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Vector Mechanics For Engineers: Statics and Dynamics 11th

Ferdinand P. Beer, E. Russell Johnston Jr., David F. Mazurek

Chapter 3

Rigid Bodies: Equivalent Systems of Forces - all with Video Answers

Educators

Section 1

Forces and Moments

06:05

Problem 1

A crate of mass $80 \mathrm{kg}$ is held in the position shown. Determine.
(a) the moment produced by the weight $\mathbf{W}$ of the crate about $E$
(b) the smallest force applied at $B$ that creates a moment of equal magnitude and opposite sense about $E.$

AS
Anderson Speed
Numerade Educator
05:47

Problem 2

A crate of mass $80 \mathrm{kg}$ is held in the position shown. Determine
(a) the moment produced by the weight $\mathbf{W}$ of the crate about $E$
(b) the smallest force applied at $A$ that creates a moment of equal magnitude and opposite sense about $E,(c)$ the magnitude, sense, and point of application on the bottom of the crate of the smallest vertical force that creates a moment of equal magnitude and opposite sense about $E.$

AS
Anderson Speed
Numerade Educator
05:04

Problem 3

It is known that a vertical force of 200 lb is required to remove the nail at $C$ from the board. As the nail first starts moving, determine.
(a) the moment about $B$ of the force exerted on the nail, (b) the magnitude of the force $\mathbf{P}$ that creates the same moment about $B$ if $\alpha=10^{\circ},$ and $(c)$ the smallest force $\mathbf{P}$ that creates the same moment about $B.$

AS
Anderson Speed
Numerade Educator
11:07

Problem 4

A 300 -N force is applied at $A$ as shown. Determine $(a)$ the moment of the 300 -N force about $D,(b)$ the smallest force applied at $B$ that creates the same moment about $D.$

Guilherme Barros
Guilherme Barros
Numerade Educator
15:56

Problem 5

A 300 -N force is applied at $A$ as shown. Determine $(a)$ the moment of the 300 -N force about $D,(b)$ the magnitude and sense of the horizontal force applied at $C$ that creates the same moment about $D$ $(c)$ the smallest force applied at $C$ that creates the same moment about $D.$

Imranul Haque
Imranul Haque
Numerade Educator
01:22

Problem 6

A 20 -lb force is applied to the control rod $A B$ as shown. Knowing that the length of the rod is 9 in. and that $\alpha=25^{\circ},$ determine the moment of the force about point $B$ by resolving the force into horizontal and vertical components.

AW
Alex Wang
Numerade Educator
05:16

Problem 7

A 20-lb force is applied to the control rod $A B$ as shown. Knowing that the length of the rod is 9 in. and that $\alpha=25^{\circ},$ determine the moment of the force about point $B$ by resolving the force into components along $A B$ and in a direction perpendicular to $A B.$

Guilherme Barros
Guilherme Barros
Numerade Educator
04:22

Problem 8

A 20-lb force is applied to the control rod $A B$ as shown. Knowing that the length of the rod is 9 in. and that the moment of the force about $B$ is 120 lb-in. clockwise, determine the value of $\alpha.$

Guilherme Barros
Guilherme Barros
Numerade Educator
03:03

Problem 9

Rod $A B$ is held in place by the cord $A C$. Knowing that the tension in the cord is $1350 \mathrm{N}$ and that $c=360 \mathrm{mm}$, determine the moment about $B$ of the force exerted by the cord at point $A$ by resolving that force into horizontal and vertical components applied ( $a$ ) at point $A$ $(b)$ at point $C.$

Prashant Bana
Prashant Bana
Numerade Educator
05:23

Problem 10

$\operatorname{Rod} A B$ is held in place by the cord $A C .$ Knowing that $c=840 \mathrm{mm}$ and that the moment about $B$ of the force exerted by the cord at point $A$ is $756 \mathrm{N}$.m, determine the tension in the cord.

Guilherme Barros
Guilherme Barros
Numerade Educator
08:04

Problem 11

The tailgate of a car is supported by the hydraulic lift $B C$. If the lift exerts a 125 -lb force directed along its centerline on the ball and socket at $B$, determine the moment of the force about $A$.

Guilherme Barros
Guilherme Barros
Numerade Educator
08:04

Problem 12

The tailgate of a car is supported by the hydraulic lift $B C$. If the lift exerts a 125 -lb force directed along its centerline on the ball and socket at $B$, determine the moment of the force about $A$.

Guilherme Barros
Guilherme Barros
Numerade Educator
04:53

Problem 13

It is known that the connecting rod $A B$ exerts on the crank $B C$ a 2.5 -kN force directed down and to the left along the centerline of $A B .$ Determine the moment of the force about $C.$

Guilherme Barros
Guilherme Barros
Numerade Educator
04:53

Problem 14

It is known that the connecting rod $A B$ exerts on the crank $B C$ a 2.5 -kN force directed down and to the left along the centerline of $A B .$ Determine the moment of the force about $C.$

Guilherme Barros
Guilherme Barros
Numerade Educator
06:45

Problem 15

Form the vector products $\mathbf{B} \times \mathbf{C}$ and $\mathbf{B}^{\prime} \times \mathbf{C},$ where $B=B^{\prime},$ and use the results obtained to prove the identity
\[
\sin \alpha \cos \beta=\frac{1}{2} \sin (\alpha+\beta)+\frac{1}{2} \sin (\alpha-\beta)
\]

Guilherme Barros
Guilherme Barros
Numerade Educator
04:47

Problem 16

The vectors $\mathbf{P}$ and $\mathbf{Q}$ are two adjacent sides of a parallelogram. Determine the area of the parallelogram when $(a) \mathbf{P}=-8 \mathbf{i}+4 \mathbf{j}-4 \mathbf{k}$
and $\mathbf{Q}=3 \mathbf{i}+3 \mathbf{j}+6 \mathbf{k},(b) \mathbf{P}=7 \mathbf{i}-6 \mathbf{j}-3 \mathbf{k}$ and $\mathbf{Q}=-3 \mathbf{i}+6 \mathbf{j}-2 \mathbf{k}.$

Guilherme Barros
Guilherme Barros
Numerade Educator
06:55

Problem 17

A plane contains the vectors A and B. Determine the unit vector normal to the plane when $\mathbf{A}$ and $\mathbf{B}$ are equal to, respectively, $(a) 2 \mathbf{i}+$
\[
3 \mathbf{j}-6 \mathbf{k} \text { and } 5 \mathbf{i}-8 \mathbf{j}-6 \mathbf{k},(b) 4 \mathbf{i}-4 \mathbf{j}+3 \mathbf{k} \text { and }-3 \mathbf{i}+7 \mathbf{j}-5 \mathbf{k}
\]

Guilherme Barros
Guilherme Barros
Numerade Educator
04:49

Problem 18

A line passes through the points $(12 \mathrm{m}, 8 \mathrm{m})$ and $(-3 \mathrm{m},-5 \mathrm{m})$ Determine the perpendicular distance $d$ from the line to the origin $O$ of the system of coordinates.

Guilherme Barros
Guilherme Barros
Numerade Educator
05:55

Problem 19

Determine the moment about the origin $O$ of the force $\mathbf{F}=4 \mathbf{i}-3 \mathbf{j}+$ 5k that acts at a point $A$. Assume that the position vector of $A$ is
$(a) \mathbf{r}=2 \mathbf{i}+3 \mathbf{j}-4 \mathbf{k}$
$(b) \mathbf{r}=-8 \mathbf{i}+6 \mathbf{j}-10 \mathbf{k}$
$(c) \mathbf{r}=8 \mathbf{i}-6 \mathbf{j}+5 \mathbf{k}$

AM
Aditya Mahendru
Numerade Educator
05:55

Problem 20

Determine the moment about the origin $O$ of the force $\mathbf{F}=2 \mathbf{i}+$ $3 \mathbf{j}-4 \mathbf{k}$ that acts at a point $A$. Assume that the position vector of $A$ is
$(a) \mathbf{r}=3 \mathbf{i}-6 \mathbf{j}+5 \mathbf{k},(b) \mathbf{r}=\mathbf{i}-4 \mathbf{j}-2 \mathbf{k},(c) \mathbf{r}=4 \mathbf{i}+6 \mathbf{j}-8 \mathbf{k}.$

AM
Aditya Mahendru
Numerade Educator
06:22

Problem 21

Before the trunk of a large tree is felled, cables $A B$ and $B C$ are attached as shown. Knowing that the tensions in cables $A B$ and $B C$ are $555 \mathrm{N}$ and $660 \mathrm{N}$, respectively, determine the moment about 0 of the resultant force exerted on the tree by the cables at $B.$

Pawan Yadav
Pawan Yadav
Numerade Educator
03:08

Problem 22

The 12 -ft boom $A B$ has a fixed end $A$. A steel cable is stretched from the free end $B$ of the boom to a point $C$ located on the vertical wall If the tension in the cable is 380 lb, determine the moment about $A$ of the force exerted by the cable at $B.$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
05:38

Problem 23

A 200 -N force is applied as shown to the bracket $A B C$. Determine the moment of the force about $A.$

Ahmed Kamel
Ahmed Kamel
Numerade Educator
10:01

Problem 24

The wire $A E$ is stretched between the corners $A$ and $E$ of a bent plate. Knowing that the tension in the wire is $435 \mathrm{N}$, determine the moment about $O$ of the force exerted by the wire $(a)$ on corner $A$ (b) on corner $E.$

Guilherme Barros
Guilherme Barros
Numerade Educator
01:29

Problem 25

A 6-ft-long fishing rod $A B$ is securely anchored in the sand of a beach. After a fish takes the bait, the resulting force in the line is 6 lb. Determine the moment about $A$ of the force exerted by the line at $B$.

Fatima Iqbal
Fatima Iqbal
Numerade Educator
05:37

Problem 26

A precast concrete wall section is temporarily held by two cables as shown. Knowing that the tension in cable $B D$ is $900 \mathrm{N}$, determine the moment about point $O$ of the force exerted by the cable at $B.$

Guilherme Barros
Guilherme Barros
Numerade Educator
08:01

Problem 27

In Prob. 3.22, determine the perpendicular distance from point $A$ to cable $B C.$

Kaitlin Coad
Kaitlin Coad
Numerade Educator
04:03

Problem 28

In Prob. 3.24, determine the perpendicular distance from point $O$ to wire $A E.$

Guilherme Barros
Guilherme Barros
Numerade Educator
06:26

Problem 29

In Prob. 3.24, determine the perpendicular distance from point $B$ to wire $A E.$

Guilherme Barros
Guilherme Barros
Numerade Educator
06:56

Problem 30

In Prob. 3.25, determine the perpendicular distance from point $A$ to a line drawn through points $B$ and $C$.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
04:15

Problem 31

In Prob. 3.25, determine the perpendicular distance from point $D$ to a line drawn through points $B$ and $C$.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:30

Problem 32

In Prob. 3.26, determine the perpendicular distance from point $O$ to cable $B D.$

BM
Brandon Matherne
Numerade Educator
04:31

Problem 33

In Prob. 3.26, determine the perpendicular distance from point $C$ to cable $B D.$

Guilherme Barros
Guilherme Barros
Numerade Educator
15:39

Problem 34

Determine the value of $a$ that minimizes the perpendicular distance from point $C$ to a section of pipeline that passes through points $A$ and $B$.

Angela Guo
Angela Guo
Numerade Educator