Engineering Mechanics: Statics and Dynamics

R. C. Hibbeler

Chapter 3

Equilibrium of a Particle - all with Video Answers

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Chapter Questions

Problem 1

The members of a truss are pin connected at joint $O$ Determine the magnitudes of $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ for equilibrium. Set $\theta=60^{\circ}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 2

The members of a truss are pin connected at joint $O$ Determine the magnitude of $\mathbf{F}_{1}$ and its angle $\theta$ for equilibrium. Set $F_{2}=6 \mathrm{kN}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 3

Determine the magnitude and direction $\theta$ of $\mathbf{F}$ so that the particle is in equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 4

The bearing consists of rollers, symmetrically confined within the housing. The bottom one is subjected to a 125 -N force at its contact $A$ due to the load on the shaft. Determine the normal reactions $N_{B}$ and $N_{C}$ on the bearing at its contact points $B$ and $C$ for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 5

The members of a truss are connected to the gusset plate. If the forces are concurrent at point $O$, determine the magnitudes of $\mathbf{F}$ and $\mathbf{T}$ for equilibrium. Take $\theta=90^{\circ}$.

Anand Jangid

Numerade Educator

Problem 6

The gusset plate is subjected to the forces of three members. Determine the tension force in member $C$ and its angle $\theta$ for equilibrium. The forces are concurrent at point $O$ Take $F=8 \mathrm{kN}$.

Vishal Gupta

Numerade Educator

Problem 7

The man attempts to pull down the tree using the cable and small pulley arrangement shown. If the tension in $A B$ is 60 Ib, determine the tension in cable $C A D$ and the angle $\theta$ which the cable makes at the pulley.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 8

The cords $A B C$ and $B D$ can each support a maximum load of 100 lb. Determine the maximum weight of the crate, and the angle $\theta$ for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 9

Determine the maximum force $\mathbf{F}$ that can be supported in the position shown if each chain can support a maximum tension of 600 lb before it fails.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 10

The block has a weight of $20 \mathrm{lb}$ and is being hoisted at uniform velocity. Determine the angle $\theta$ for equilibrium and the force in cord $A B$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 11

Determine the maximum weight $W$ of the block that can be suspended in the position shown if cords $A B$ and $C A D$ can each support a maximum tension of 80 lb. Also, what is the angle $\theta$ for equilibrium?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 12

The lift sling is used to hoist a container having a mass of 500 kg. Determine the force in each of the cables $A B$ and $A C$ as a function of $\theta .$ If the maximum tension allowed in each cable is $5 \mathrm{kN}$, determine the shortest length of cables $A B$ and $A C$ that can be used for the lift. The center of gravity of the container is located at $G$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 13

A nuclear-reactor vessel has a weight of $500\left(10^{3}\right)$ lb. Determine the horizontal compressive force that the spreader bar $A B$ exerts on point $A$ and the force that each cable segment $C A$ and $A D$ exert on this point while the vessel is hoisted upward at constant velocity.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 14

Determine the stretch in each spring for equilibrium of the 2 -kg block. The springs are shown in the equilibrium position.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 15

The unstretched length of spring $A B$ is $3 \mathrm{m}$. If the block is held in the equilibrium position shown, determine the mass of the block at $D$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 16

Determine the mass of each of the two cylinders if they cause a sag of $s=0.5 \mathrm{m}$ when suspended from the rings at $A$ and $B .$ Note that $s=0$ when the cylinders are removed.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 17

Determine the stiffness $k_{T}$ of the single spring such that the force $\mathbf{F}$ will stretch it by the same amount $s$ as the force $\mathbf{F}$ stretches the two springs. Express $k_{T}$ in terms of stiffness $k_{1}$ and $k_{2}$ of the two springs.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 18

If the spring $D B$ has an unstretched length of $2 \mathrm{m}$ determine the stiffness of the spring to hold the 40 -kg crate in the position shown.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 19

Determine the unstretched length of $D B$ to hold the $40-\mathrm{kg}$ crate in the position shown. Take $k=180 \mathrm{N} / \mathrm{m}$.

Vipender Yadav

Numerade Educator

Problem 20

A vertical force $P=10$ lb is applied to the ends of the 2 -ft cord $A B$ and spring $A C$. If the spring has an unstretched length of 2 ft, determine the angle $\theta$ for equilibrium. Take $k=15 \mathrm{lb} / \mathrm{ft}$.

Prabhat Tyagi

Numerade Educator

Problem 21

Determine the unstretched length of spring $A C$ if a force $P=80$ lb causes the angle $\theta=60^{\circ}$ for equilibrium. Cord $A B$ is 2 ft long. Take $k=50$ lb/ft.

Vishal Gupta

Numerade Educator

Problem 22

The springs $B A$ and $B C$ each have a stiffiness of $500 \mathrm{N} / \mathrm{m}$ and an unstretched length of $3 \mathrm{m} .$ Determine the horizontal force $\mathbf{F}$ applied to the cord which is attached to the small ring $B$ so that the displacement of $A B$ from the wall is $d=1.5 \mathrm{m}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 23

The springs $B A$ and $B C$ each have a stiffiness of $500 \mathrm{N} / \mathrm{m}$ and an unstretched length of $3 \mathrm{m} .$ Determine the displacement $d$ of the cord from the wall when a force $F=175 \mathrm{N}$ is applied to the cord.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 24

Determine the distances $x$ and $y$ for equilibrium if $F_{1}=800 \mathrm{N}$ and $F_{2}=1000 \mathrm{N}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 25

Determine the magnitude of $F_{1}$ and the distance $y$ if $x=1.5 \mathrm{m}$ and $F_{2}=1000 \mathrm{N}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 26

The 30 -kg pipe is supported at $A$ by a system of five cords. Determine the force in each cord for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 27

Each cord can sustain a maximum tension of $500 \mathrm{N}$ Determine the largest mass of pipe that can be supported.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 28

The street-lights at $A$ and $B$ are suspended from the two poles as shown. If each light has a weight of $50 \mathrm{lb}$, determine the tension in each of the three supporting cables and the required height $h$ of the pole $D E$ so that cable $A B$ is horizontal.

Sheh Lit Chang

University of Washington

Problem 29

Determine the tension developed in each cord required for equilibrium of the 20 -kg lamp.

Keshav Singh

Numerade Educator

Problem 30

Determine the maximum mass of the lamp that the cord system can support so that no single cord develops a tension exceeding $400 \mathrm{N}$.

Keshav Singh

Numerade Educator

Problem 31

Blocks $D$ and $E$ have a mass of $4 \mathrm{kg}$ and $6 \mathrm{kg}$ respectively. If $x=2 \mathrm{m}$ determine the force $\mathbf{F}$ and the $\operatorname{sag} s$ for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 32

Blocks $D$ and $E$ have a mass of $4 \mathrm{kg}$ and $6 \mathrm{kg}$ respectively. If $F=80 \mathrm{N}$, determine the $\operatorname{sag} s$ and distance $x$ for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 33

The lamp has a weight of 15 lb and is supported by the six cords connected together as shown. Determine the tension in each cord and the angle $\theta$ for equilibrium. Cord $B C$ is horizontal.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 34

Each cord can sustain a maximum tension of $20 \mathrm{lb}$ Determine the largest weight of the lamp that can be supported. Also, determine $\theta$ of cord $D C$ for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 35

The ring of negligible size is subjected to a vertical force of 200 lb. Determine the required length $l$ of cord $A C$ such that the tension acting in $A C$ is 160 lb. Also, what is the force in cord $A B ?$ Hint: Use the equilibrium condition to determine the required angle $\theta$ for attachment, then determine $l$ using trigonometry applied to triangle $A B C$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 36

Cable $A B C$ has a length of $5 \mathrm{m}$. Determine the position $x$ and the tension developed in $A B C$ required for equilibrium of the 100 -kg sack. Neglect the size of the pulley at $B$.

Vipender Yadav

Numerade Educator

Problem 37

A $4-\mathrm{kg}$ sphere rests on the smooth parabolic surface. Determine the normal force it exerts on the surface and the mass $m_{B}$ of block $B$ needed to hold it in the equilibrium position shown.

Sheh Lit Chang

University of Washington

Problem 38

Determine the forces in cables $A C$ and $A B$ needed to hold the 20 -kg ball $D$ in equilibrium. Take $F=300 \mathrm{N}$ and $d=1 \mathrm{m}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 39

The ball $D$ has a mass of $20 \mathrm{kg} .$ If a force of $F=100 \mathrm{N}$ is applied horizontally to the ring at $A,$ determine the dimension $d$ so that the force in cable $A C$ is zero.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 40

The 200 -lb uniform container is suspended by means of a 6 -ft-long cable, which is attached to the sides of the tank and passes over the small pulley located at $O .$ If the cable can be attached at either points $A$ and $B,$ or $C$ and $D$ determine which attachment produces the least amount of tension in the cable. What is this tension?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 41

The single elastic cord $A B C$ is used to support the 40 -lb load. Determine the position $x$ and the tension in the cord that is required for equilibrium. The cord passes through the smooth ring at $B$ and has an unstretched length of $6 \mathrm{ft}$ and stiffness of $k=50 \mathrm{lb} / \mathrm{ft}$.

Keshav Singh

Numerade Educator

Problem 42

A "scale" is constructed with a 4 -ft-long cord and the 10 -lb block $D$. The cord is fixed to a pin at $A$ and passes over two small pulleys. Determine the weight of the suspended block $B$ if the system is in equilibrium when $s=1.5 \mathrm{ft}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 43

The three cables are used to support the $40-\mathrm{kg}$ flowerpot. Determine the force developed in each cable for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 44

Determine the magnitudes of $\mathbf{F}_{1}, \mathbf{F}_{2},$ and $\mathbf{F}_{3}$ for equilibrium of the particle.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 45

If the bucket and its contents have a total weight of 20 Ib, determine the force in the supporting cables $D A, D B$ and $D C$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 46

Determine the stretch in each of the two springs required to hold the 20 -kg crate in the equilibrium position shown. Each spring has an unstretched length of $2 \mathrm{m}$ and a stiffness of $k=300 \mathrm{N} / \mathrm{m}$.

Sheh Lit Chang

University of Washington

Problem 47

Determine the force in each cable needed to support the 20 -kg flowerpot.

Keshav Singh

Numerade Educator

Problem 48

Determine the tension in the cables in order to support the 100 -kg crate in the equilibrium position shown.

Keshav Singh

Numerade Educator

Problem 49

Determine the maximum mass of the crate so that the tension developed in any cable does not exceeded $3 \mathrm{kN}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 50

Determine the force in each cable if $F=500$ lb.

Keshav Singh

Numerade Educator

Problem 51

Determine the greatest force $\mathbf{F}$ that can be applied to the ring if each cable can support a maximum force of $800 \mathrm{lb}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 52

Determine the tension developed in cables $A B$ and $A C$ and the force developed along strut $A D$ for equilibrium of the 400 -lb crate.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 53

If the tension developed in each cable cannot exceed 300 lb, determine the largest weight of the crate that can be supported. Also, what is the force developed along strut $A D ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 54

Determine the tension developed in each cable for equilibrium of the 300 -lb crate.

Keshav Singh

Numerade Educator

Problem 55

Determine the maximum weight of the crate that can be suspended from cables $A B, A C,$ and $A D$ so that the tension developed in any one of the cables does not exceed $250 \mathrm{lb}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 56

The 25 -kg flowerpot is supported at $A$ by the three cords. Determine the force acting in each cord for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 57

If each cord can sustain a maximum tension of $50 \mathrm{N}$ before it fails, determine the greatest weight of the flowerpot the cords can support.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 58

Determine the tension developed in the three cables required to support the traffic light, which has a mass of 15 kg. Take $h=4 \mathrm{m}$.

Meghan Miholics

Meghan Miholics

Numerade Educator

Problem 59

Determine the tension developed in the three cables required to support the traffic light, which has a mass of 20 kg. Take $h=3.5 \mathrm{m}$.

Vipender Yadav

Numerade Educator

Problem 60

The 800 -lb cylinder is supported by three chains as shown. Determine the force in each chain for equilibrium. Take $d=1 \mathrm{ft}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 61

Determine the tension in each cable for equilibrium.

Sheh Lit Chang

University of Washington

Problem 62

If the maximum force in each rod can not exceed $1500 \mathrm{N},$ determine the greatest mass of the crate that can be supported.

Anand Jangid

Numerade Educator

Problem 63

The crate has a mass of 130 kg. Determine the tension developed in each cable for equilibrium.

Nick Johnson

Numerade Educator

Problem 64

If cable $A D$ is tightened by a turnbuckle and develops a tension of 1300 lb, determine the tension developed in cables $A B$ and $A C$ and the force developed along the antenna tower $A E$ at point $A$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 65

If the tension developed in either cable $A B$ or $A C$ can not exceed 1000 lb, determine the maximum tension that can be developed in cable $A D$ when it is tightened by the turnbuckle. Also, what is the force developed along the antenna tower at point $A ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 66

Determine the tension developed in cables $A B, A C$ and $A D$ required for equilibrium of the 300 -lb crate.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 67

Determine the maximum weight of the crate so that the tension developed in any cable does not exceed 450 lb.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator