sum of the forces acting on the beam is zero, and the sum of the moments about the left end of the beam is zero.
(a) Determine the forces $A_x$ and $A_y$, and the couple $M_A$.
(b) Determine the sum of the moments about the right end of the beam.
(c) If you represent the $600-\mathrm{N}$ force, the $200-\mathrm{N}$ force, and the
$30 \mathrm{~N}-\mathrm{m}$ couple by a force $\mathbf{F}$ acting at the left end of the beam and a couple $M$, what are $\mathbf{F}$ and $M$ ?
(FIGURE CAN'T COPY)

Eduard Sanchez
Eduard Sanchez
Numerade Educator
03:05

Problem 142

The vector sum of the forces acting on the truss is zero, and the sum of the moments about the origin $O$ is zero.
(a) Determine the forces $A_s, A_1$, and $B$.
(b) If you represent the 2-kip, 4-kip, and 6-kip forces by a force $\mathbf{F}$, what is $\mathbf{F}$, and where does its line of action intersect the $y$ axis?
(c) If you replace the 2-kip, 4-kip, and 6-kip forces by the force you determined in (b), what are the vector sum of the forces acting on the truss and the sum of the moments about $O$ ?
(FIGURE CAN'T COPY)

Colleen Qiu
Colleen Qiu
Numerade Educator
05:35

Problem 143

The distributed force exerted on part of a building foundation by the soil is represented by five forces. If you represent them by a force $\mathbf{F}$, what is $\mathbf{F}$, and where does its line of action intersect the $x$ axis?
(FIGURE CAN'T COPY)

Donald Albin
Donald Albin
Numerade Educator
02:44

Problem 144

At a particular instant, aerodynamic forces distributed over the airplane's surface exert the $88-\mathrm{kN}$ and $16-\mathrm{kN}$ vertical forces and the $22 \mathrm{kN}$-m counterclockwise couple shown. If you represent these forces and couple by a system consisting of a force $\mathbf{F}$ acting at the center of mass $G$ and a couple $M$, what are $\mathbf{F}$ and $M$ ?
(FIGURE CAN'T COPY)

Surjit Tewari
Surjit Tewari
Numerade Educator
02:13

Problem 145

If you represent the two forces and couple acting on the airplane by a force $\mathbf{F}$, what is $\mathbf{F}$, and where does its line of action intersect the $x$ axis?
(FIGURE CAN'T COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
08:57

Problem 146

The system is in equilibrium. If you represent the forces $\mathbf{F}_{A B}$ and $\mathbf{F}_{A C}$ by a force $\mathbf{F}$ acting at $A$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and M?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
08:57

Problem 147

Three forces act on the beam.
(a) Represent the system by a force $\mathbf{F}$ acting at the origin $O$ and a couple $M$.
(b) Represent the system by a single force. Where does the line of action of the force intersect the $x$ axis?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator

Problem 148

The tension in cable $A B$ is $400 \mathrm{~N}$, and the tension in cable $C D$ is $600 \mathrm{~N}$.
(a) If you represent the forces exerted on the left post by the cables by a force $\mathbf{F}$ acting at the origin $O$ and a couple $M$, what are $\mathbf{F}$ and $M$ ?
(b) If you represent the forces exerted on the left post by the cables by the force $\mathbf{F}$ alone, where does its line of action intersect the $y$ axis?
(FIGURE CAN'T COPY)

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04:03

Problem 149

The tension in each of the cables $A B$ and $C D$ is $400 \mathrm{~N}$. If you represent the forces exerted on the right post by the cables by a force $\mathbf{F}$, what is $\mathbf{F}$, and where does its line of action intersect the $y$ axis?
(FIGURE CAN'T COPY)

Ryan Pollard
Ryan Pollard
Numerade Educator
05:41

Problem 150

If you represent the three forces acting on the beam cross section by a force $\mathbf{F}$, what is $\mathbf{F}$, and where does its line of action intersect the $x$ axis?
(FIGURE CAN'T COPY)

Gordon Ayadju
Gordon Ayadju
Numerade Educator
08:28

Problem 151

In Active Example 4.12, suppose that the force $\mathbf{F}_B$ is changed to $\mathbf{F}_B=20 \mathbf{i}-15 \mathbf{j}+30 \mathbf{k}(\mathrm{kN})$, and you want to represent system 1 by an equivalent system consisting of a force $\mathbf{F}$ acting at the point $P$ with coordinates $(4,3,-2) \mathrm{m}$ and a couple $\mathbf{M}$ (system 2). Determine $\mathbf{F}$ and $\mathbf{M}$.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
07:28

Problem 152

The wall bracket is subjected to the force shown.
(a) Determine the moment exerted by the force about the $z$ axis.
(b) Determine the moment exerted by the force about the $y$ axis.
(c) If you represent the force by a force $\mathbf{F}$ acting at $O$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
04:56

Problem 153

A basketball player executes a "slam dunk" shot, then hangs momentarily on the rim, exerting the two $100-1 \mathrm{~b}$ forces shown. The dimensions are $h=14 \frac{1}{2}$ in and $r=9 \frac{1}{2}$ in, and the angle $\alpha=120^{\circ}$.
(a) If you represent the forces he exerts by a force $\mathbf{F}$ acting at $O$ and a couple M, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(b) The glass backboard will shatter if $|\mathbf{M}|>4000 \mathrm{in}-\mathrm{lb}$. Does it break?
(FIGURE CAN'T COPY)

Suzanne W.
Suzanne W.
Numerade Educator

Problem 154

In Example 4.14, suppose that the 30-lb upward force in system 1 is changed to a $25-\mathrm{lb}$ upward force. If you want to represent system 1 by a single force $\mathbf{F}$ (system 2), where does the line of action of $\mathbf{F}$ intersect the $x-z$ plane?

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03:44

Problem 155

The normal forces exerted on the car's tires by the road are
$$
\begin{aligned}
& \mathbf{N}_A=5104 \mathbf{j}(\mathrm{N}), \\
& \mathbf{N}_B=5027 \mathbf{j}(\mathrm{N}), \\
& \mathbf{N}_C=3613 \mathbf{j}(\mathrm{N}), \\
& \mathbf{N}_D=3559 \mathbf{j}(\mathrm{N}) .
\end{aligned}
$$
If you represent these forces by a single equivalent force $\mathbf{N}$, what is $\mathbf{N}$ and where does its line of action intersect the $x-z$ plane?
(FIGURE CAN'T COPY)

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
05:41

Problem 156

Two forces act on the beam. If you represent them by a force $\mathbf{F}$ acting at $C$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(FIGURE CAN'T COPY)

Gordon Ayadju
Gordon Ayadju
Numerade Educator
06:07

Problem 157

An axial force of magnitude $P$ acts on the beam. If you represent it by a force $\mathbf{F}$ acting at the origin $O$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
13:21

Problem 158

The brace is being used to remove a screw.
(a) If you represent the forces acting on the brace by a force $\mathbf{F}$ acting at the origin $O$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(b) If you represent the forces acting on the brace by a force $\mathbf{F}^{\prime}$ acting at a point $P$ with coordinates $\left(x_P, y_P, z_P\right)$ and a couple $\mathbf{M}^{\prime}$, what are $\mathbf{F}^{\prime}$ and $\mathbf{M}^{\prime}$ ?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
04:25

Problem 159

Two forces and a couple act on the cube. If you represent them by a force $\mathbf{F}$ acting at point $P$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
11:53

Problem 160

The two shafts are subjected to the torques (couples) shown.
(a) If you represent the two couples by a force $\mathbf{F}$ acting at the origin $O$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(b) What is the magnitude of the total moment exerted by the two couples?
(FIGURE CAN'T COPY)

Jonathan Ibarra
Jonathan Ibarra
Numerade Educator

Problem 161

The two systems of forces and moments acting on the bar are equivalent. If
$$
\begin{aligned}
& \mathbf{F}_A=30 \mathbf{i}+30 \mathbf{j}-20 \mathbf{k}(\mathrm{kN}), \\
& \mathbf{F}_B=40 \mathbf{i}-20 \mathbf{j}+25 \mathbf{k}(\mathrm{kN}), \\
& \mathbf{M}_B=10 \mathbf{i}+40 \mathbf{j}-10 \mathbf{k}(\mathrm{kN}-\mathrm{m}),
\end{aligned}
$$
what are $\mathbf{F}$ and $\mathbf{M}$ ?
(FIGURE CAN'T COPY)

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08:21

Problem 162

Point $G$ is at the center of the block. The forces are
$$
\begin{aligned}
& \mathbf{F}_A=-20 \mathbf{i}+10 \mathbf{j}+20 \mathbf{k}(\mathrm{lb}), \\
& \mathbf{F}_B=10 \mathbf{j}-10 \mathbf{k}(\mathrm{lb}) .
\end{aligned}
$$
If you represent the two forces by a force $\mathbf{F}$ acting at $G$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
03:40

Problem 163

The engine above the airplane's fuselage exerts a thrust $T_0=16 \mathrm{kip}$, and each of the engines under the wings exerts a thrust $T_U=12 \mathrm{kip}$. The dimensions are $h=8 \mathrm{ft}, c=12 \mathrm{ft}$, and $b=16 \mathrm{ft}$. If you represent the three thrust forces by a force $\mathbf{F}$ acting at the origin $O$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(FIGURE CAN'T COPY)

Donald Albin
Donald Albin
Numerade Educator
03:56

Problem 164

Consider the airplane described in Problem 4.163 and suppose that the engine under the wing to the pilot's right loses thrust.
(a) If you represent the two remaining thrust forces by a force $\mathbf{F}$ acting at the origin $O$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(b) If you represent the two remaining thrust forces by the force $\mathbf{F}$ alone, where does its line of action intersect the $x-y$ plane?
(FIGURE CAN'T COPY)

Mike Gaerlan
Mike Gaerlan
Numerade Educator
06:15

Problem 165

The tension in cable $A B$ is $100 \mathrm{lb}$, and the tension in cable $C D$ is $60 \mathrm{lb}$. Suppose that you want to replace these two cables by a single cable $E F$ so that the force exerted on the wall at $E$ is equivalent to the two forces exerted by cables $A B$ and $C D$ on the walls at $A$ and $C$. What is the tension in cable $E F$, and what are the coordinates of points $E$ and $F$ ?
(FIGURE CAN'T COPY)

Vidhi Bhatt
Vidhi Bhatt
Numerade Educator
06:46

Problem 166

The distance $s=4 \mathrm{~m}$. If you represent the force and the $200-\mathrm{N}-\mathrm{m}$ couple by a force $\mathbf{F}$ acting at the origin $O$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator

Problem 167

The force $\mathbf{F}$ and couple $\mathbf{M}$ in system 1 are
$$
\begin{gathered}
\mathbf{F}=12 \mathbf{i}+4 \mathbf{j}-3 \mathbf{k}(\mathrm{l} \mathbf{b}) \\
\mathbf{M}=4 \mathbf{i}+7 \mathbf{j}+4 \mathbf{k}(\mathrm{ft}-\mathbf{l} \mathbf{b}) .
\end{gathered}
$$
Suppose you want to represent system 1 by a wrench (system 2). Determine the couple $\mathbf{M}_{\mathrm{p}}$ and the coordinates $x$ and $z$ where the line of action of the force intersects the $x-z$ plane.
System 1
System 2
(FIGURE CAN'T COPY)

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08:28

Problem 168

A system consists of a force $\mathbf{F}$ acting at the origin $O$ and a couple M, where
$$
\mathbf{F}=10 \mathrm{i}(\mathrm{lb}), \quad \mathbf{M}=20 \mathrm{j}(\mathrm{ft}-\mathrm{lb}) .
$$
If you represent the system by a wrench consisting of the force $\mathbf{F}$ and a parallel couple $\mathbf{M}_{\mathrm{p}}$, what is $\mathbf{M}_{\mathrm{p}}$, and where does the line of action of $\mathbf{F}$ intersect the $y$ - $z$ plane?

Sanu Kumar
Sanu Kumar
Numerade Educator

Problem 169

A system consists of a force $\mathbf{F}$ acting at the origin $O$ and a couple M, where
$$
\mathbf{F}=\mathbf{i}+2 \mathbf{j}+5 \mathbf{k}(\mathrm{N}), \quad \mathbf{M}=10 \mathbf{i}+8 \mathbf{j}-4 \mathbf{k}(\mathrm{N}-\mathrm{m}) .
$$
If you represent it by a wrench consisting of the force $\mathbf{F}$ and a parallel couple $\mathbf{M}_{\mathrm{p}}$ (a) determine $\mathbf{M}_{\mathrm{p}}$, and determine where the line of action of $\mathbf{F}$ intersects (b) the $x-z$ plane, (c) the $y$-z plane.

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Problem 170

Consider the force $\mathbf{F}$ acting at the origin $O$ and the couple $\mathbf{M}$ given in Example 4.15. If you represent this system by a wrench, where does the line of action of the force intersect the $x-y$ plane?

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Problem 171

Consider the force $\mathbf{F}$ acting at the origin $O$ and the couple M given in Example 4.15. If you represent this system by a wrench, where does the line of action of the force intersect the plane $y=3 \mathrm{~m}$ ?

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01:59

Problem 172

A wrench consists of a force of magnitude $100 \mathrm{~N}$ acting at the origin $O$ and a couple of magnitude $60 \mathrm{~N}-\mathrm{m}$. The force and couple point in the direction from $O$ to the point $(1,1,2) \mathrm{m}$. If you represent the wrench by a force $\mathbf{F}$ acting at the point $(5,3,1) \mathrm{m}$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and $\mathbf{M}$ ?

Vikash Ranjan
Vikash Ranjan
Numerade Educator
08:28

Problem 173

System 1 consists of two forces and a couple. Suppose that you want to represent it by a wrench (system 2). Determine the force $\mathbf{F}$, the couple $\mathbf{M}_{\mathrm{p}}$, and the coordinates $x$ and $z$ where the line of action of $\mathbf{F}$ intersects the $x-z$ plane.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
07:16

Problem 174

A plumber exerts the two forces shown to loosen a pipe.
(a) What total moment does he exert about the axis of the pipe?
(b) If you represent the two forces by a force $\mathbf{F}$ acting at $O$ and a couple M, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(c) If you represent the two forces by a wrench consisting of the force $\mathbf{F}$ and a parallel couple $\mathbf{M}_{\mathrm{p}}$, what is $\mathbf{M}_{\mathrm{p}}$, and where does the line of action of $\mathbf{F}$ intersect the $x-y$ plane?
(FIGURE CAN'T COPY)

Jonathan Ibarra
Jonathan Ibarra
Numerade Educator
02:02

Problem 175

The Leaning Tower of Pisa is approximately $55 \mathrm{~m}$ tall and $7 \mathrm{~m}$ in diameter. The horizontal displacement of the top of the tower from the vertical is approximately $5 \mathrm{~m}$. Its mass is approximately $3.2 \times 10^6 \mathrm{~kg}$. If you model the tower as a cylinder and assume that its weight acts at the center, what is the magnitude of the moment exerted by the weight about the point at the center of the tower's base?
(FIGURE CAN'T COPY)

Stephen Zaffke
Stephen Zaffke
Numerade Educator
15:56

Problem 176

The cable $A B$ exerts a $300-\mathrm{N}$ force on the support $A$ that points from $A$ toward $B$. Determine the magnitude of the moment the force exerts about point $P$.
(FIGURE CAN'T COPY)

Imranul Haque
Imranul Haque
Numerade Educator

Problem 177

Three forces act on the structure. The sum of the moments due to the forces about $A$ is zero. Determine the magnitude of the force $F$.
(FIGURE CAN'T COPY)

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15:56

Problem 178

Determine the moment of the $400-\mathrm{N}$ force (a) about $A$, (b) about $B$.
(FIGURE CAN'T COPY)

Imranul Haque
Imranul Haque
Numerade Educator
12:02

Problem 179

Determine the sum of the moments exerted about $A$ by the three forces and the couple.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
08:57

Problem 180

If you represent the three forces and the couple by an equivalent system consisting of a force $\mathbf{F}$ acting at $A$ and a couple $\mathbf{M}$, what are the magnitudes of $\mathbf{F}$ and $\mathbf{M}$ ?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator

Problem 181

The vector sum of the forces acting on the beam is zero, and the sum of the moments about $A$ is zero.
(a) What are the forces $A_x, A_y$, and $B$ ?
(b) What is the sum of the moments about $B$ ?
(FIGURE CAN'T COPY)

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31:04

Problem 182

The hydraulic piston $B C$ exerts a $970-\mathrm{lb}$ force on the boom at $C$ in the direction parallel to the piston. The angle $\alpha=40^{\circ}$. The sum of the moments about $A$ due to the force exerted on the boom by the piston and the weight of the suspended load is zero. What is the weight of the suspended load?
(FIGURE CAN'T COPY)

Donald Albin
Donald Albin
Numerade Educator
12:02

Problem 183

The force $\mathbf{F}=-60 \mathbf{i}+60 \mathbf{j}(\mathrm{lb})$.
(a) Determine the moment of $\mathbf{F}$ about point $A$.
(b) What is the perpendicular distance from point $A$ to the line of action of $\mathbf{F}$ ?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
06:59

Problem 184

The $20-\mathrm{kg}$ mass is suspended by cables attached to three vertical 2 -m posts. Point $A$ is at $(0,1.2,0) \mathrm{m}$. Determine the moment about the base $E$ due to the force exerted on the post $B E$ by the cable $A B$.
(FIGURE CAN'T COPY)

Jonathan Ibarra
Jonathan Ibarra
Numerade Educator
02:08

Problem 185

What is the total moment due to the two couples?
(a) Express the answer by giving the magnitude and stating whether the moment is clockwise or counterclockwise.
(b) Express the answer as a vector.
(FIGURE CAN'T COPY)

Ahmed Kamel
Ahmed Kamel
Numerade Educator
02:53

Problem 186

The bar $A B$ supporting the lid of the grand piano exerts a force $\mathbf{F}=-6 \mathbf{i}+35 \mathbf{j}-12 \mathbf{k}(\mathrm{lb})$ at $B$. The coordinates of $B$ are $(3,4,3) \mathrm{ft}$ What is the moment of the force about the hinge line of the lid (the $x$ axis)?
(FIGURE CAN'T COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator

Problem 187

Determine the moment of the vertical $800-\mathrm{lb}$ force about point $C$.
(FIGURE CAN'T COPY)

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11:33

Problem 188

Determine the moment of the vertical $800-\mathrm{lb}$ force about the straight line through points $C$ and $D$.
(FIGURE CAN'T COPY)

Narayan Hari
Narayan Hari
Numerade Educator
04:03

Problem 189

The system of cables and pulleys supports the $300-1 \mathrm{~b}$ weight of the work platform. If you represent the upward force exerted at $E$ by cable $E F$ and the upward force exerted at $G$ by cable $G H$ by a single equivalent force $\mathbf{F}$, what is $\mathbf{F}$, and where does its line of action intersect the $x$ axis?
(FIGURE CAN'T COPY)

Stephen Zaffke
Stephen Zaffke
Numerade Educator
01:19

Problem 190

The system of cables and pulleys supports the $300-1 \mathrm{l}$ weight of the work platform.
(a) What are the tensions in cables $A B$ and $C D$ ?
(b) If you represent the forces exerted on the work platform by the cables at $A$ and $C$ by a single equivalent force $\mathbf{F}$, what is $\mathbf{F}$ and where does its line of action intersect the $x$ axis?
(FIGURE CAN'T COPY)

Carson Merrill
Carson Merrill
Numerade Educator
09:33

Problem 191

The two systems are equivalent. Determine the forces $A_x$ and $A_y$, and the couple $M_A$
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
08:28

Problem 192

If you represent the equivalent systems in Problem 4.191 by a force $\mathbf{F}$ acting at the origin and a couple $M$, what are $\mathbf{F}$ and $M$ ?
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
03:18

Problem 193

If you represent the equivalent systems in Problem 4.191 by a force $\mathbf{F}$, what is $\mathbf{F}$, and where does its line of action intersect the $x$ axis?
(FIGURE CAN'T COPY)

Monica Miller
Monica Miller
Numerade Educator
08:28

Problem 194

The two systems are equivalent. If
$$
\begin{aligned}
\mathbf{F} & =-100 \mathbf{i}+40 \mathbf{j}+30 \mathbf{k}(\mathrm{lb}), \\
\mathbf{M}^{\prime} & =-80 \mathbf{i}+120 \mathbf{j}+40 \mathbf{k}(\mathrm{in}-\mathrm{lb}),
\end{aligned}
$$
determine $\mathbf{F}^{\prime}$ and $\mathbf{M}$.
(FIGURE CAN'T COPY)

Sanu Kumar
Sanu Kumar
Numerade Educator
06:07

Problem 195

The tugboats $A$ and $B$ exert forces $F_A=1 \mathrm{kN}$ and $F_B=1.2 \mathrm{kN}$ on the ship. The angle $\theta=30^{\circ}$. If you represent the two forces by a force $\mathbf{F}$ acting at the origin $O$ and a couple $M$, what are $\mathbf{F}$ and $M$ ?
(FIGURE CAN'T COPY)

Donald Albin
Donald Albin
Numerade Educator
03:17

Problem 196

The tugboats $A$ and $B$ exert forces $F_A=600 \mathrm{~N}$ and $F_B=800 \mathrm{~N}$ on the ship. The angle $\theta=45^{\circ}$. If you represent the two forces by a force $\mathbf{F}$, what is $\mathbf{F}$, and where does its line of action intersect the $y$ axis?
(FIGURE CAN'T COPY)

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
06:07

Problem 197

The tugboats $A$ and $B$ want to exert two forces on the ship that are equivalent to a force $\mathbf{F}$ acting at the origin $O$ of $2-\mathrm{kN}$ magnitude. If $F_A=800 \mathrm{~N}$, determine the necessary values of $F_B$ and $\theta$.
(FIGURE CAN'T COPY)

Donald Albin
Donald Albin
Numerade Educator
01:04

Problem 198

If you represent the forces exerted by the floor on the table legs by a force $\mathbf{F}$ acting at the origin $O$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(FIGURE CAN'T COPY)

Breanna Ollech
Breanna Ollech
Numerade Educator
01:04

Problem 199

If you represent the forces exerted by the floor on the table legs by a force $\mathbf{F}$, what is $\mathbf{F}$, and where does its line of action intersect the $x-z$ plane?
(FIGURE CAN'T COPY)
(FIGURE CAN'T COPY)

Breanna Ollech
Breanna Ollech
Numerade Educator

Problem 200

Two forces are exerted on the crankshaft by the connecting rods. The direction cosines of $\mathbf{F}_A$ are $\cos \theta_x=-0.182$, $\cos \theta_y=0.818$, and $\cos \theta_z=0.545$, and its magnitude is $4 \mathrm{kN}$. The direction cosines of $\mathbf{F}_B$ are $\cos \theta_x=0.182, \cos \theta_y=0.818$, and $\cos \theta_z=-0.545$, and its magnitude is $2 \mathrm{kN}$. If you represent the two forces by a force $\mathbf{F}$ acting at the origin $O$ and a couple $\mathbf{M}$, what are $\mathbf{F}$ and $\mathbf{M}$ ?
(FIGURE CAN'T COPY)

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Problem 201

If you represent the two forces exerted on the crankshaft in Problem 4.200 by a wrench consisting of a force $\mathbf{F}$ and a parallel couple $\mathbf{M}_{\mathrm{p}}$, what are $\mathbf{F}$ and $\mathbf{M}_{\mathrm{p}}$, and where does the line of action of $\mathbf{F}$ intersect the $x-z$ plane?

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