• Home
  • Textbooks
  • Vector Mechanics for Engineers: Statics and Dynamics
  • Rigid Bodies: Equivalent Systems of Forces

Vector Mechanics for Engineers: Statics and Dynamics

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

01:11

Problem 1

A foor valve for a pneumatic system is hinged at $B$. Knowing that $\alpha=$ $28^{\circ}$, determine the moment of the 16 -N force about point $B$ by resolving the force into horizontal and vertical components.

Prashant Bana
Prashant Bana
Numerade Educator
01:11

Problem 2

A foot valve for a pneumatic system is hinged at $B$. Knowing that $a=$ $28^{\circ}$, determine the moment of the 16 -N force about point $B$ by resolving the force into components along $A B C$ and in a direction perpendicular to $A B C$.

Prashant Bana
Prashant Bana
Numerade Educator
05:04

Problem 3

It is known that a vertical force of $200 \mathrm{lb}$ 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 $\alpha=10^{\circ},(\mathrm{c})$ 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 $300-\mathrm{N}$ 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
01:12

Problem 6

An 8 -lb force $\mathbf{P}$ is applied to a shift lever. Determine the moment of $\mathbf{P}$ about $B$ when $\alpha$ is equal to $25^{\circ}$

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
01:12

Problem 7

For the shift lever shown, determine the magnitude and the direction of the smallest force $\mathbf{P}$ that has a 210 -lb-in. clockwise moment about $B$.

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
01:12

Problem 8

An 11 -lb force $\mathbf{P}$ is applied to a shift lever. The moment of $\mathbf{P}$ about $B$ is clockwise and has a magnitude of 250 lb-in. Determine the value of $\alpha$.

Kratika Bhadauria
Kratika Bhadauria
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 N and that $c=360$ 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 $756 \mathrm{N}$. $\mathrm{m}$, 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 $2.5-\mathrm{kN}$ 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 $2.5-\mathrm{kN}$ 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
00:36

Problem 15

Form the vector product $\mathbf{P}_{1} \times \mathbf{P}_{2}$ and use the result obtained to prove the identity
$$\sin \left(\theta_{1}-\theta_{2}\right)=\sin \theta_{1} \cos \theta_{2}-\cos \theta_{1} \sin \theta_{2}$$

Tony Ni
Tony Ni
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 $(a) \mathbf{P}=-2 \mathbf{i}+2 \mathbf{j}-6 \mathbf{k}$ and $\mathbf{Q}=8 \mathbf{i}+2 \mathbf{j}+4 \mathbf{k},(b) \mathbf{P}=3 \mathbf{i}-9 \mathbf{j}-7 \mathbf{k}$ and $\mathbf{Q}=-4 \mathbf{i}+2 \mathbf{j}-5 \mathbf{k}$.

Guilherme Barros
Guilherme Barros
Numerade Educator
06:55

Problem 17

A plane contains the vectors $\mathbf{A}$ and $\mathbf{B}$. Determine the unit vector normal to the plane when $\mathbf{A}$ and $\mathbf{B}$ are equal to, respectively, $(a) 7 \mathbf{i}+8 \mathbf{j}$ $-2 \mathbf{k}$ and $9 \mathbf{i}-4 \mathbf{j}-5 \mathbf{k},(b) 6 \mathbf{i}-3 \mathbf{j}+9 \mathbf{k}$ and $-5 \mathbf{i}+4 \mathbf{j}-3 \mathbf{k}$.

Guilherme Barros
Guilherme Barros
Numerade Educator
04:49

Problem 18

A line passes through the points $(-4 \mathrm{m},-3 \mathrm{m})$ and $(2 \mathrm{m}, 7 \mathrm{m})$ 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 $\mathbf{F}=-2 \mathbf{i}-3 \mathbf{j}+$ 5k that acts at a point $A$. Assume that the position vector of $A$ is $(a) \mathbf{r}=\mathbf{i}+\mathbf{j}+\mathbf{k},(b) \mathbf{r}=4 \mathbf{i}+6 \mathbf{j}-10 \mathbf{k},(c) \mathbf{r}=4 \mathbf{i}+3 \mathbf{j}-5 \mathbf{k}$.

AM
Aditya Mahendru
Numerade Educator
05:55

Problem 20

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

AM
Aditya Mahendru
Numerade Educator
14:10

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 $O$ of the resultant force exerted on the tree by the cables at $B$.

JM
Joseph Martinez
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 $380 \mathrm{lb}$, 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
04:32

Problem 24

A force $\mathbf{P}$ of magnitude $200 \mathrm{N}$ acts along the diagonal $B C$ of the bent plate shown. Determine the moment of $\mathbf{P}$ about point $E$.

Vipender Yadav
Vipender Yadav
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 $6 \mathrm{lb}$. 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
01:19

Problem 28

In Prob. $3.23,$ determine the perpendicular distance from point $A$ to the line of action of the 200 -N force.

Surendra Kumar
Surendra Kumar
Numerade Educator
10:11

Problem 29

In Prob. 3.24 , determine the perpendicular distance from point $E$ to the line of action of force $\mathbf{P}$.

Jonathan Ibarra
Jonathan Ibarra
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